LifeWiki - User contributions [en]

Infinite growth

2026-05-03T04:14:55Z

Ch91:

{{Glossary}}
A finite [[pattern]] is said to exhibit '''infinite growth''' if its population is unbounded. That is, for any number N there exists a generation n such that the population in [[generation]] n is greater than N.

Apparent infinite growth may occur in many cellular automata, and rules in which such patterns are commonplace are known as [[class three cellular automata]]. However, in many cases there is no known ''proof'' that any such pattern in fact will continue to grow indefinitely (and is not simply a particularly vigorous [[methuselah]]). Most patterns known to exhibit infinite growth start growing in a predictable way at some point in their evolution.

In [[Conway's Game of Life]], the first known pattern to exhibit infinite growth was the [[Gosper glider gun]]. In {{year|1971}}, [[Charles Corderman]] found that a [[switch engine]] could be stabilized by a [[pre-block]] in a number of different ways to produce either a [[block-laying switch engine]] or a [[glider-producing switch engine]], giving several 11-cell patterns with infinite growth. This record for smallest infinitely-growing pattern stood for more than quarter of a century until [[Paul Callahan]] found, in November {{year|1997}}, two 10-cell patterns with infinite growth (it was later determined that twenty-four 10-cell patterns exhibit infinite growth, with 17 unique pattern types). [[Nick Gotts]] and Paul Callahan have since shown that there is no infinite growth pattern with fewer than 10 cells, so the question of the smallest infinite growth pattern in terms of number of cells has been answered completely.

{{EmbedViewer
|pname = 10cellinfinitegrowth
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|position = center
|caption = Paul Callahan's 10-cell infinite growth pattern. No pattern with fewer cells can exhibit infinite growth
|style = width:300px;
}}

== Growth rates ==
Infinite-growth patterns can be classified by their growth rate. In any cellular automaton, the maximum rate of growth is determined by the geometry of the space. In cellular automata set in 2D Euclidean space such as Life, the maximum growth rate is quadratic; cubic, quartic, quintic etc. growth require spaces of higher dimensionality.{{refn|group="note"|Alternatively, a faster-than-quadratic growth (including possibility of exponential growth) may be possible on a two-dimensional hyperbolic plane.<ref>{{cite web|url=https://cp4space.hatsya.com/2012/11/12/self-replication/ |title=Self-replication |author=Adam P. Goucher |date=November 12, 2012}}</ref>}}

Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other growth rates are possible. The following table summarizes asymptotic growth rates that have been explicitly constructed in [[Game of Life]]:

{| class="wikitable" style="margin:auto;"
|-
! Classification
! Growth rate f(t)
! Examples
|-
| rowspan="6" | [[Superlinear growth]]
| t2 ([[Quadratic growth]])
| [[breeder 1]], [[max]], [[mosquito 5]], [[metacatacryst]]
|-
| t3/2
| t{{sup|3/2}} infinite growth<ref name="hickref">[https://conwaylife.com/ref/DRH/life.html Dean Hickerson's Game of Life Page: Unusual growth rates]</ref> (see gallery), unnamed<ref name="post8518" /> (see gallery)
|-
| t{{sup|tlog(t)/2}}
| {{sup|log(t)/2}} infinite growth<ref name="hickref" /> (see gallery)
|-
| tlog(t)
| [[tlog(t) growth]], [[Gotts dots]]
|-
| tlog(log(t))
| [[tlog(log(t)) growth]]
|-
| tlog*(n)(t)
| [[Sawmill]]
|-
| [[Linear growth]]
| t
| [[block-laying switch engine]], [[Gosper glider gun]], [[space rake]], [[blockstacker]]
|-
| rowspan="10" | [[Sublinear growth]]
| sqrt(t)
| [[sqrtgun]]
|-
| t1/3
| t{{sup|1/3}} infinite growth<ref name="hickref" /> (see gallery)
|-
| t{{sup|2/3}}
| t{{sup|2/3}} infinite growth<ref name="post160495" />
|-
| t{{sup|3/4}}
| t{{sup|3/4}} infinite growth<ref name="post160495" />
|-
| t2-n{{citation needed}}
| ?
|-
| log(t)2
| [[log(t)^2 growth]]
|-
| log(t) (logarithmic)
| [[Caber tosser 1]]
|-
| sqrt(log(t))
| [[O(sqrt(log(t)))]]
|-
| log(n)(t){{citation needed}}
| ?
|-
| log*(n)(t)
| [[Sawmill]]
|-
|}

It is not difficult to see that quadratic growth is the fastest possible growth rate,{{refn|group="note"|Even if everything expanded at the speed of light, the number of cells that would be "on" would be limited by the number of cells within ''n'' generations from the starting region, which is n2. Temporary cubic growth is possible, but will rapidly revert to quadratic growth from a lack of space.}} and many patterns that grow at such speed are now known. logn(t)1/m is the lowest possible rate at which bounding box may grow in any n-state m-dimensional cellular automaton; however, arbitrarily slow computable rates of population growth are possible. There are patterns that exhibit infinite growth but whose population does not tend toward infinity – see [[sawtooth]]. By combining a sawtooth with a pattern that grows infinitely at a different rate, it is possible to construct patterns that grow (for example) logarithmically at some times and linearly at other times. There are even patterns with [[unknown fate]], such as the [[Fermat prime calculator]], for which it is not known if they grow infinitely or not.

== Gallery ==

{|style="margin:auto;width:400px;"
|{{EmbedViewer
|pname = t1point5infinitegrowth2
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = t1.5 infinite growth<ref name="hickref" />
}}
|{{EmbedViewer
|pname = t1point5infinitegrowth
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = unnamed t3/2 infinite growth<ref name="post8518" />
}}
|-
|{{EmbedViewer
|pname = tlogtsquared
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = t log(t)2 infinite growth<ref name="hickref" />
}}
|{{EmbedViewer
|pname = tonethirdinfinitgrowth
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = t1/3 infinite growth<ref name="hickref" />
}}
|}

== See also ==
* [[Chaotic growth]]

== Notes ==
<references group="note"/>

==References==
<references>
<ref name="post8518">{{LinkForumThread
|format = ref
|p = 8518
|title = Re: t^1.5 Growth
|author = Extrementhusiast
|date = July 14, 2013
}}</ref>
<ref name="post160495">{{LinkForumThread
|format = ref
|p = 160495
|title = Re: Discussion thread for infinite growth patterns
|author = Jormungant
|date = April 15, 2023
}}</ref>
</references>

== External links ==
* {{LinkForumThread|f=2|t=2274|title=Discussion thread for infinite growth patterns}}
* {{LinkLexicon|lex_i.htm#infinitegrowth}}

[[Category:Infinite growth| ]]
__NOTOC__

OCA:Langton's loops

2026-02-02T22:10:09Z

Ch91:

{{stub}}
'''Langton's loops''' are a specific type of artificial life in a [[cellular automaton]] discovereded in {{year|1984}} by Christopher Langton. They consist of a loop of cells containing genetic information, which flows continuously around the loop and out along an "arm", which will become the daughter loop. The "genes" instruct it to make three left turns, completing the loop, which then disconnects from its parent. Modified variations exist that grant it life-like properties, such as "dying" at the end of its life cycle, response to evolutionary pressure (generally in the form of competition for space), and a form of sexual reproduction via the exchange of "genetic material".
==See also==
*{{rl|Langton's Ant}}
*{{rl|Codd}}
==External links==
{{LinkWikipedia}}
[[Category:Alien rules]] [[Category:Multistate rules]]

Reverse caber-tosser

2023-12-27T06:08:18Z

Ch91:

A '''reverse caber-tosser''' (RCT) is a [[universal constructor]] with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}. Its 15-glider version tied for first in 2022 with the solution to the [[unique father problem]].

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 15-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankovskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations and has been designed to use as few bits per glider as possible; it also includes a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the [[DBCA]] and ECCT drastically improved the efficiency of the RCT mechanism. That being said, synthesizing most patterns currently requires the constituent GPSEs to be so far apart that the RCT's bounding box becomes too large for Golly to run without crashing, so its applications will likely remain theoretical until a new version of Golly capable of handling it can be developed.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the "Sakapuffer"<ref name="post145196" /> [[ark]] synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the "Sakapuffer"<ref name="post145196" /> [[ark]] is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time is beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==Future==
At the time of RCT17 and RCT16, MathAndCode believed that the absolute smallest possible RCT would require 13 gliders by using one fewer switch engine.<ref name="post104600" /> The subsequent reduction from RCT16 to RCT15 suggests that MathAndCode's hypothetical 13-glider design ''might'' be reduced to 12 gliders in the same way.<ref name="message1046450382357938306" /> However, it is far from guaranteed that the exact same reduction method could be carried over to a three-switch-engine design.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{cite web|url=https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/|title=Building arbitrary Life patterns in 15 gliders|author=Brett Berger|date=November 16, 2022}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-fifteen-gliders-can.html|title=In Conway's Life, Fifteen Gliders Can Build Anything* !|author=Dave Greene|date=November 18, 2022}}

* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
<ref name="post104600">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104600
|author = MathAndCode
|date = September 20, 2020
}}</ref>
<ref name="message1046450382357938306">{{CiteDiscord
|author = Dave Greene
|date = November 27, 2022
|channel = general-discussion
|id = 1046450382357938306
}}</ref>
<ref name
</references>

[[Category:Universal construction]]
[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Crawler

2023-12-05T15:41:21Z

Ch91: /* Half-bakery reaction */

{{Glossary}}
A '''crawler''' or '''climber''' is a [[reaction]] in which two objects (or groups of objects) [[Collision|collide]], leaving one of the objects moved backwards or forwards to a degree, and the other forward. Crawler reactions are commonly used to create [[engineered spaceship]]s, also known as caterpillars.

==List of crawlers==

===17c/45 pi heptomino crawler===
{{EmbedViewer
|pname = 17c45reaction
|viewerconfig = #C [[ TRACKLOOP 45 0 -17/45 GPS 22.5 ZOOM 12 Y 12 THUMBSIZE 2 AUTOSTART ]]
|position = center
}}

Perhaps the first and most well known climber is the infamous [[17c/45 reaction]], consisting of [[pi heptomino]] running over a [[blinker]], moving it back 6 cells and rephasing it, whilst the pi heptomino moves forward 17 cells. This takes place in 45 generations.

The reaction was known for a long time, however the idea of a spaceship powered by this reaction was mentioned much later in 2002 by [[David Bell]] who had discovered reactions between multiple pies, which [[Rake|emitted gliders]]. After much work, [[Gabriel Nivasch]] finished construction of [[caterpillar]], the first [[17c/45 orthogonal]] spaceship, on 31 December {{year|2004}}.

Research has been conducted into building much smaller 17c/45 spaceships with pi crawlers, analogously to the silverfish. Discussion has been ongoing since as early as 2013.<ref name="post10028" />

===31c/240 Herschel crawler===
{{EmbedViewer
|pname = 31c240reaction
|viewerconfig = #C [[ AUTOSTART GPS 60 X 0 Y 40 TRACKLOOP 240 0/240 -31/240 THUMBSIZE 2 ZOOM 4 HEIGHT 480 ]]
|position = center
}}

Another orthogonal crawler, the [[31c/240 reaction]], consisting of a Herschel crawling though blocks.

Four 31c/240 spaceships are known, three of which use the crawler; [[shield bug]], [[centipede]], and [[silverfish]]. The fourth, [[centipede caterloopillar]], relies on universal constructor technology instead of conventional crawlers.

===(23,5)c/79 Herschel climber===
{{EmbedViewer
|pname = 235c79climber
|viewerconfig = #C [[ AUTOSTART GPS 39.5 X -10 Y 15 TRACKLOOP 79 5/79 -23/79 THUMBSIZE 2 ZOOM 10 HEIGHT 480 ]]
|position = center
}}

The [[(23,5)c/79 Herschel climber]] involves a [[Herschel]] reacting with a stream of gliders, emitting more gliders behind it in the same way, displacing the Herschel by 23 cells vertically and 5 horizontally in the space of 79 generations. It can also crawl on certain still lifes as well as gliders.

This climber has been engineered and other components assembled by hand to create [[waterbear]], which was the fastest known oblique spaceship until the discovery of [[Sir Robin]] in 2018.

===(34,7)c/156 Herschel climber===
{{EmbedViewer
|pname = 347c156climber
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 4 X 70 Y -40 AUTOSTART TRACKLOOP 312 -34/156 7/156 ]]
|position = center
}}

The [[(34,7)c/156 Herschel climber]] is another notable oblique climber. An [[Unnamed (34,7)c/156 spaceship|unnamed (34,7)c/156 caterpillar]] has been built using this climber.

===(13,1)c/31 Pseudo-B climber===
{{EmbedViewer
|pname = 131c31climber
|viewerconfig = #C [[ HEIGHT 640 THUMBSIZE 2 GPS 15.5 X 5 Y 10 ZOOM 12 AUTOSTART TRACKLOOP 31 1/31 -13/31 ]]
|position = center
}}

An interesting climber, the [[(13,1)c/31 Pseudo-B climber]] involves a climbing reaction that never isolates itself into a [[Herschel]] or [[B-heptomino]]. A spaceship based on it was first mentioned by Gabriel Nivasch as an afterthought on his caterpillar article.

No spaceships have been built with this reaction as of yet.

===(27,1)c/72 Herschel climber===
{{EmbedViewer
|pname = 271c72climber
|viewerconfig = #C [[ AUTOSTART GPS 36 X -10 Y 1 TRACKLOOP 72 1/72 -27/72 THUMBSIZE 2 ZOOM 4 HEIGHT 480 ]]
|position = center
}}

Much research has been conducted into a spaceship based on the [[(27,1)c/72 Herschel climber]], though discussion on it died out in mid-2019.

===(13,4)c/41 B-heptomino climber===
{{EmbedViewer
|pname = 134c41climber
|viewerconfig = #C [[ AUTOSTART GPS 34 X -17 Y 16 TRACKLOOP 41 4/41 -13/41 THUMBSIZE 2 ZOOM 13 HEIGHT 480 ]]
|position = center
}}

Consists of a B-heptomino climbing on gliders. Was initially proposed in 2014,<ref name="post15241" /> but no development started until early 2021.<ref name="post123822" />

===(31,5)c/137 climber===
{{EmbedViewer
|rle = x = 142, y = 301, rule = B3/S23
118bo5bo$118bo5bo$118bo5bo2$120b3o$47b3o3b3o2$51bo$51bo$51bo6$133b3o3b
3o2$137bo$72bo5bo58bo$72bo5bo58bo$72bo5bo2$74b3o10$112b3o3b3o2$116bo$
43bo5bo66bo$43bo5bo66bo$43bo5bo2$45b3o6$129bo5bo$129bo5bo$129bo5bo2$131b
3o$66b3o3b3o2$70bo$70bo$70bo8$108bo5bo$108bo5bo$108bo5bo2$110b3o$37b3o
3b3o2$41bo$41bo$41bo6$101b3o19b3o3b3o$102bo$102b3o22bo$62bo5bo58bo$62b
o5bo58bo$62bo5bo$31b3o$31bobo30b3o$31bo2bo$32b3o$32b3o$30bo2bo$33bo68b
o$30bo72bo$101b3o$32bo68b3o$31bo70b2o$31b2o$100bo5bo$100bo5bo$100bo5b
o$33bo$32b3o67b3o$31b2ob2o$32b3o$33bo5$104b2o13bo5bo$104b2o13bo5bo$119b
o5bo2$34b2o85b3o$34b2o20b3o3b3o2$60bo$60bo$60bo11$94b3o3b3o2$98bo$25b
o5bo66bo$25bo5bo66bo$25bo5bo2$27b3o3$69bo$69bobo27b2o$2bo66b2o28b2o12b
3o3b3o$2o$b2o114bo$29b2o86bo$29b2o16bo2bo6b3o57bo$47bo2bo5bob2o$47bo2b
o3bob2o$45bo8b3o$47bo$45bob2o$46bo2b2o57b2o$48bo58b3o$107bo2bo$107b2o
b2o$107b2ob2o$106b2ob2o$107bo$53b2o53b3o$53b2o35bo5bo12bo$90bo5bo$84b
o5bo5bo$83b2o$83bobo6b3o$19b3o3b3o2$23bo$23bo$23bo6$105b3o3b3o2$109bo
$44bo5bo58bo$44bo5bo58bo$44bo5bo2$46b3o4$110b2o$110b2o3$48b2o$48b2o$84b
3o3b3o2$88bo$15bo5bo22bobo41bo$15bo5bo23b2o41bo$15bo5bo23bo2$17b3o6$101b
o5bo$101bo5bo$101bo5bo2$103b3o$38b3o3b3o2$42bo$42bo$42bo3$105b2o$74bo
30b2o$72b2o$73b2o$43b2o$43b2o35bo5bo$80bo5bo$80bo5bo2$82b3o$9b3o3b3o2$
13bo$13bo$13bo6$95b3o3b3o2$99bo$34bo5bo58bo$34bo5bo58bo$34bo5bo2$36b3o
4$100b2o$100b2o3$38b2o$38b2o$74b3o3b3o2$78bo$5bo5bo66bo$5bo5bo66bo$5b
o5bo$75bo$7b3o63bobo$74b2o5$91bo5bo$91bo5bo$91bo5bo2$93b3o$28b3o3b3o2$
32bo$32bo$32bo3$95b2o$95b2o4$70bo5bo$70bo5bo$70bo5bo2$72b3o11$85b3o3b3o2$89bo$89bo$89bo!
|viewerconfig = #C [[ THUMBSIZE 2 Y -15 AUTOSTART TRACKLOOP 137 5/137 -31/137 THUMBSIZE 2 ZOOM 4 HEIGHT 600 ]]
|position = center
}}

This has been discussed somewhat as of late 2022.<ref name="thread5867"/>

===(10,7)c/75 climber===
{{EmbedViewer
|rle = x = 116, y = 141, rule = B3/S23
2bo$obo$b2o27$26bobo$27b2o$27bo26$53bo$54bo$52b3o27$78bo$79b2o$78b2o27$
105bo$103bobo$104b2o13$113bo$112bobo$111bo3bo$112bobo5$112bo$111bobo$
112bo!
|viewerconfig = #C [[ AUTOSTART GPS 45 X 57 Y 67 TRACKLOOP 450 -42/450 -60/450 THUMBSIZE 2 ZOOM 10 HEIGHT 480 ]]
|position = center
}}

A spaceship based on this fuse has also been discussed, however its potential is doubtful.<ref name="thread6025" />

===Half-bakery reaction===
{{EmbedViewer
|pname = hbkreaction
|viewerconfig = #C [[ AUTOSTART GPS 45 X -15 Y 15 TRACKLOOP 290 -3/290 -6/290 THUMBSIZE 2 ZOOM 10 HEIGHT 480 ]]
|position = center
}}

There is a well-known reaction in which a glider crashes into the side of a [[half-bakery]], shifting the loaves and releasing a glider. This reaction has been used to create [[Half-baked knightship]] and [[parallel HBK]], and was later used to create the [[HBK caterpillar]].

== Fuses which could be made into climbers ==
The following lists fuses which show potential for being made into workable climbers, but progress is yet to be made.

=== (8,1)c/32 p128 Herschel fuse ===
{{EmbedViewer
|rle = x = 193, y = 88, rule = B3/S23
bo$2bo$3o26$65bo$66bo$64b3o26$129bo$130bo$128b3o25$192bo$191b2o$190b2o
$191bo$192bo!
|viewerconfig = #C [[ AUTOSTART GPS 45 X 95 Y 42 TRACKLOOP 384 -24/96 3/96 THUMBSIZE 2 ZOOM 10 HEIGHT 480 ]]
|position = center
}}
This fuse eats gliders, spitting out double the amount of gliders, but leaving blocks behind in the process.<ref name="post13104" />

=== (40,7)c/244 Herschel fuse ===
{{EmbedViewer
|rle = x = 138, y = 29, rule = B3/S23
137bo$137bo$137bo5$97bo$97bo$97bo5$57bo$57bo$57bo5$17bo$17bo$17bo$o$2o
$b2o$bo$o!
|viewerconfig = #C [[ AUTOSTART GPS 45 X -80 Y 5 TRACKLOOP 976 160/976 -28/976 THUMBSIZE 2 ZOOM 8 HEIGHT 480 ]]
|position = center
}}
Consuming blinkers, a new blinker is produced by a significant shift. However, a large cluster of debris is left in the other direction, making stabilisation appear challenging.<ref name="post10714" />

==See also==
*[[Herschel climber]]
*[[Herschel-pair climber]]
*[[Reburnable fuse]]

==References==
<references>
<ref name="post10028">{{LinkForumThread
|format = ref
|p = 10028
|title = Caterpillar's little brother research
|author = Ivan Fomichev
|date = December 8, 2013
}}</ref>
<ref name="post10714">{{LinkForumThread
|format = ref
|p = 10714
|title = Interesting simple fuses
|author = Sphenocorona
|date = February 9, 2014
}}</ref>
<ref name="post13104">{{LinkForumThread
|format = ref
|p = 13104
|title = Re: Interesting simple fuses
|author = Sphenocorona
|date = September 6, 2014
}}</ref>
<ref name="post15241">{{LinkForumThread
|format = ref
|p = 15241
|title = (13,4)c/41 crawlers
|author = Ivan Fomichev
|date = December 26, 2014
}}</ref>
<ref name="post15549">{{LinkForumThread
|format = ref
|p = 15549
|title = HBK as Caterpillar
|author = Brett Berger
|date = January 2, 2015
}}</ref>
<ref name="post123822">{{LinkForumThread
|format = ref
|p = 123822
|title = Re: (13,4)c/41 crawlers
|author = Christopher D'Agostino
|date = February 26, 2021
}}</ref>
<ref name="thread5867">{{LinkForumThread
|format = ref
|f = 2
|t = 5867
|p = 153737
|title = (31,5)c/137 Caterpillar
}}</ref>
<ref name="thread6025">{{LinkForumThread
|format = ref
|f = 2
|t = 6025
|p = 162040
|title = Can we make a (10,7)c/75 spaceship?
}}</ref>
</references>

==External links==
* {{LinkForumThread|f=2|t=1182|title=13131: The B-Heptomino/Glider Spaceship Thread}}
* {{LinkForumThread|f=2|t=1142|title=(23,5)c/79 spaceship components}}
* {{LinkForumThread|f=2|t=2130|title=(27,1)c/72 caterpillar challenge}}
* {{LinkForumThread|f=2|t=2286|title=(34,7)c/156 caterpillar}}
* {{LinkForumThread|f=2|t=1539|title=(13,4)c/41 crawlers}}

Engineered diehard

2023-10-06T15:16:13Z

Ch91: My mistake. It seems I misunderstood the definition of pentation.

{{stub}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|pname = diehard30273
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 ZOOM 14 ]]
|position = center
|caption = 30,273-tick diehard with bounding box {{times|32|32}} by Hickerson<ref name="post143921" />
}}
|}
{{main|Die hard#"Die hard" as a general term}}
Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes. On March 1, [[Dean Hickerson]] shared a 9044-tick {{times|32|32}} diehard in a private email to [[Dave Greene]]. After a complex series of interactions between an active reaction and various still lifes, a single [[lightweight spaceship]] is produced which eventually catches up to and collides with [[30P5H2V0]], producing a single [[loaf]]. Finally, an even slower [[25P3H1V0.1]] eventually collides with the loaf, destroying both of them.<ref name="post143573" /> On March 6, more optimized versions using different combinations of spaceships (including the especially slow [[copperhead]]) were shared, including a 14,010-tick diehard at {{times|32|32}} and an 18,477-tick diehard at {{times|36|36}}.<ref name="post143574" />

Although Hickerson's results were not initially posted publicly, a forum thread was coincidentally started a few weeks later dedicated to diehards, including engineered ones.<ref name="post143559" /> On March 31, [[Pavel Grankovskiy]] posted a 50,716-tick diehard in which a [[Simkin glider gun]] and [[pulse divider|pulse-dividing]] glider reflectors are used to slowly eat through a series of [[tub]]s. Although significantly larger than Hickerson's constructions at {{times|90|86}}, Grankovskiy's 50,716-tick diehard does not use the "spaceship-chasing" technique, meaning that throughout its evolution, the pattern only slightly exceeds its initial bounds. Using spaceship-chasing, however, the pattern's lifespan can be increased by an order of magnitude to 518,476 ticks without further increasing the bounding box.<ref name="post143605" /> [[Jiahao Yu]] optimized the bounding box of both of these patterns to {{times|87|86}},<ref name="post143624" /> as shown below.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = diehard50716
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 50,716-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = diehard518476
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 518,476-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery bottom}}

== Sawtooth-based designs ==
Using a [[sawtooth]] allows for the creation of extremely long-lasting diehards. On April 7, 2022, Pavel Grankovskiy successfully constructed a diehard using a sawtooth an {{c|Sawtooths with expansion factor 121|expansion factor of 121}}. The pattern fits within a bounding box of {{times|99|101}} (just barely meeting the 10,000-cell restriction specified in the original post<ref name="post143559" />) and lasts approximately {{times|2.280624|10{{sup|870}}}} generations.<ref name="post143908" /> Further optimizations, with the help of [[toroidalet]],<ref name="post143914" /> Dean Hickerson,<ref name="post143920" /> [[EvinZL]],<ref name="post143997" /> [[Rocknlol]],<ref name="post144020" /> and [[Adam P. Goucher]]<ref name="post144030" /> increased its lifespan to {{times|~1.33616|10{{sup|1443}}}} ticks<ref name="post144027" /> and decreased its bounding box to {{times|94|98}}.<ref name="post144045" />

{{EmbedViewer
|pname = diehard1e1443
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 700 ZOOM 6 ]]
|position = center
|caption = {{times|94|98}} exponential diehard by Grankovskiy et al.
|style = width:300px;
}}

On April 9, Grankovskiy posted a concept for a pattern whose lifespan is measured via [[tetration]], the next hyperoperator after exponentiation. Originally posted in the form of a methuselah,<ref name="post144034" /> the diehard version was completed on April 11.<ref name="post144077" /> With optimization by [[Tanner Jacobi]]<ref name="post144087" /> and toroidalet,<ref name="post144162" /><ref name="post149066" /> its lifespan is somewhere between 1510 and 1610 ticks.<ref>{{Cite web|url=https://btm.qva.mybluehost.me/telling-the-tale-of-two-tetrations/|author=Brett Berger|title=Telling the tale of two tetrations|work=a blog by biggiemac42|date=April 17, 2022|accessdate=April 17, 2022}}</ref>

{{EmbedViewer
|pname = diehardtetration
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|111|90}} tetrational diehard by Grankovskiy et al.
|style = width:300px;
}}

On July 9, 2023, [[EvinZL]] proposed adding loaf-making fuse to increase the lifespan of the methuselah by extending power tower length,<ref name="post163493" /> based on the original idea of [[Tanner Jacobi]].<ref name="post148684" /> In a flurry of activity that followed after, [[toroidalet]], [[Adam P. Goucher]], [[Pavel Grankovskiy]] and [[EvinZL]] pushed the number of loaves from 15<ref name="tetrational_15_loaves" /> to approximately {{times|3.52|10{{sup|48}}}}<ref name="tetrational_1e48" />, with the latter improvement based on idea by [[Adam P. Goucher]] to use gliders from exponential part of diehard to ignite the fuse.<ref name="tetrational_exp_idea" /> This was subsequently improved to {{times|1.1|10{{sup|1046}}}}<ref name="tetrational_1e1046" /><ref name="tetrational_exp_cp4space" />.

{{EmbedViewer
|pname = diehardtetration1046
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|109|91}} tetrational diehard with a lifespan exceeding 10104610.
|style = width:300px;
}}

== Double-tetrational designs ==
On 15th September 2023, [[Tim Coe]] and b3s23love increased the height of the tetrational tower from {{times|1.1|10{{sup|1046}}}} to 121{{sup|{{times|8.46|10{{sup|1059}}}}}}. The following day, Tim Coe further improved this height to 121{{sup|121{{sup|121{{sup|121{{sup|498}}}}}}}}, so the height of the tetrational tower is itself a tetrational tower. This was subsequently further improved by Tim Coe, toroidalet, EvinZL, and b3s23love, culminating in a height of 121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|1356648129958673823266622201465466300}}}}}}}}}}}}}}}}}} as of the 28th September 2023. The overall lifespan of the diehard exceeds {{sup|{{sup|11}}11}}11, or 11^^^3 in Knuth's up-arrow notation. More recent designs have further improved lifespans, with the current record holder taking 17^^^3 generations to die out entirely.

== References ==
<references>
<ref name="post143573">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143573
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143574">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143574
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143559">{{LinkForumThread
|format = ref
|title = (Engineered) diehards
|p = 143559
|author = squareroot12621
|date = March 30, 2022
}}</ref>
<ref name="post143605">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143605
|author = Pavel Grankovskiy
|date = March 31, 2022
}}</ref>
<ref name="post143624">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143624
|author = Jiahao Yu
|date = March 31, 2022
}}</ref>
<ref name="post143921">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143921
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143908">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143908
|author = Pavel Grankovskiy
|date = April 7, 2022
}}</ref>
<ref name="post143914">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143914
|author = toroidalet
|date = April 7, 2022
}}</ref>
<ref name="post143920">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143920
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143997">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143997
|author = EvinZL
|date = April 9, 2022
}}</ref>
<ref name="post144020">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144020
|author = Rocknlol
|date = April 10, 2022
}}</ref>
<ref name="post144030">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144030
|author = Adam P. Goucher
|date = April 10, 2022
}}</ref>
<ref name="post144027">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144027
|author = Dean Hickerson
|date = April 10, 2022
}}</ref>
<ref name="post144045">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144045
|author = toroidalet
|date = April 10, 2022
}}</ref>
<ref name="post144034">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144034
|author = Pavel Grankovskiy
|date = April 9, 2022
}}</ref>
<ref name="post144077">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144077
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144087">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144087
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144162">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144162
|author = toroidalet
|date = April 13, 2022
}}</ref>
<ref name="post149066">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 149066
|author = toroidalet
|date = August 2, 2022
}}</ref>
<ref name="post163493">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163493
|author = EvinZL
|date = July 9, 2023
}}</ref>
<ref name="post148684">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 148684
|author = Tanner Jacobi
|date = July 25, 2022
}}</ref>
<ref name="tetrational_15_loaves">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163828
|author = toroidalet
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e48">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163888
|author = Adam P. Goucher
|date = July 19, 2023
}}</ref>
<ref name="tetrational_exp_idea">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163848
|author = Adam P. Goucher
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e1046">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 164085
|author = Adam P. Goucher
|date = July 23, 2023
}}</ref>
<ref name="tetrational_exp_cp4space">{{cite web|url=https://cp4space.hatsya.com/2023/07/23/miscellaneous-discoveries/|title=Miscellaneous discoveries|work=Complex Projective 4-Space|accessdate=May 23, 2023}}</ref>
</references>

== External links ==
* {{LinkForumThread|title=Re: (Engineered) diehards|p=144151|author=Pavel Grankovskiy|date=April 12, 2022}} (analysis of the tetrational diehard's total runtime)

Engineered diehard

2023-10-06T15:14:46Z

Ch91: Undo revision 138219 by Ch91 (talk)

{{stub}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|pname = diehard30273
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 ZOOM 14 ]]
|position = center
|caption = 30,273-tick diehard with bounding box {{times|32|32}} by Hickerson<ref name="post143921" />
}}
|}
{{main|Die hard#"Die hard" as a general term}}
Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes. On March 1, [[Dean Hickerson]] shared a 9044-tick {{times|32|32}} diehard in a private email to [[Dave Greene]]. After a complex series of interactions between an active reaction and various still lifes, a single [[lightweight spaceship]] is produced which eventually catches up to and collides with [[30P5H2V0]], producing a single [[loaf]]. Finally, an even slower [[25P3H1V0.1]] eventually collides with the loaf, destroying both of them.<ref name="post143573" /> On March 6, more optimized versions using different combinations of spaceships (including the especially slow [[copperhead]]) were shared, including a 14,010-tick diehard at {{times|32|32}} and an 18,477-tick diehard at {{times|36|36}}.<ref name="post143574" />

Although Hickerson's results were not initially posted publicly, a forum thread was coincidentally started a few weeks later dedicated to diehards, including engineered ones.<ref name="post143559" /> On March 31, [[Pavel Grankovskiy]] posted a 50,716-tick diehard in which a [[Simkin glider gun]] and [[pulse divider|pulse-dividing]] glider reflectors are used to slowly eat through a series of [[tub]]s. Although significantly larger than Hickerson's constructions at {{times|90|86}}, Grankovskiy's 50,716-tick diehard does not use the "spaceship-chasing" technique, meaning that throughout its evolution, the pattern only slightly exceeds its initial bounds. Using spaceship-chasing, however, the pattern's lifespan can be increased by an order of magnitude to 518,476 ticks without further increasing the bounding box.<ref name="post143605" /> [[Jiahao Yu]] optimized the bounding box of both of these patterns to {{times|87|86}},<ref name="post143624" /> as shown below.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = diehard50716
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 50,716-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = diehard518476
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 518,476-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery bottom}}

== Sawtooth-based designs ==
Using a [[sawtooth]] allows for the creation of extremely long-lasting diehards. On April 7, 2022, Pavel Grankovskiy successfully constructed a diehard using a sawtooth an {{c|Sawtooths with expansion factor 121|expansion factor of 121}}. The pattern fits within a bounding box of {{times|99|101}} (just barely meeting the 10,000-cell restriction specified in the original post<ref name="post143559" />) and lasts approximately {{times|2.280624|10{{sup|870}}}} generations.<ref name="post143908" /> Further optimizations, with the help of [[toroidalet]],<ref name="post143914" /> Dean Hickerson,<ref name="post143920" /> [[EvinZL]],<ref name="post143997" /> [[Rocknlol]],<ref name="post144020" /> and [[Adam P. Goucher]]<ref name="post144030" /> increased its lifespan to {{times|~1.33616|10{{sup|1443}}}} ticks<ref name="post144027" /> and decreased its bounding box to {{times|94|98}}.<ref name="post144045" />

{{EmbedViewer
|pname = diehard1e1443
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 700 ZOOM 6 ]]
|position = center
|caption = {{times|94|98}} exponential diehard by Grankovskiy et al.
|style = width:300px;
}}

On April 9, Grankovskiy posted a concept for a pattern whose lifespan is measured via [[tetration]], the next hyperoperator after exponentiation. Originally posted in the form of a methuselah,<ref name="post144034" /> the diehard version was completed on April 11.<ref name="post144077" /> With optimization by [[Tanner Jacobi]]<ref name="post144087" /> and toroidalet,<ref name="post144162" /><ref name="post149066" /> its lifespan is somewhere between 1510 and 1610 ticks.<ref>{{Cite web|url=https://btm.qva.mybluehost.me/telling-the-tale-of-two-tetrations/|author=Brett Berger|title=Telling the tale of two tetrations|work=a blog by biggiemac42|date=April 17, 2022|accessdate=April 17, 2022}}</ref>

{{EmbedViewer
|pname = diehardtetration
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|111|90}} tetrational diehard by Grankovskiy et al.
|style = width:300px;
}}

On July 9, 2023, [[EvinZL]] proposed adding loaf-making fuse to increase the lifespan of the methuselah by extending power tower length,<ref name="post163493" /> based on the original idea of [[Tanner Jacobi]].<ref name="post148684" /> In a flurry of activity that followed after, [[toroidalet]], [[Adam P. Goucher]], [[Pavel Grankovskiy]] and [[EvinZL]] pushed the number of loaves from 15<ref name="tetrational_15_loaves" /> to approximately {{times|3.52|10{{sup|48}}}}<ref name="tetrational_1e48" />, with the latter improvement based on idea by [[Adam P. Goucher]] to use gliders from exponential part of diehard to ignite the fuse.<ref name="tetrational_exp_idea" /> This was subsequently improved to {{times|1.1|10{{sup|1046}}}}<ref name="tetrational_1e1046" /><ref name="tetrational_exp_cp4space" />.

{{EmbedViewer
|pname = diehardtetration1046
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|109|91}} tetrational diehard with a lifespan exceeding 10104610.
|style = width:300px;
}}

== Pentational designs ==
On 15th September 2023, [[Tim Coe]] and b3s23love increased the height of the tetrational tower from {{times|1.1|10{{sup|1046}}}} to 121{{sup|{{times|8.46|10{{sup|1059}}}}}}. The following day, Tim Coe further improved this height to 121{{sup|121{{sup|121{{sup|121{{sup|498}}}}}}}}, so the height of the tetrational tower is itself a tetrational tower (and thus moving to pentation, the level of operation beyond tetration). This was subsequently further improved by Tim Coe, toroidalet, EvinZL, and b3s23love, culminating in a height of 121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|1356648129958673823266622201465466300}}}}}}}}}}}}}}}}}} as of the 28th September 2023. The overall lifespan of the diehard exceeds {{sup|{{sup|11}}11}}11, or 11^^^3 in Knuth's up-arrow notation. More recent designs have further improved lifespans, with the current record holder taking 17^^^3 generations to die out entirely.

== References ==
<references>
<ref name="post143573">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143573
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143574">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143574
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143559">{{LinkForumThread
|format = ref
|title = (Engineered) diehards
|p = 143559
|author = squareroot12621
|date = March 30, 2022
}}</ref>
<ref name="post143605">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143605
|author = Pavel Grankovskiy
|date = March 31, 2022
}}</ref>
<ref name="post143624">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143624
|author = Jiahao Yu
|date = March 31, 2022
}}</ref>
<ref name="post143921">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143921
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143908">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143908
|author = Pavel Grankovskiy
|date = April 7, 2022
}}</ref>
<ref name="post143914">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143914
|author = toroidalet
|date = April 7, 2022
}}</ref>
<ref name="post143920">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143920
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143997">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143997
|author = EvinZL
|date = April 9, 2022
}}</ref>
<ref name="post144020">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144020
|author = Rocknlol
|date = April 10, 2022
}}</ref>
<ref name="post144030">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144030
|author = Adam P. Goucher
|date = April 10, 2022
}}</ref>
<ref name="post144027">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144027
|author = Dean Hickerson
|date = April 10, 2022
}}</ref>
<ref name="post144045">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144045
|author = toroidalet
|date = April 10, 2022
}}</ref>
<ref name="post144034">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144034
|author = Pavel Grankovskiy
|date = April 9, 2022
}}</ref>
<ref name="post144077">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144077
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144087">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144087
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144162">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144162
|author = toroidalet
|date = April 13, 2022
}}</ref>
<ref name="post149066">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 149066
|author = toroidalet
|date = August 2, 2022
}}</ref>
<ref name="post163493">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163493
|author = EvinZL
|date = July 9, 2023
}}</ref>
<ref name="post148684">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 148684
|author = Tanner Jacobi
|date = July 25, 2022
}}</ref>
<ref name="tetrational_15_loaves">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163828
|author = toroidalet
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e48">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163888
|author = Adam P. Goucher
|date = July 19, 2023
}}</ref>
<ref name="tetrational_exp_idea">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163848
|author = Adam P. Goucher
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e1046">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 164085
|author = Adam P. Goucher
|date = July 23, 2023
}}</ref>
<ref name="tetrational_exp_cp4space">{{cite web|url=https://cp4space.hatsya.com/2023/07/23/miscellaneous-discoveries/|title=Miscellaneous discoveries|work=Complex Projective 4-Space|accessdate=May 23, 2023}}</ref>
</references>

== External links ==
* {{LinkForumThread|title=Re: (Engineered) diehards|p=144151|author=Pavel Grankovskiy|date=April 12, 2022}} (analysis of the tetrational diehard's total runtime)

Engineered diehard

2023-10-06T15:12:47Z

Ch91: /* Pentational designs */

{{stub}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|pname = diehard30273
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 ZOOM 14 ]]
|position = center
|caption = 30,273-tick diehard with bounding box {{times|32|32}} by Hickerson<ref name="post143921" />
}}
|}
{{main|Die hard#"Die hard" as a general term}}
Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes. On March 1, [[Dean Hickerson]] shared a 9044-tick {{times|32|32}} diehard in a private email to [[Dave Greene]]. After a complex series of interactions between an active reaction and various still lifes, a single [[lightweight spaceship]] is produced which eventually catches up to and collides with [[30P5H2V0]], producing a single [[loaf]]. Finally, an even slower [[25P3H1V0.1]] eventually collides with the loaf, destroying both of them.<ref name="post143573" /> On March 6, more optimized versions using different combinations of spaceships (including the especially slow [[copperhead]]) were shared, including a 14,010-tick diehard at {{times|32|32}} and an 18,477-tick diehard at {{times|36|36}}.<ref name="post143574" />

Although Hickerson's results were not initially posted publicly, a forum thread was coincidentally started a few weeks later dedicated to diehards, including engineered ones.<ref name="post143559" /> On March 31, [[Pavel Grankovskiy]] posted a 50,716-tick diehard in which a [[Simkin glider gun]] and [[pulse divider|pulse-dividing]] glider reflectors are used to slowly eat through a series of [[tub]]s. Although significantly larger than Hickerson's constructions at {{times|90|86}}, Grankovskiy's 50,716-tick diehard does not use the "spaceship-chasing" technique, meaning that throughout its evolution, the pattern only slightly exceeds its initial bounds. Using spaceship-chasing, however, the pattern's lifespan can be increased by an order of magnitude to 518,476 ticks without further increasing the bounding box.<ref name="post143605" /> [[Jiahao Yu]] optimized the bounding box of both of these patterns to {{times|87|86}},<ref name="post143624" /> as shown below.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = diehard50716
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 50,716-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = diehard518476
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 518,476-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery bottom}}

== Sawtooth-based designs ==
Using a [[sawtooth]] allows for the creation of extremely long-lasting diehards. On April 7, 2022, Pavel Grankovskiy successfully constructed a diehard using a sawtooth an {{c|Sawtooths with expansion factor 121|expansion factor of 121}}. The pattern fits within a bounding box of {{times|99|101}} (just barely meeting the 10,000-cell restriction specified in the original post<ref name="post143559" />) and lasts approximately {{times|2.280624|10{{sup|870}}}} generations.<ref name="post143908" /> Further optimizations, with the help of [[toroidalet]],<ref name="post143914" /> Dean Hickerson,<ref name="post143920" /> [[EvinZL]],<ref name="post143997" /> [[Rocknlol]],<ref name="post144020" /> and [[Adam P. Goucher]]<ref name="post144030" /> increased its lifespan to {{times|~1.33616|10{{sup|1443}}}} ticks<ref name="post144027" /> and decreased its bounding box to {{times|94|98}}.<ref name="post144045" />

{{EmbedViewer
|pname = diehard1e1443
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 700 ZOOM 6 ]]
|position = center
|caption = {{times|94|98}} exponential diehard by Grankovskiy et al.
|style = width:300px;
}}

On April 9, Grankovskiy posted a concept for a pattern whose lifespan is measured via [[tetration]], the next hyperoperator after exponentiation. Originally posted in the form of a methuselah,<ref name="post144034" /> the diehard version was completed on April 11.<ref name="post144077" /> With optimization by [[Tanner Jacobi]]<ref name="post144087" /> and toroidalet,<ref name="post144162" /><ref name="post149066" /> its lifespan is somewhere between 1510 and 1610 ticks.<ref>{{Cite web|url=https://btm.qva.mybluehost.me/telling-the-tale-of-two-tetrations/|author=Brett Berger|title=Telling the tale of two tetrations|work=a blog by biggiemac42|date=April 17, 2022|accessdate=April 17, 2022}}</ref>

{{EmbedViewer
|pname = diehardtetration
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|111|90}} tetrational diehard by Grankovskiy et al.
|style = width:300px;
}}

On July 9, 2023, [[EvinZL]] proposed adding loaf-making fuse to increase the lifespan of the methuselah by extending power tower length,<ref name="post163493" /> based on the original idea of [[Tanner Jacobi]].<ref name="post148684" /> In a flurry of activity that followed after, [[toroidalet]], [[Adam P. Goucher]], [[Pavel Grankovskiy]] and [[EvinZL]] pushed the number of loaves from 15<ref name="tetrational_15_loaves" /> to approximately {{times|3.52|10{{sup|48}}}}<ref name="tetrational_1e48" />, with the latter improvement based on idea by [[Adam P. Goucher]] to use gliders from exponential part of diehard to ignite the fuse.<ref name="tetrational_exp_idea" /> This was subsequently improved to {{times|1.1|10{{sup|1046}}}}<ref name="tetrational_1e1046" /><ref name="tetrational_exp_cp4space" />.

{{EmbedViewer
|pname = diehardtetration1046
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|109|91}} tetrational diehard with a lifespan exceeding 10104610.
|style = width:300px;
}}

== Pentational designs ==
On 15th September 2023, [[Tim Coe]] and b3s23love increased the height of the tetrational tower from {{times|1.1|10{{sup|1046}}}} to 121{{sup|{{times|8.46|10{{sup|1059}}}}}}. The following day, Tim Coe further improved this height to 121{{sup|121{{sup|121{{sup|121{{sup|498}}}}}}}}, so the height of the tetrational tower is itself a tetrational tower (and thus moving to pentation, the hyperoperator beyond tetration). This was subsequently further improved by Tim Coe, toroidalet, EvinZL, and b3s23love, culminating in a height of 121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|1356648129958673823266622201465466300}}}}}}}}}}}}}}}}}} as of the 28th September 2023. The overall lifespan of the diehard exceeds {{sup|{{sup|11}}11}}11, or 11^^^3 in Knuth's up-arrow notation. More recent designs have further improved lifespans, with the current record holder taking 17^^^3 generations to die out entirely.

== References ==
<references>
<ref name="post143573">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143573
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143574">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143574
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143559">{{LinkForumThread
|format = ref
|title = (Engineered) diehards
|p = 143559
|author = squareroot12621
|date = March 30, 2022
}}</ref>
<ref name="post143605">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143605
|author = Pavel Grankovskiy
|date = March 31, 2022
}}</ref>
<ref name="post143624">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143624
|author = Jiahao Yu
|date = March 31, 2022
}}</ref>
<ref name="post143921">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143921
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143908">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143908
|author = Pavel Grankovskiy
|date = April 7, 2022
}}</ref>
<ref name="post143914">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143914
|author = toroidalet
|date = April 7, 2022
}}</ref>
<ref name="post143920">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143920
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143997">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143997
|author = EvinZL
|date = April 9, 2022
}}</ref>
<ref name="post144020">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144020
|author = Rocknlol
|date = April 10, 2022
}}</ref>
<ref name="post144030">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144030
|author = Adam P. Goucher
|date = April 10, 2022
}}</ref>
<ref name="post144027">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144027
|author = Dean Hickerson
|date = April 10, 2022
}}</ref>
<ref name="post144045">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144045
|author = toroidalet
|date = April 10, 2022
}}</ref>
<ref name="post144034">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144034
|author = Pavel Grankovskiy
|date = April 9, 2022
}}</ref>
<ref name="post144077">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144077
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144087">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144087
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144162">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144162
|author = toroidalet
|date = April 13, 2022
}}</ref>
<ref name="post149066">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 149066
|author = toroidalet
|date = August 2, 2022
}}</ref>
<ref name="post163493">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163493
|author = EvinZL
|date = July 9, 2023
}}</ref>
<ref name="post148684">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 148684
|author = Tanner Jacobi
|date = July 25, 2022
}}</ref>
<ref name="tetrational_15_loaves">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163828
|author = toroidalet
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e48">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163888
|author = Adam P. Goucher
|date = July 19, 2023
}}</ref>
<ref name="tetrational_exp_idea">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163848
|author = Adam P. Goucher
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e1046">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 164085
|author = Adam P. Goucher
|date = July 23, 2023
}}</ref>
<ref name="tetrational_exp_cp4space">{{cite web|url=https://cp4space.hatsya.com/2023/07/23/miscellaneous-discoveries/|title=Miscellaneous discoveries|work=Complex Projective 4-Space|accessdate=May 23, 2023}}</ref>
</references>

== External links ==
* {{LinkForumThread|title=Re: (Engineered) diehards|p=144151|author=Pavel Grankovskiy|date=April 12, 2022}} (analysis of the tetrational diehard's total runtime)

Engineered diehard

2023-10-06T15:12:14Z

Ch91: Correct me if I am wrong but I believe this is the term for iterated tetration.

{{stub}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|pname = diehard30273
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 ZOOM 14 ]]
|position = center
|caption = 30,273-tick diehard with bounding box {{times|32|32}} by Hickerson<ref name="post143921" />
}}
|}
{{main|Die hard#"Die hard" as a general term}}
Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes. On March 1, [[Dean Hickerson]] shared a 9044-tick {{times|32|32}} diehard in a private email to [[Dave Greene]]. After a complex series of interactions between an active reaction and various still lifes, a single [[lightweight spaceship]] is produced which eventually catches up to and collides with [[30P5H2V0]], producing a single [[loaf]]. Finally, an even slower [[25P3H1V0.1]] eventually collides with the loaf, destroying both of them.<ref name="post143573" /> On March 6, more optimized versions using different combinations of spaceships (including the especially slow [[copperhead]]) were shared, including a 14,010-tick diehard at {{times|32|32}} and an 18,477-tick diehard at {{times|36|36}}.<ref name="post143574" />

Although Hickerson's results were not initially posted publicly, a forum thread was coincidentally started a few weeks later dedicated to diehards, including engineered ones.<ref name="post143559" /> On March 31, [[Pavel Grankovskiy]] posted a 50,716-tick diehard in which a [[Simkin glider gun]] and [[pulse divider|pulse-dividing]] glider reflectors are used to slowly eat through a series of [[tub]]s. Although significantly larger than Hickerson's constructions at {{times|90|86}}, Grankovskiy's 50,716-tick diehard does not use the "spaceship-chasing" technique, meaning that throughout its evolution, the pattern only slightly exceeds its initial bounds. Using spaceship-chasing, however, the pattern's lifespan can be increased by an order of magnitude to 518,476 ticks without further increasing the bounding box.<ref name="post143605" /> [[Jiahao Yu]] optimized the bounding box of both of these patterns to {{times|87|86}},<ref name="post143624" /> as shown below.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = diehard50716
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 50,716-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = diehard518476
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 518,476-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery bottom}}

== Sawtooth-based designs ==
Using a [[sawtooth]] allows for the creation of extremely long-lasting diehards. On April 7, 2022, Pavel Grankovskiy successfully constructed a diehard using a sawtooth an {{c|Sawtooths with expansion factor 121|expansion factor of 121}}. The pattern fits within a bounding box of {{times|99|101}} (just barely meeting the 10,000-cell restriction specified in the original post<ref name="post143559" />) and lasts approximately {{times|2.280624|10{{sup|870}}}} generations.<ref name="post143908" /> Further optimizations, with the help of [[toroidalet]],<ref name="post143914" /> Dean Hickerson,<ref name="post143920" /> [[EvinZL]],<ref name="post143997" /> [[Rocknlol]],<ref name="post144020" /> and [[Adam P. Goucher]]<ref name="post144030" /> increased its lifespan to {{times|~1.33616|10{{sup|1443}}}} ticks<ref name="post144027" /> and decreased its bounding box to {{times|94|98}}.<ref name="post144045" />

{{EmbedViewer
|pname = diehard1e1443
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 700 ZOOM 6 ]]
|position = center
|caption = {{times|94|98}} exponential diehard by Grankovskiy et al.
|style = width:300px;
}}

On April 9, Grankovskiy posted a concept for a pattern whose lifespan is measured via [[tetration]], the next hyperoperator after exponentiation. Originally posted in the form of a methuselah,<ref name="post144034" /> the diehard version was completed on April 11.<ref name="post144077" /> With optimization by [[Tanner Jacobi]]<ref name="post144087" /> and toroidalet,<ref name="post144162" /><ref name="post149066" /> its lifespan is somewhere between 1510 and 1610 ticks.<ref>{{Cite web|url=https://btm.qva.mybluehost.me/telling-the-tale-of-two-tetrations/|author=Brett Berger|title=Telling the tale of two tetrations|work=a blog by biggiemac42|date=April 17, 2022|accessdate=April 17, 2022}}</ref>

{{EmbedViewer
|pname = diehardtetration
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|111|90}} tetrational diehard by Grankovskiy et al.
|style = width:300px;
}}

On July 9, 2023, [[EvinZL]] proposed adding loaf-making fuse to increase the lifespan of the methuselah by extending power tower length,<ref name="post163493" /> based on the original idea of [[Tanner Jacobi]].<ref name="post148684" /> In a flurry of activity that followed after, [[toroidalet]], [[Adam P. Goucher]], [[Pavel Grankovskiy]] and [[EvinZL]] pushed the number of loaves from 15<ref name="tetrational_15_loaves" /> to approximately {{times|3.52|10{{sup|48}}}}<ref name="tetrational_1e48" />, with the latter improvement based on idea by [[Adam P. Goucher]] to use gliders from exponential part of diehard to ignite the fuse.<ref name="tetrational_exp_idea" /> This was subsequently improved to {{times|1.1|10{{sup|1046}}}}<ref name="tetrational_1e1046" /><ref name="tetrational_exp_cp4space" />.

{{EmbedViewer
|pname = diehardtetration1046
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|109|91}} tetrational diehard with a lifespan exceeding 10104610.
|style = width:300px;
}}

== Pentational designs ==
On 15th September 2023, [[Tim Coe]] and b3s23love increased the height of the tetrational tower from {{times|1.1|10{{sup|1046}}}} to 121{{sup|{{times|8.46|10{{sup|1059}}}}}}. The following day, Tim Coe further improved this height to 121{{sup|121{{sup|121{{sup|121{{sup|498}}}}}}}}, so the height of the tetrational tower is itself a tetrational tower (and thus moving to pentation, the level of operation beyond tetration). This was subsequently further improved by Tim Coe, toroidalet, EvinZL, and b3s23love, culminating in a height of 121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|1356648129958673823266622201465466300}}}}}}}}}}}}}}}}}} as of the 28th September 2023. The overall lifespan of the diehard exceeds {{sup|{{sup|11}}11}}11, or 11^^^3 in Knuth's up-arrow notation. More recent designs have further improved lifespans, with the current record holder taking 17^^^3 generations to die out entirely.

== References ==
<references>
<ref name="post143573">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143573
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143574">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143574
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143559">{{LinkForumThread
|format = ref
|title = (Engineered) diehards
|p = 143559
|author = squareroot12621
|date = March 30, 2022
}}</ref>
<ref name="post143605">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143605
|author = Pavel Grankovskiy
|date = March 31, 2022
}}</ref>
<ref name="post143624">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143624
|author = Jiahao Yu
|date = March 31, 2022
}}</ref>
<ref name="post143921">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143921
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143908">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143908
|author = Pavel Grankovskiy
|date = April 7, 2022
}}</ref>
<ref name="post143914">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143914
|author = toroidalet
|date = April 7, 2022
}}</ref>
<ref name="post143920">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143920
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143997">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143997
|author = EvinZL
|date = April 9, 2022
}}</ref>
<ref name="post144020">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144020
|author = Rocknlol
|date = April 10, 2022
}}</ref>
<ref name="post144030">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144030
|author = Adam P. Goucher
|date = April 10, 2022
}}</ref>
<ref name="post144027">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144027
|author = Dean Hickerson
|date = April 10, 2022
}}</ref>
<ref name="post144045">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144045
|author = toroidalet
|date = April 10, 2022
}}</ref>
<ref name="post144034">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144034
|author = Pavel Grankovskiy
|date = April 9, 2022
}}</ref>
<ref name="post144077">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144077
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144087">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144087
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144162">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144162
|author = toroidalet
|date = April 13, 2022
}}</ref>
<ref name="post149066">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 149066
|author = toroidalet
|date = August 2, 2022
}}</ref>
<ref name="post163493">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163493
|author = EvinZL
|date = July 9, 2023
}}</ref>
<ref name="post148684">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 148684
|author = Tanner Jacobi
|date = July 25, 2022
}}</ref>
<ref name="tetrational_15_loaves">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163828
|author = toroidalet
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e48">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163888
|author = Adam P. Goucher
|date = July 19, 2023
}}</ref>
<ref name="tetrational_exp_idea">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163848
|author = Adam P. Goucher
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e1046">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 164085
|author = Adam P. Goucher
|date = July 23, 2023
}}</ref>
<ref name="tetrational_exp_cp4space">{{cite web|url=https://cp4space.hatsya.com/2023/07/23/miscellaneous-discoveries/|title=Miscellaneous discoveries|work=Complex Projective 4-Space|accessdate=May 23, 2023}}</ref>
</references>

== External links ==
* {{LinkForumThread|title=Re: (Engineered) diehards|p=144151|author=Pavel Grankovskiy|date=April 12, 2022}} (analysis of the tetrational diehard's total runtime)

Engineered diehard

2023-10-06T15:07:33Z

Ch91: /* Double-tetrational designs */

Reverse caber-tosser

2023-01-29T16:31:34Z

Ch91: /* MathAndCode's RCT */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 15-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations and has been designed to use as few bits per glider as possible; it also includes a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the [[DBCA]] and ECCT drastically improved the efficiency of the RCT mechanism. That being said, synthesizing most patterns currently requires the constituent GPSEs to be so far apart that the RCT's bounding box becomes too large for Golly to run without crashing, so its applications will likely remain theoretical until a new version of Golly capable of handling it can be developed.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time is beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==Future==
At the time of RCT17 and RCT16, MathAndCode believed that the absolute smallest possible RCT would require 13 gliders by using one fewer switch engine.<ref name="post104600" /> The subsequent reduction from RCT16 to RCT15 suggests that MathAndCode's hypothetical 13-glider design ''might'' be reduced to 12 gliders in the same way.<ref name="message1046450382357938306" /> However, it is far from guaranteed that the exact same reduction method could be carried over to a three-switch-engine design.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{cite web|url=https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/|title=Building arbitrary Life patterns in 15 gliders|author=Brett Berger|date=November 16, 2022}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-fifteen-gliders-can.html|title=In Conway's Life, Fifteen Gliders Can Build Anything* !|author=Dave Greene|date=November 18, 2022}}

* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
<ref name="post104600">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104600
|author = MathAndCode
|date = September 20, 2020
}}</ref>
<ref name="message1046450382357938306">{{CiteDiscord
|author = Dave Greene
|date = November 27, 2022
|channel = general-discussion
|id = 1046450382357938306
}}</ref>
<ref name
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2023-01-29T16:30:01Z

Ch91: /* Applications */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 15-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations and has been designed to use as few bits per glider as possible; it also includes a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the [[DBCA]] and ECCT drastically improved the efficiency of the RCT mechanism. That being said, synthesizing most patterns currently requires the constituent GPSEs to be so far apart that the RCT's bounding box becomes too large for Golly to run without crashing, so its applications will likely remain theoretical until a new version of Golly capable of handling it can be developed.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==Future==
At the time of RCT17 and RCT16, MathAndCode believed that the absolute smallest possible RCT would require 13 gliders by using one fewer switch engine.<ref name="post104600" /> The subsequent reduction from RCT16 to RCT15 suggests that MathAndCode's hypothetical 13-glider design ''might'' be reduced to 12 gliders in the same way.<ref name="message1046450382357938306" /> However, it is far from guaranteed that the exact same reduction method could be carried over to a three-switch-engine design.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{cite web|url=https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/|title=Building arbitrary Life patterns in 15 gliders|author=Brett Berger|date=November 16, 2022}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-fifteen-gliders-can.html|title=In Conway's Life, Fifteen Gliders Can Build Anything* !|author=Dave Greene|date=November 18, 2022}}

* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
<ref name="post104600">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104600
|author = MathAndCode
|date = September 20, 2020
}}</ref>
<ref name="message1046450382357938306">{{CiteDiscord
|author = Dave Greene
|date = November 27, 2022
|channel = general-discussion
|id = 1046450382357938306
}}</ref>
<ref name
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2023-01-29T16:28:14Z

Ch91: /* Terminology */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 15-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations and has been designed to use as few bits per glider as possible; it also includes a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements. That being said, synthesizing complex patterns requires the constituent GPSEs to be so far apart that the RCT's bounding box becomes too large for Golly to run without crashing, so its applications will likely remain theoretical until a new version of Golly capable of handling it can be developed.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==Future==
At the time of RCT17 and RCT16, MathAndCode believed that the absolute smallest possible RCT would require 13 gliders by using one fewer switch engine.<ref name="post104600" /> The subsequent reduction from RCT16 to RCT15 suggests that MathAndCode's hypothetical 13-glider design ''might'' be reduced to 12 gliders in the same way.<ref name="message1046450382357938306" /> However, it is far from guaranteed that the exact same reduction method could be carried over to a three-switch-engine design.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{cite web|url=https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/|title=Building arbitrary Life patterns in 15 gliders|author=Brett Berger|date=November 16, 2022}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-fifteen-gliders-can.html|title=In Conway's Life, Fifteen Gliders Can Build Anything* !|author=Dave Greene|date=November 18, 2022}}

* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
<ref name="post104600">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104600
|author = MathAndCode
|date = September 20, 2020
}}</ref>
<ref name="message1046450382357938306">{{CiteDiscord
|author = Dave Greene
|date = November 27, 2022
|channel = general-discussion
|id = 1046450382357938306
}}</ref>
<ref name
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Sir Robin

2023-01-29T15:36:13Z

Ch91: I can't seem to get the reference format right, so if someone could help with that I'd be grateful.

{{Spaceship
|name = Sir Robin
|pname = sirrobin
|c = 282
|bx = 31
|by = 79
|dir = Oblique
|slope = 2
|p = 6
|m = 6
|s = (2,1)c/6
|z = (2,1)c/6
|h = 271
|discoverer = Adam P. Goucher
|discoverer2 = Tomas Rokicki
|discoveryear = 2018
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S234ce
|rulespecial = [[Conway's Game of Life|Conway Life]]
|plaintext = true
|rle = true
|apgcode = xq6_yyocxukcy6gocs20h0a38bac2qq73uszyjo4w8y0e4mo0vu0o606s6444u08clav0h03g440qq1333333x11zy9ecec2ik032i210sw3f0hy011w70401011033547442zy0emj896he1e1kif6q2gc50ew9qb30dzgo403gg066m32w11z34407q441n6zy311
|animated = true
|viewerconfig = #C [[ TRACKLOOP 6 -1/6 -1/3 THUMBSIZE 3 HEIGHT 1000 ZOOM 12 GPS 12 ]]
}}
'''Sir Robin'''{{refn|group=note|The name is in reference to [https://www.youtube.com/watch?v{{=}}BZwuTo7zKM8 Sir Robin], the knight who "bravely ran away", from Monty Python's movie ''[https://en.wikipedia.org/wiki/Monty_Python_and_the_Holy_Grail Monty Python and the Holy Grail]''.}} is a [[(2,1)c/6]] [[spaceship]] found by [[Adam P. Goucher]] on March 6, {{year|2018}} using his [[ikpx]] search program.

Sir Robin is also known by its systematic name '''282P6H2V1''', and is alternatively called '''seahorse''' or '''Minstrel 0''' / '''M0''' (see [[Sir Robin#Tagalongs|Tagalongs]] below). It is based on a partial found by [[Tomas Rokicki]], which makes up about 62% of the ship,<ref name="thread3303" /> and roughly half of which was itself an independent rediscovery of a partial found by [[Josh Ball]] in April {{year|2017}}.<ref name="post42467" /> Sir Robin is the first [[elementary]] [[knightship]] in [[Conway's Game of Life]], and the only elementary knightship in that rule until the discovery of the [[sprayer]]. A scientific paper describing the method used to find the ship is forthcoming.<ref name="post57456" />

{{POTY|year=2018|rank=1}}

With the discovery of [[Soba]] in December 2020, Sir Robin is the largest elementary spaceship which is the smallest for a given speed and displacement.

==Partials==
Josh Ball's original partial from April 2017 is shown below:

{{Template:EmbedViewer
|pname = knightshippartial
|position = center
|viewerconfig = #C [[ ZOOM 10 THUMBSIZE 2 GPS 6 HEIGHT 500 ]]
}}

==Synthesis==
No [[glider synthesis]] for Sir Robin is known; finding a synthesis is considered a challenging task at best, due to the large size of the ship, and the amount of [[space dust]] it contains. A fake 87-glider synthesis (actually a clever [[LifeViewer]] loop) was posted by [[Dave Greene]] on April Fools' Day 2018.<ref name="post58732" />

==Reactions==
[[Martin Grant]] constructed a Sir Robin [[eater]] with a [[repeat time]] of 557 on March 8, 2018:<ref name="post57499" />

{{EmbedViewer
|pname = sirrobineater
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 2 HEIGHT 800 ]]
}}

==Tagalongs==
[[Tagalong]]s of Sir Robin are dubbed '''minstrels'''.{{refn|group=note|"Minstrel", like "Sir Robin", is a reference to Monty Python's movie ''Monty Python and the Holy Grail''.}} There are many ways in which Sir Robin can be extended by attaching minstrels:

{{EmbedViewer
|pname = davegreenesminstrelcollection
|position = center
|caption = In order to expand and view annotations:
|viewerconfig = #C [[ X -23 Y -43 TRACKLOOP 6000 -1/6 -2/6 LABELANGLE 70 GPS 6 ]]
#C [[ LABEL -5 -40 1 "Minstrel 0\n(Sir Robin)" ]]
#C [[ COLOR LABEL Red LABEL 30 -40 1 "Minstrel 1" ]]
#C [[ COLOR LABEL Orange LABEL 70 -40 1 "Minstrel 2" ]]
#C [[ COLOR LABEL Yellow LABEL 110 -40 1 "Minstrel 3" ]]
#C [[ COLOR LABEL Green LABEL 150 -40 1 "Minstrel 4" ]]
#C [[ COLOR LABEL Blue LABEL 190 -40 1 "Minstrel 5" ]]
#C [[ COLOR LABEL Brown LABEL 240 -40 1 "Minstrel 6" ]]
#C [[ COLOR LABEL Purple LABEL 280 -40 1 "Minstrel 7" ]]
#C [[ COLOR LABEL Pink LABEL 320 -40 1 "Minstrel 8" ]]
#C [[ COLOR LABEL Violet LABEL 360 -40 1 "Minstrel 9" ]]
#C [[ COLOR LABEL Gray LABEL 400 -40 1 "Minstrel 10" ]]
#C [[ COLOR LABEL Cyan LABEL 440 -40 1 "Minstrel 11" ]]
#C [[ COLOR LABEL Magenta LABEL 480 -40 1 "Minstrel 12" ]]
#C [[ COLOR LABEL Beige LABEL 520 -40 1 "Minstrel 13" ]]
#C [[ COLOR LABEL Maroon LABEL 560 -40 1 "Minstrel 14" ]]
#C [[ COLOR LABEL Silver LABEL 600 -40 1 "Minstrel 15" ]]
#C [[ COLOR LABEL Chartreuse LABEL 720 -40 1 "Minstrel 18" ]]
#C [[ LABELANGLE 0 LABELALPHA .75 LABELSIZE 32 COLOR LABEL SpringGreen ]]
#C [[ LABEL 20 35 3 "M0" ]]
#C [[ LABEL 60 35 3 "M0" ]]
#C [[ LABEL 100 35 3 "M0" ]]
#C [[ LABEL 140 35 3 "M0" ]]
#C [[ LABEL 180 35 3 "M0" ]]
#C [[ LABEL 220 35 3 "M0" ]]
#C [[ LABEL 260 35 3 "M0" ]]
#C [[ LABEL 300 35 3 "M0" ]]
#C [[ LABEL 340 35 3 "M0" ]]
#C [[ LABEL 380 35 3 "M0" ]]
#C [[ LABEL 420 35 3 "M0" ]]
#C [[ LABEL 460 35 3 "M0" ]]
#C [[ LABEL 500 35 3 "M0" ]]
#C [[ LABEL 540 35 3 "M0" ]]
#C [[ LABEL 580 35 3 "M0" ]]
#C [[ LABEL 620 35 3 "M0" ]]
#C [[ LABEL 740 35 3 "M0" ]]
#C [[ COLOR LABEL Red LABELSIZE 24 LABELALPHA .5 ]]
#C [[ LABEL 73 84 3.5 "errant\nminstrel" ]]
#C [[ LABEL 206 109 3.5 "errant\nminstrel" ]]
#C [[ LABEL 335 129 3.5 "errant\nminstrel" ]]
#C [[ LABEL 513 84 3.5 "errant\nminstrel" ]]
#C [[ LABEL 646 109 3.5 "errant\nminstrel" ]]
#C [[ LABEL 775 129 3.5 "errant\nminstrel" ]]
#C [[ COLOR LABEL SkyBlue LABELSIZE 24 LABELALPHA .6 ]]
#C [[ LABEL 113 82 3.5 "lightweight\nminstrel" ]]
#C [[ LABEL 275 85 3.5 "lightweight\nminstrel" ]]
#C [[ LABEL 315 85 3.5 "lightweight\nminstrel" ]]
#C [[ LABEL 355 85 3.5 "lightweight\nminstrel" ]]
#C [[ LABEL 395 85 3.5 "lightweight\nminstrel" ]]
#C [[ LABEL 555 85 3.5 "lightweight\nminstrel" ]]
#C [[ LABEL 595 85 3.5 "lightweight\nminstrel" ]]
#C [[ LABEL 755 85 3.5 "lightweight\nminstrel" ]]
#C [[ COLOR LABEL LawnGreen LABELSIZE 24 LABELALPHA .45 ]]
#C [[ LABEL 153 82 3.5 "heavyweight\nminstrel" ]]
#C [[ LABEL 193 82 3.5 "heavyweight\nminstrel" ]]
#C [[ LABEL 233 82 3.5 "heavyweight\nminstrel" ]]
#C [[ LABEL 435 85 3.5 "heavyweight\nminstrel" ]]
#C [[ LABEL 475 85 3.5 "heavyweight\nminstrel" ]]
#C [[ LABEL 635 85 3.5 "heavyweight\nminstrel" ]]
#C [[ COLOR LABEL Gold LABELSIZE 24 LABELALPHA .55 ]]
#C [[ LABEL 285 110 3.5 "ragged\nminstrel" ]]
#C [[ LABEL 325 110 3.5 "ragged\nminstrel" ]]
#C [[ LABEL 365 110 3.5 "ragged\nminstrel" ]]
#C [[ LABEL 405 110 3.5 "ragged\nminstrel" ]]
#C [[ LABEL 565 110 3.5 "ragged\nminstrel" ]]
#C [[ LABEL 605 105 3.5 "ragged\nminstrel" ]]
#C [[ LABEL 765 110 3.5 "ragged\nminstrel" ]]
#C [[ COLOR LABEL Magenta LABELSIZE 20 LABELALPHA .65 ]]
#C [[ LABEL 247 115 3.5 "wandering\nminstrel" ]]
#C [[ LABEL 378 135 3.5 "wandering\nminstrel" ]]
#C [[ LABEL 486 102 3.5 "wandering\nminstrel" ]]
#C [[ LABEL 615 123 3.5 "wandering\nminstrel" ]]
#C [[ COLOR LABEL Silver LABELSIZE 20 LABELALPHA .70 ]]
#C [[ LABEL 411 134 3.5 "featherweight\nminstrel" ]]
#C [[ COLOR LABEL Bisque LABELSIZE 20 LABELALPHA .70 ]]
#C [[ LABEL 445 110 3.5 "pi\nminstrel" ]]
#C [[ LABEL 575 129 3.5 "pi\nminstrel" ]]
#C [[ COLOR LABEL Blue LABELSIZE 20 LABELALPHA .60 ]]
#C [[ LABEL 500 140 3.5 "connecting\nminstrel" ]]
#C [[ LABEL 630 160 3.5 "connecting\nminstrel" ]]
#C [[ COLOR LABEL Violet LABELSIZE 20 LABELALPHA .60 ]]
#C [[ LABEL 520 120 3.5 "fountain\nminstrel" ]]
#C [[ LABEL 650 140 3.5 "fountain\nminstrel" ]]
#C [[ LABEL 780 160 3.5 "fountain\nminstrel" ]]
#C [[ WIDTH 1700 HEIGHT 580 POPUPWIDTH 1700 POPUPHEIGHT 580 ZOOM 2 THUMBSIZE 2 ]]
}}

The complete spaceships are named '''Minstrel 0''' (Sir Robin) through to '''Minstrel 15''' and '''Minstrel 18''', agreeing with order of discovery up to Minstrel 10 and departing slightly thereafter. The [[elementary]] components are given the following names:

* Sir Robin := Minstrel 0
* Errant minstrel := Minstrel 1 - Minstrel 0
* Lightweight minstrel := Minstrel 2 - Minstrel 0
* Heavyweight minstrel := Minstrel 3 - Minstrel 0
* Wandering minstrel := Minstrel 5 - Minstrel 3
* Ragged minstrel := Minstrel 6 - Minstrel 2
* Featherweight minstrel := Minstrel 9 - Minstrel 6
* Pi minstrel := Minstrel 10 - Minstrel 3
* Connecting minstrel := Minstrel 11 - Minstrel 5
* Fountain minstrel := Minstrel 12 - Minstrel 1

Several of these "elementary minstrels" are not technically true tagalongs, because they slightly modify the trailing sparks on the spaceship to which they attach.

===History===

The first tagalong, '''Minstrel 1''', was discovered by [[Adam P. Goucher]] on July 15, {{year|2018}}, after resuming the original [[ikpx]] search.<ref name="post61918" />

[[Dave Greene]] modified [[Martin Grant]]'s Sir Robin eater to act as a Minstrel 1 detector the same day, which removes the errant minstrel to yield the original Sir Robin.<ref name="post61925" />

On July 19, {{year|2018}}, [[Adam P. Goucher]] found a second and third minstrel, dubbed '''Minstrel 2''' and '''Minstrel 3''', that follow Sir Robin more closely. The lightweight and heavyweight minstrels are not true tagalongs because they change the evolution of the Sir Robin itself.<ref name="post62007" />

On July 20, {{year|2018}}, [[Goldtiger997]] built a [[stable]] circuit that can accept any of Minstrel 0 through to Minstrel 3,<ref name="post62052" /> emitting a glider in one of four directions (depending on the input spaceship) along with an unadorned Sir Robin travelling along the original path. When the original input is a Sir Robin, this circuit is a [[Heisenburp]]; otherwise, it is a [[downconverter]]. The circuit was later optimised by including a bend in the [[2c/3 signal]] wire, among other bounding-box reductions.

On Christmas Day in 2018, [[Entity Valkyrie]] discovered that the heavyweight and errant can be composed, yielding '''Minstrel 4'''<ref name="post66748" />. Two days later, Goldtiger997 updated the previous minstrel remover/detector to accept any of the known tagalongs including the composite Minstrel 4.<ref name="post66802" />

On December 31, 2018, [[Adam P. Goucher]] resumed the [[ikpx]] search and another Minstrel 3 tagalong was found, dubbed '''Minstrel 5'''.<ref name="post67054" /> Again, Goldtiger997's minstrel remover/detector was updated to accept the newest spaceship.<ref name="post67162" />

The following month a further tagalong, '''Minstrel 6''', was discovered by the ikpx search program, and was added to existing components to produce two new spaceships, '''Minstrels 7 and 8'''.<ref name="post67995" /> '''Minstrel 9''' followed shortly after, on the 18th January,<ref name="post68168" /> and another "pi minstrel" tagalong was discovered on the 21st of January which created '''Minstrels 10 and 13'''.<ref name="post68354" /> A longer tagalong discovered in early February produced '''Minstrels 11 and 14''' in the same way,<ref name="post69295" /> and also enabled much simpler [[branching spaceship|branching knightships]].<ref name="post69314" /> The following day a tagalong to the errant minstrel was discovered, yielding '''Minstrels 12, 15, and 18'''.<ref name="post69417" /><ref name="post69419" /> Of these high-numbered minstrels, only Minstrel 10 is accepted by Goldtiger997's remover.<ref name="post69467" />

On January 20, 2023, [[Darren Li]] used a modified ikpx and Open Science Grid to discover a surprisingly small tagalong able to connect to Sir Robin, the sprayer, and many other minstrels (including itself) in a wide variety of ways. While it is currently unnamed, proposed names for it include "wild minstrel" and "sticky minstrel".

===Minstrel arithmetic===

Due to increasingly large liberties taken with the initial chronological numbering (beginning with the dicovery of minstrel 13), the relationships between these spaceships can be encapsulated by 'minstrel arithmetic': the observation that integer 'weights' can be assigned to Sir Robin and its indecomposable tagalongs such that the sum of the weights of the components of '''Minstrel n''' is exactly n:

* Sir Robin: 0
* Errant minstrel: 1
* Lightweight minstrel: 2
* Heavyweight minstrel: 3
* Wandering minstrel: 2
* Ragged minstrel: 4
* Featherweight minstrel: 3
* Pi minstrel: 7
* Connecting minstrel: 6
* Fountain minstrel: 11

In particular, we have:

* Minstrel 0 = 0 (Sir Robin)
* Minstrel 1 = 0 + 1 (Sir Robin + errant minstrel)
* Minstrel 2 = 0 + 2 (Sir Robin + lightweight minstrel)
* Minstrel 3 = 0 + 3 (Sir Robin + heavyweight minstrel)
* Minstrel 4 = 0 + 3 + 1 (Sir Robin + heavyweight minstrel + errant minstrel)
* Minstrel 5 = 0 + 3 + 2 (Sir Robin + heavyweight minstrel + wandering minstrel)
* Minstrel 6 = 0 + 2 + 4 (Sir Robin + lightweight minstrel + ragged minstrel)
* Minstrel 7 = 0 + 2 + 4 + 1 (Sir Robin + lightweight minstrel + ragged minstrel + errant minstrel)
* Minstrel 8 = 0 + 2 + 4 + 2 (Sir Robin + lightweight minstrel + ragged minstrel + wandering minstrel)
* Minstrel 9 = 0 + 2 + 4 + 3 (Sir Robin + lightweight minstrel + ragged minstrel + featherweight minstrel)
* Minstrel 10 = 0 + 3 + 7 (Sir Robin + heavyweight minstrel + pi minstrel)
* Minstrel 11 = 0 + 3 + 2 + 6 (Sir Robin + heavyweight minstrel + wandering minstrel + connecting minstrel)
* Minstrel 12 = 0 + 1 + 11 (Sir Robin + errant minstrel + fountain minstrel)
* Minstrel 13 = 0 + 2 + 4 + 7 (Sir Robin + lightweight minstrel + ragged minstrel + pi minstrel)
* Minstrel 14 = 0 + 2 + 4 + 2 + 6 (Sir Robin + lightweight minstrel + ragged minstrel + wandering minstrel + connecting minstrel)
* Minstrel 15 = 0 + 3 + 1 + 11 (Sir Robin + heavyweight minstrel + errant minstrel + fountain minstrel)
* Minstrel 18 = 0 + 2 + 4 + 1 + 11 (Sir Robin + lightweight minstrel + ragged minstrel + errant minstrel + fountain minstrel)

==Other spaceships==

The lightweight minstrel is also capable of supporting both ends of [[knightwave]], as noted by Adam P. Goucher<ref name="post62026" /> and Matthias Merzenich<ref name="post68044" /> respectively. The heavyweight minstrel can support the left end in the same manner.<ref name="post57379" />

{{EmbedViewer
|pname = knightwavesupported
|position = center
|caption = Knightwave supported between Minstrel 9 (upper right), Minstrel 7 (center), and Minstrel 5 (lower left) 
|viewerconfig = #C [[ TRACKLOOP 6 -1/6 -1/3 THUMBSIZE 2 WIDTH 600 HEIGHT 800 ZOOM 4 GPS 6 ]]
#C [[ LABELALPHA .75 LABELANGLE 70 LABELSIZE 32 COLOR LABEL SpringGreen ]]
#C [[ LABEL 75 35 6 "Sir Robin" ]]
#C [[ LABEL 53 68 6 "Two Sir Robins" ]]
#C [[ LABEL 5 115 6 "Sir Robin" ]]
#C [[ LABELANGLE 331 COLOR LABEL Orange ]]
#C [[ LABEL 55 145 6 "knightwave" ]]
#C [[ LABEL 91 104 6 "knightwave" ]]
#C [[ LABELANGLE 0 COLOR LABEL Red ]]
#C [[ LABEL 100 170 6 "errant\nminstrel" ]]
#C [[ COLOR LABEL SkyBlue ]]
#C [[ LABEL 105 85 6 "lightweight\nminstrel" ]]
#C [[ LABEL 75 120 6 "lightweight\nminstrel" ]]
#C [[ COLOR LABEL LawnGreen ]]
#C [[ LABEL 38 175 6 "heavyweight\nminstrel" ]]
#C [[ COLOR LABEL Yellow ]]
#C [[ LABEL 90 145 6 "ragged\nminstrel" ]]
#C [[ LABEL 114 110 6 "ragged\nminstrel" ]]
#C [[ COLOR LABEL Magenta ]]
#C [[ LABEL 46 188 6 "wandering\nminstrel" ]]
#C [[ COLOR LABEL Cyan ]]
#C [[ LABEL 115 125 6 "featherweight\nminstrel" ]]
}}

If direct connections to the left and right sides of Sir Robin spaceships are included, (2,1)c/6 technology now allows [[branching spaceship]]s, since it is possible to make connections in three directions from a single spaceship. The known direct connection between two Sir Robin spaceships makes a slightly steeper angle than a knightwave -- (15, -13) instead of (5, -3). This means that any added branch on the left side (as in the example shown above) runs out of space after six direct connections have been made. However, direct-connection branches on the right eventually allow additional three-way branch points to be connected.<ref name="post69094" /> The "connecting minstrel" enables another type of branching-spaceship connection with much more clearance.<ref name="post69314" />

Thus, until the discovery of the [[sprayer]], every known (2,1)c/6 spaceship was either:

* Minstrel n (for some n between 0 and 15, as well as 18), or
* A sequence of two or more spaceships, each of the above form, with adjacent spaceships joined by one of three types of connections:
# a horizontal segment of [[knightwave]] containing any sufficiently large number of repeating components (where 'sufficiently large' is such that the two knightships do not interact, i.e. 3 units), or
# a direct diagonal connection between two Sir Robin spaceships, changing the position of one cell along the connected edge for a single tick (compare the right edges of the two directly connected Sir Robins at T=0 in the example above), or
# a connection between the tail of '''Minstrel 14''' and the direct-connection point on any '''Minstrel 0 to 15''' (or '''18'''), or
* a branching spaceship consisting of multiple connected sequences as described above.

The leftmost spaceship in a knightwave sequence must contain either a lightweight or heavyweight minstrel, and the remaining spaceships must all contain lightweight minstrels.

==See also==
*[[Sprayer]]

==Notes==
<references group="note" />

==References==
<references>
<ref name="thread3303">{{LinkForumThread
|format = ref
|t = 3303
|accessdate = 2018-03-07
|date = 2018-03-06
|title = Elementary knightship
|author = Adam P. Goucher
}}</ref>
<ref name="post42467">{{LinkForumThread
|format = ref
|t = 2031
|p = 42467
|accessdate = 2018-03-09
|date = 2017-04-08
|title = Re: Spaceship Discussion Thread
|author = Josh Ball
}}</ref>
<ref name="post57456">{{LinkForumThread
|format = ref
|p = 57456
|accessdate = 2018-03-08
|date = 2018-03-07
|title = Re: Elementary knightship
|author = Adam P. Goucher
}}</ref>
<ref name="post58732">{{LinkForumThread
|format = ref
|title = Re: Elementary knightship
|p = 58732
|author = Dave Greene
|date = April 1, 2018
}}</ref>
<ref name="post57499">{{LinkForumThread
|format = ref
|p = 57499
|accessdate = 2018-03-08
|date = 2018-03-08
|title = Re: Elementary knightship
|author = Martin Grant
}}</ref>
<ref name="post61918">{{LinkForumThread
|format = ref
|p = 61918
|accessdate = 2018-07-15
|date = 2018-07-15
|title = Minstrel
|author = Adam P. Goucher
}}</ref>
<ref name="post61925">{{LinkForumThread
|format = ref
|p = 61925
|accessdate = 2018-07-15
|date = 2018-07-15
|title = Re: Minstrel
|author = Dave Greene
}}</ref>
<ref name="post62007">{{LinkForumThread
|format = ref
|p = 62007
|accessdate = 2018-07-19
|date = 2018-07-19
|title = Re: Minstrel
|author = Adam P. Goucher
}}</ref>
<ref name="post66802">{{LinkForumThread
|format = ref
|p = 66802
|accessdate = 2018-12-27
|date = 2018-12-27
|title = Re: Minstrel
|author = Goldtiger997
}}</ref>
<ref name="post67054">{{LinkForumThread
|format = ref
|p = 67054
|accessdate = 2022-01-09
|date = 2019-01-01
|title = Re: Minstrel
|author = Adam P. Goucher
}}</ref>
<ref name="post67162">{{LinkForumThread
|format = ref
|p = 67162
|accessdate = 2022-01-09
|date = 2019-01-03
|title = Re: Minstrel
|author = Goldtiger997
}}</ref>
<ref name="post67995">{{LinkForumThread
|format = ref
|p = 67995
|accessdate = 2022-01-09
|date = 2019-01-16
|title = Re: Minstrel
|author = Adam P. Goucher
}}</ref>
<ref name="post68168">{{LinkForumThread
|format = ref
|p = 68168
|accessdate = 2022-01-09
|date = 2019-01-18
|title = Re: Minstrel
|author = Adam P. Goucher
}}</ref>
<ref name="post68354">{{LinkForumThread
|format = ref
|p = 68354
|accessdate = 2022-01-09
|date = 2019-01-21
|title = Re: Minstrel
|author = alphazelf
}}</ref>
<ref name="post69295">{{LinkForumThread
|format = ref
|p = 69295
|accessdate = 2022-01-09
|date = 2019-02-01
|title = Re: Minstrel
|author = Adam P. Goucher
}}</ref>
<ref name="post69314">{{LinkForumThread
|format = ref
|p = 69314
|accessdate = 2022-01-09
|date = 2019-02-01
|title = Re: Minstrel
|author = Dave Greene
}}</ref>
<ref name="post69417">{{LinkForumThread
|format = ref
|p = 69417
|accessdate = 2022-01-09
|date = 2019-02-02
|title = Re: Minstrel
|author = Adam P. Goucher
}}</ref>
<ref name="post69419">{{LinkForumThread
|format = ref
|p = 69419
|accessdate = 2022-01-09
|date = 2019-02-02
|title = Re: Minstrel
|author = Moosey
}}</ref>
<ref name="post69467">{{LinkForumThread
|format = ref
|p = 69467
|accessdate = 2022-01-09
|date = 2019-02-02
|title = Re: Minstrel
|author = Goldtiger997
}}</ref>
<ref name="post62026">{{LinkForumThread
|format = ref
|p = 62026
|date = July 19, 2018
|title = Re: Minstrel
|author = Adam P. Goucher
}}</ref>
<ref name="post68044">{{LinkForumThread
|format = ref
|title = Re: Minstrel
|p = 68044
|author = Matthias Merzenich
|date = January 16, 2019
}}</ref>
<ref name="post57379">{{LinkForumThread
|format = ref
|p = 57379
|accessdate = 2018-12-27
|date = 2018-07-20
|title = Re: Elementary knightship
|author = PHPBB12345
}}</ref>
<ref name="post66748">{{LinkForumThread
|format = ref
|p = 66748
|accessdate = 2018-12-27
|date = 2018-12-24
|title = Re: Minstrel
|author = Entity Valkyrie
}}</ref>
<ref name="post62052">{{LinkForumThread
|format = ref
|p = 62052
|accessdate = 2018-12-27
|date = 2018-07-20
|title = Re: Minstrel
|author = Goldtiger997
}}</ref>
<ref name="post69094">{{LinkForumThread
|format = ref
|p = 69094
|accessdate = 2019-01-30
|date = 2019-01-30
|title = Re: Minstrel
|author = Dave Greene
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_s.htm#sirrobin}}

===Articles and announcements===
* [https://cp4space.wordpress.com/2018/03/11/a-rather-satisfying-winter/ ''A rather satisfying winter'': cp4space article] describing the events leading to the discovery
* [http://b3s23life.blogspot.co.uk/2018/03/on-6-march-2018-first-member-of-new.html b3s23life article] announcing the discovery itself
* [https://news.ycombinator.com/item?id=16546152 Elementary Knightship found in Conway's Game of Life] on Hacker News
* [https://www.reddit.com/r/cellular_automata/comments/82lj8j/an_elementary_knightship_an_obliquelytraveling/ An elementary knightship has been found in Conway's Game of Life] on Reddit

===Object catalogues===
{{LinkCatagolue|xq6_yyocxukcy6gocs20h0a38bac2qq73uszyjo4w8y0e4mo0vu0o606s6444u08clav0h03g440qq1333333x11zy9ecec2ik032i210sw3f0hy011w70401011033547442zy0emj896he1e1kif6q2gc50ew9qb30dzgo403gg066m32w11z34407q441n6zy311|format=extended}}

===Forum threads===
{{LinkForumThread|f=2|t=3303|title=Elementary knightship}}
{{LinkForumThread|f=2|t=3305|title=Synthesizing the elementary knightship}}
{{LinkForumThread|f=2|t=3313|title=What are the odds that Sir Robin will appear naturally?}}

===Tools===
* [https://gitlab.com/apgoucher/metasat/blob/master/ikpx.py ikpx] on Gitlab

Grandfather problem

2023-01-27T01:13:52Z

Ch91: /* Next levels */

{{Pattern
|name = Grandfather problem
|pname = grandfatherproblemsolved
|type = Problem
|c = 298
|bx = 24
|by = 23
|synthesis = 0
|discoverer = mtve
|discoveryear = 2016
|plaintext = true
|rle = true
|viewerconfig = #C [[ ZOOM 16 WIDTH 500 HEIGHT 500 ]]
}}
The '''grandfather problem''' is the following question, posed by [[John Conway]] in 1972 in [[Lifeline Volume 6]],<ref name="lifelinevol6" /> along with the [[unique father problem]]:

:''Is there a configuration which has a father but no [[grandfather]]?''

Conway offered a $50 cash prize to "the first person to settle the grandfather problem either way". But the problem of a '''grandfatherless''' pattern remained open until May {{year|2016}}, when [[mtve]] presented such a pattern.<ref name="mtve1" /> {{POTY|name=This pattern|year=2016|rank=3|behind=the [[copperhead]] and the [[Caterloopillar]]s}}

==Generation==
The pattern was found with the [http://fmv.jku.at/picosat/ PicoSAT] SAT solver, using an algorithm similar to the one employed by [[Nicolay Beluchenko]] to discover {{OEIS|A196447}}:<ref name="mtve2" />

# Try setting the next cell on and off;
# Skip first level [[Gardens of Eden]];
# Choose the minimum number of grandparents, where "minimum number" is not the exact number but a minimal distance between first and last.

The final configuration has a total of 17920 parents, but no grandparents.

==Verification==
"mtve"'s discovery was confirmed to solve the grandfather problem by [[Matthias Merzenich]] with [[JLS]], using the following steps<ref name="sokwe" />:

# Run a search to find all 1-generation predecessors of mtve's pattern. Copy the cells that had the same setting in all solutions to the pattern.
# Mark all of unset cells with "X", increase the period by 1 and shift the pattern to the future by 1 generation. Set the outer cells to "X" in generation 0 and run another search, which eventually gives "Search finished: 0 solutions found".

==Optimization==
It is possible to reduce the size of this pattern by removing some cells, and also some other patterns with the same property exist<ref name="mtve3" />.

==Next levels==
"A father and grandfather, but no great-grandfather" pattern<ref name="mtve4" />, and a "father, grandfather and great-grandfather, but no great-great-grandfather" pattern<ref name="mtve5" />, have also been constructed by the same method.

On January 6, {{year|2022}}, [[Ilkka Törmä]] and [[Ville Salo]] solved a generalized version of the grandfather problem, proving that for every natural number n, there exists a pattern that has an n-tick predecessor but not an (n+1)-tick predecessor.<ref name="post139854" /> Furthermore, this pattern will fit in a box whose diameter is equal to o(sqrt(log(n))).

==References==
<references>
<ref name="lifelinevol6">{{CiteLifeline
|vol = 6
|pages = p. 1
}}</Ref>
<ref name="mtve1">{{LinkForumThread
|format = ref
|title = Re: Thread for your unsure discoveries
|p = 30646
|author = mtve
|date = May 5, 2016
}}</ref>
<ref name="mtve2">{{LinkForumThread
|format = ref
|title = Re: Thread for your unsure discoveries
|p = 30667
|author = mtve
|date = May 6, 2016
}}</ref>
<ref name="sokwe">{{LinkForumThread
|format = ref
|title = Re: Thread for your unsure discoveries
|p = 30694
|author = Matthias Merzenich
|date = May 6, 2016
}}</ref>
<ref name="mtve3">{{cite web
|url = http://frox25.no-ip.org/~mtve/wiki/GardenOfEden2G.html
|author = mtve
|title = Garden Of Eden 2G
|date = June 2016
|accessdate = July 8, 2016
}}</ref>
<ref name="mtve4">{{cite web
|url = http://frox25.no-ip.org/~mtve/wiki/GardenOfEden3G.html
|author = mtve
|title = Garden Of Eden 3G
|date = June 2016
|accessdate = July 8, 2016
}}</ref>
<ref name="mtve5">{{cite web
|url = http://frox25.no-ip.org/~mtve/wiki/GardenOfEden4G.html
|author = mtve
|title = Garden Of Eden 4G
|date = December 12, 2016
|accessdate = December 14, 2016
}}</ref>
<ref name="post139854">{{LinkForumThread
|format = ref
|title = Re: Unproven conjectures
|p = 139854
|author = Ilkka Törmä
|date = January 6, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|filename=lex_g.htm#grandfatherless|patternname=Grandfatherless}}

[[Category:Patterns discovered by pseudonymous users]]

Grandfather problem

2023-01-27T01:12:59Z

Ch91: /* Next levels */

{{Pattern
|name = Grandfather problem
|pname = grandfatherproblemsolved
|type = Problem
|c = 298
|bx = 24
|by = 23
|synthesis = 0
|discoverer = mtve
|discoveryear = 2016
|plaintext = true
|rle = true
|viewerconfig = #C [[ ZOOM 16 WIDTH 500 HEIGHT 500 ]]
}}
The '''grandfather problem''' is the following question, posed by [[John Conway]] in 1972 in [[Lifeline Volume 6]],<ref name="lifelinevol6" /> along with the [[unique father problem]]:

:''Is there a configuration which has a father but no [[grandfather]]?''

Conway offered a $50 cash prize to "the first person to settle the grandfather problem either way". But the problem of a '''grandfatherless''' pattern remained open until May {{year|2016}}, when [[mtve]] presented such a pattern.<ref name="mtve1" /> {{POTY|name=This pattern|year=2016|rank=3|behind=the [[copperhead]] and the [[Caterloopillar]]s}}

==Generation==
The pattern was found with the [http://fmv.jku.at/picosat/ PicoSAT] SAT solver, using an algorithm similar to the one employed by [[Nicolay Beluchenko]] to discover {{OEIS|A196447}}:<ref name="mtve2" />

# Try setting the next cell on and off;
# Skip first level [[Gardens of Eden]];
# Choose the minimum number of grandparents, where "minimum number" is not the exact number but a minimal distance between first and last.

The final configuration has a total of 17920 parents, but no grandparents.

==Verification==
"mtve"'s discovery was confirmed to solve the grandfather problem by [[Matthias Merzenich]] with [[JLS]], using the following steps<ref name="sokwe" />:

# Run a search to find all 1-generation predecessors of mtve's pattern. Copy the cells that had the same setting in all solutions to the pattern.
# Mark all of unset cells with "X", increase the period by 1 and shift the pattern to the future by 1 generation. Set the outer cells to "X" in generation 0 and run another search, which eventually gives "Search finished: 0 solutions found".

==Optimization==
It is possible to reduce the size of this pattern by removing some cells, and also some other patterns with the same property exist<ref name="mtve3" />.

==Next levels==
"A father and grandfather, but no great-grandfather" pattern<ref name="mtve4" />, and a "father, grandfather and great-grandfather, but no great-great-grandfather" pattern<ref name="mtve5" />, have also been constructed by the same method.

On January 6, {{year|2022}}, [[Ilkka Törmä]] and [[Ville Salo]] solved a generalized version of the grandfather problem, proving that for every natural number n, there exists a pattern that has an n-tick predecessor but not an (n+1)-tick predecessor.<ref name="post139854" /> Furthermore, this pattern will have a diameter that fits in a box of size o(sqrt(log(n))).

==References==
<references>
<ref name="lifelinevol6">{{CiteLifeline
|vol = 6
|pages = p. 1
}}</Ref>
<ref name="mtve1">{{LinkForumThread
|format = ref
|title = Re: Thread for your unsure discoveries
|p = 30646
|author = mtve
|date = May 5, 2016
}}</ref>
<ref name="mtve2">{{LinkForumThread
|format = ref
|title = Re: Thread for your unsure discoveries
|p = 30667
|author = mtve
|date = May 6, 2016
}}</ref>
<ref name="sokwe">{{LinkForumThread
|format = ref
|title = Re: Thread for your unsure discoveries
|p = 30694
|author = Matthias Merzenich
|date = May 6, 2016
}}</ref>
<ref name="mtve3">{{cite web
|url = http://frox25.no-ip.org/~mtve/wiki/GardenOfEden2G.html
|author = mtve
|title = Garden Of Eden 2G
|date = June 2016
|accessdate = July 8, 2016
}}</ref>
<ref name="mtve4">{{cite web
|url = http://frox25.no-ip.org/~mtve/wiki/GardenOfEden3G.html
|author = mtve
|title = Garden Of Eden 3G
|date = June 2016
|accessdate = July 8, 2016
}}</ref>
<ref name="mtve5">{{cite web
|url = http://frox25.no-ip.org/~mtve/wiki/GardenOfEden4G.html
|author = mtve
|title = Garden Of Eden 4G
|date = December 12, 2016
|accessdate = December 14, 2016
}}</ref>
<ref name="post139854">{{LinkForumThread
|format = ref
|title = Re: Unproven conjectures
|p = 139854
|author = Ilkka Törmä
|date = January 6, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|filename=lex_g.htm#grandfatherless|patternname=Grandfatherless}}

[[Category:Patterns discovered by pseudonymous users]]

Fully universal Turing machine

2023-01-20T19:06:40Z

Ch91: This is now redundant.

{{Pattern
|name = Fully universal Turing machine
|pname = fullyuniversalturingmachine
|discoverer = Paul Rendell
|discoveryear = 2011
|zip = true
}}
The '''fully universal Turing machine''' is an extension of [[Paul Rendell]]'s [[universal Turing machine]]. Its tape is perfectly diagonal (instead of oblique), and the memory cells of the tape are continuously produced by two complex [[rake]] convoys. Rendell experimented with three different variants of this mechanism:

* A [[c/12 diagonal]] stack constructor using [[Cordership]]-based rakes (very large);
* A [[c/5 diagonal]] stack constructor using [[Matthias Merzenich]]'s [[c/5 diagonal rake]]s;
* An expanding stack constructor comprising two perpendicular [[c/2 orthogonal]] convoys of rakes (the final version).

{{POTY|name=The fully universal Turing machine|year=2011|rank=1|tie=the [[Lobster (spaceship)|Lobster]]}}

{|class="wikitable" style="width:425px;"
|[[File:fullyuniversalturingmachine1.png]]{{br}}The initial UTM state. The dotted line going NW is the program for the stack.<ref name="utm1" />
|-
|[[File:fullyuniversalturingmachine2.png]]{{br}}After 149 million generations. The line running SE in the middle is the trace of each address of the finite state machine and is very sparse. The distance this line has moved from the stack is related to the time that [[Golly]] was running after the UTM stopped. The length of this line is related to the time the UTM was running.<ref name="utm1" />
|}

==See also==
*[[Turing machine]]
*[[Universal computer]]
*[[Universal constructor]]

==References==
<references>
<ref name="utm1">[http://rendell-attic.org/gol/fullutm/index.htm A Fully Universal Turing Machine] - Official site by Paul Rendell</ref>
</references>

Reverse caber-tosser

2023-01-14T15:36:38Z

Ch91: /* Applications */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 15-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations, and it will include a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements. That being said, synthesizing complex patterns requires the constituent GPSEs to be so far apart that the RCT's bounding box becomes too large for Golly to run without crashing, so its applications will likely remain theoretical until a new version of Golly capable of handling it can be developed.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==Future==
At the time of RCT17 and RCT16, MathAndCode believed that the absolute smallest possible RCT would require 13 gliders by using one fewer switch engine.<ref name="post104600" /> The subsequent reduction from RCT16 to RCT15 suggests that MathAndCode's hypothetical 13-glider design ''might'' be reduced to 12 gliders in the same way.<ref name="message1046450382357938306" /> However, it is far from guaranteed that the exact same reduction method could be carried over to a three-switch-engine design.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{cite web|url=https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/|title=Building arbitrary Life patterns in 15 gliders|author=Brett Berger|date=November 16, 2022}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-fifteen-gliders-can.html|title=In Conway's Life, Fifteen Gliders Can Build Anything* !|author=Dave Greene|date=November 18, 2022}}

* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
<ref name="post104600">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104600
|author = MathAndCode
|date = September 20, 2020
}}</ref>
<ref name="message1046450382357938306">{{CiteDiscord
|author = Dave Greene
|date = November 27, 2022
|channel = general-discussion
|id = 1046450382357938306
}}</ref>
<ref name
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2023-01-14T15:36:03Z

Ch91: /* Applications */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 15-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations, and it will include a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements. That being said, synthesizing complex patterns require the constituent GPSEs to be so far apart that the bounding box becomes too large for Golly to run without crashing, so its applications will likely remain theoretical until a new version of Golly capable of handling it can be developed.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==Future==
At the time of RCT17 and RCT16, MathAndCode believed that the absolute smallest possible RCT would require 13 gliders by using one fewer switch engine.<ref name="post104600" /> The subsequent reduction from RCT16 to RCT15 suggests that MathAndCode's hypothetical 13-glider design ''might'' be reduced to 12 gliders in the same way.<ref name="message1046450382357938306" /> However, it is far from guaranteed that the exact same reduction method could be carried over to a three-switch-engine design.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{cite web|url=https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/|title=Building arbitrary Life patterns in 15 gliders|author=Brett Berger|date=November 16, 2022}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-fifteen-gliders-can.html|title=In Conway's Life, Fifteen Gliders Can Build Anything* !|author=Dave Greene|date=November 18, 2022}}

* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
<ref name="post104600">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104600
|author = MathAndCode
|date = September 20, 2020
}}</ref>
<ref name="message1046450382357938306">{{CiteDiscord
|author = Dave Greene
|date = November 27, 2022
|channel = general-discussion
|id = 1046450382357938306
}}</ref>
<ref name
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2023-01-14T15:20:06Z

Ch91: /* Applications */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 15-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations, and it will include a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements. That being said, the current version has a bounding box that is far too large for Golly to run without crashing so such applications will have to remain theoretical unless a new emulator is developed to handle them.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==Future==
At the time of RCT17 and RCT16, MathAndCode believed that the absolute smallest possible RCT would require 13 gliders by using one fewer switch engine.<ref name="post104600" /> The subsequent reduction from RCT16 to RCT15 suggests that MathAndCode's hypothetical 13-glider design ''might'' be reduced to 12 gliders in the same way.<ref name="message1046450382357938306" /> However, it is far from guaranteed that the exact same reduction method could be carried over to a three-switch-engine design.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{cite web|url=https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/|title=Building arbitrary Life patterns in 15 gliders|author=Brett Berger|date=November 16, 2022}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-fifteen-gliders-can.html|title=In Conway's Life, Fifteen Gliders Can Build Anything* !|author=Dave Greene|date=November 18, 2022}}

* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
<ref name="post104600">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104600
|author = MathAndCode
|date = September 20, 2020
}}</ref>
<ref name="message1046450382357938306">{{CiteDiscord
|author = Dave Greene
|date = November 27, 2022
|channel = general-discussion
|id = 1046450382357938306
}}</ref>
<ref name
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Max

2023-01-09T03:41:22Z

Ch91:

{{Pattern
|name = Max
|pname = max
|type = Spacefiller
|c = 187
|bx = 27
|by = 27
|discoverer = Tim Coe
|discoveryear = 1995
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-c/S23
|isorulemax = B34q5k6e7e8/S234eqt5ack6cei7e8
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
}}
'''Max''' is a [[spacefiller]] that was found by [[Tim Coe]]<ref>{{LinkCallahan|patterns/sf/sfiller.html|patternname=Coe's improvements on the spacefiller}}</ref> in October {{year|1995}} that fills the plane with [[zebra stripes]]. In terms of its 187 [[cell]]s, it was formerly tied with [[spacefiller 2]] as the smallest known spacefiller, and in terms of its {{times|27|27}} [[bounding box]] it was the outright smallest for many years.<ref>Spacefiller.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>

In February {{year|2020}}, [[Alex Greason]] and [[Adam P. Goucher]] found {{times|26|26}} and {{times|25|25}} [[predecessor]]s to Max that improved on the bounding box at the cost of increased [[population]].<ref name="message678458385414488064" /><ref name="message678530168649678850" /> In April, [[Mateusz Naściszewski]] found a {{times|25|25}} predecessor with a population of only 215,<ref name="message700361705988816907" /> as well as a Max variant with a {{times|27|27}} bounding box but a population of only 183 cells.<ref name="message700583344085139496" /> In November {{year|2021}}, [[Rocknlol]] found several new patterns with [[LogicLifeSearch]] which separately break the records for smallest population (151) and bounding box ({{times|23|23}}) of known Max predecessors.<ref name="post137788" /> In December 2022, iNoMed constructed a 127-cell {{times|27|23}} variant of Rocknlol's 151-cell pattern<ref name="post155354" />,l; a few days later Rocknlol found a 134-cell {{times|21|21}} variation as well as a 110-cell {{times|27|23}} variation. Both of these records were reduced further still to a 107-cell predecessor and a {{times|21|19}} predecessor.

{|style="margin:auto;width:300px;"
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = maxpredecessor25x25
|caption = A smaller but higher-population grandparent of the Max spacefiller, by [[Mateusz Naściszewski]]
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max183
|caption = 183-cell Max variant, by [[Mateusz Naściszewski]]
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max151
|caption = 151-cell {{times|27|23}} predecessor, by [[Rocknlol]]
|position = center
}}
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max155
|caption = 155-cell {{times|25|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max161
|caption = 161-cell {{times|25|21}} predecessor, by Rocknlol
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max189
|caption = 189-cell {{times|23|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max127
|caption = 127-cell {{times|27|23}} spacefiller, by iNoMed
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max110
|caption = 110-cell {{times|27|23}} spacefiller, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max134
|caption = 134-cell {{times|21|21}} spacefiller, by Rocknlol
|position = center
}}
|}

Alternatively, the term '''Max''' may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{CiteLexicon|file=lex_m.htm#max|name=Max|accessdate=May 24, 2009}}</ref>

==Image gallery==
{|
|-
|[[Image:Max_gen50.png|framed|left|Max at [[generation]] 50]]
|}

==See also==
*[[Halfmax]]
*[[Quartermax]]
*[[Spacefiller 1]]

==References==
<references>
<ref name="message678458385414488064">{{CiteDiscord
|author = Alex Greason
|date = February 15, 2020
|channel = cgol
|id = 678458385414488064
}}</ref>
<ref name="message678530168649678850">{{CiteDiscord
|author = Adam P. Goucher
|date = February 16, 2020
|channel = cgol
|id = 678530168649678850
}}</ref>
<ref name="message700361705988816907">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 16, 2020
|channel = cgol
|id = 700361705988816907
}}</ref>
<ref name="message700583344085139496">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 17, 2020
|channel = cgol
|id = 700583344085139496
}}</ref>
<ref name="post137788">{{LinkForumThread
|format = ref
|title = Small Spacefillers
|p = 137788
|author = Rocknlol
|date = November 17, 2021
}}</ref>
<ref name="post155354">{{LinkForumThread
|format = ref
|title = Re: Small Spacefillers
|p = 155354
|author = iNoMed
|date = December 29, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_s.htm#spacefiller}}

{{Symmetry|180degree}}
[[Category:Infinite growth]]
[[Category:Breeders]]

__NOTOC__

Max

2023-01-09T03:40:36Z

Ch91:

{{Pattern
|name = Max
|pname = max
|type = Spacefiller
|c = 187
|bx = 27
|by = 27
|discoverer = Tim Coe
|discoveryear = 1995
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-c/S23
|isorulemax = B34q5k6e7e8/S234eqt5ack6cei7e8
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
}}
'''Max''' is a [[spacefiller]] that was found by [[Tim Coe]]<ref>{{LinkCallahan|patterns/sf/sfiller.html|patternname=Coe's improvements on the spacefiller}}</ref> in October {{year|1995}} that fills the plane with [[zebra stripes]]. In terms of its 187 [[cell]]s, it was formerly tied with [[spacefiller 2]] as the smallest known spacefiller, and in terms of its {{times|27|27}} [[bounding box]] it was the outright smallest for many years.<ref>Spacefiller.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>

In February {{year|2020}}, [[Alex Greason]] and [[Adam P. Goucher]] found {{times|26|26}} and {{times|25|25}} [[predecessor]]s to Max that improved on the bounding box at the cost of increased [[population]].<ref name="message678458385414488064" /><ref name="message678530168649678850" /> In April, [[Mateusz Naściszewski]] found a {{times|25|25}} predecessor with a population of only 215,<ref name="message700361705988816907" /> as well as a Max variant with a {{times|27|27}} bounding box but a population of only 183 cells.<ref name="message700583344085139496" /> In November {{year|2021}}, [[Rocknlol]] found several new patterns with [[LogicLifeSearch]] which separately break the records for smallest population (151) and bounding box ({{times|23|23}}) of known Max predecessors.<ref name="post137788" /> In December 2022, iNoMed constructed a 127-cell {{times|27|23}} variant of Rocknlol's 151-cell pattern<ref name="post155354" />,l; a few days later Rocknlol found a 134-cell {{times|21|21}} variation as well as a 110-cell {{times|27|23}} variation. Both of these were reduced further still to a 107-cell predecessor and a {{times|21|19}} predecessor.

{|style="margin:auto;width:300px;"
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = maxpredecessor25x25
|caption = A smaller but higher-population grandparent of the Max spacefiller, by [[Mateusz Naściszewski]]
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max183
|caption = 183-cell Max variant, by [[Mateusz Naściszewski]]
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max151
|caption = 151-cell {{times|27|23}} predecessor, by [[Rocknlol]]
|position = center
}}
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max155
|caption = 155-cell {{times|25|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max161
|caption = 161-cell {{times|25|21}} predecessor, by Rocknlol
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max189
|caption = 189-cell {{times|23|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max127
|caption = 127-cell {{times|27|23}} spacefiller, by iNoMed
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max110
|caption = 110-cell {{times|27|23}} spacefiller, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max134
|caption = 134-cell {{times|21|21}} spacefiller, by Rocknlol
|position = center
}}
|}

Alternatively, the term '''Max''' may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{CiteLexicon|file=lex_m.htm#max|name=Max|accessdate=May 24, 2009}}</ref>

==Image gallery==
{|
|-
|[[Image:Max_gen50.png|framed|left|Max at [[generation]] 50]]
|}

==See also==
*[[Halfmax]]
*[[Quartermax]]
*[[Spacefiller 1]]

==References==
<references>
<ref name="message678458385414488064">{{CiteDiscord
|author = Alex Greason
|date = February 15, 2020
|channel = cgol
|id = 678458385414488064
}}</ref>
<ref name="message678530168649678850">{{CiteDiscord
|author = Adam P. Goucher
|date = February 16, 2020
|channel = cgol
|id = 678530168649678850
}}</ref>
<ref name="message700361705988816907">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 16, 2020
|channel = cgol
|id = 700361705988816907
}}</ref>
<ref name="message700583344085139496">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 17, 2020
|channel = cgol
|id = 700583344085139496
}}</ref>
<ref name="post137788">{{LinkForumThread
|format = ref
|title = Small Spacefillers
|p = 137788
|author = Rocknlol
|date = November 17, 2021
}}</ref>
<ref name="post155354">{{LinkForumThread
|format = ref
|title = Re: Small Spacefillers
|p = 155354
|author = iNoMed
|date = December 29, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_s.htm#spacefiller}}

{{Symmetry|180degree}}
[[Category:Infinite growth]]
[[Category:Breeders]]

__NOTOC__

Max

2023-01-09T03:39:32Z

Ch91:

{{Pattern
|name = Max
|pname = max
|type = Spacefiller
|c = 187
|bx = 27
|by = 27
|discoverer = Tim Coe
|discoveryear = 1995
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-c/S23
|isorulemax = B34q5k6e7e8/S234eqt5ack6cei7e8
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
}}
'''Max''' is a [[spacefiller]] that was found by [[Tim Coe]]<ref>{{LinkCallahan|patterns/sf/sfiller.html|patternname=Coe's improvements on the spacefiller}}</ref> in October {{year|1995}} that fills the plane with [[zebra stripes]]. In terms of its 187 [[cell]]s, it was formerly tied with [[spacefiller 2]] as the smallest known spacefiller, and in terms of its {{times|27|27}} [[bounding box]] it was the outright smallest for many years.<ref>Spacefiller.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>

In February {{year|2020}}, [[Alex Greason]] and [[Adam P. Goucher]] found {{times|26|26}} and {{times|25|25}} [[predecessor]]s to Max that improved on the bounding box at the cost of increased [[population]].<ref name="message678458385414488064" /><ref name="message678530168649678850" /> In April, [[Mateusz Naściszewski]] found a {{times|25|25}} predecessor with a population of only 215,<ref name="message700361705988816907" /> as well as a Max variant with a {{times|27|27}} bounding box but a population of only 183 cells.<ref name="message700583344085139496" /> In November {{year|2021}}, [[Rocknlol]] found several new patterns with [[LogicLifeSearch]] which separately break the records for smallest population (151) and bounding box ({{times|23|23}}) of known Max predecessors.<ref name="post137788" /> In December 2022, iNoMed constructed a 127-cell {{times|27|23}} variant of Rocknlol's 151-cell pattern<ref name="post155354" />,l; a few days later Rocknlol found a 134-cell {{times|21|21}} variation as well as a 110-cell {{times|27|23}} variation. Both of these were reduced further still to a 107-cell predecessor and a {{times|21|21}} predecessor.

{|style="margin:auto;width:300px;"
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = maxpredecessor25x25
|caption = A smaller but higher-population grandparent of the Max spacefiller, by [[Mateusz Naściszewski]]
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max183
|caption = 183-cell Max variant, by [[Mateusz Naściszewski]]
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max151
|caption = 151-cell {{times|27|23}} predecessor, by [[Rocknlol]]
|position = center
}}
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max155
|caption = 155-cell {{times|25|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max161
|caption = 161-cell {{times|25|21}} predecessor, by Rocknlol
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max189
|caption = 189-cell {{times|23|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max127
|caption = 127-cell {{times|27|23}} spacefiller, by iNoMed
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max110
|caption = 110-cell {{times|27|23}} spacefiller, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max134
|caption = 134-cell {{times|21|21}} spacefiller, by Rocknlol
|position = center
}}
|}

Alternatively, the term '''Max''' may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{CiteLexicon|file=lex_m.htm#max|name=Max|accessdate=May 24, 2009}}</ref>

==Image gallery==
{|
|-
|[[Image:Max_gen50.png|framed|left|Max at [[generation]] 50]]
|}

==See also==
*[[Halfmax]]
*[[Quartermax]]
*[[Spacefiller 1]]

==References==
<references>
<ref name="message678458385414488064">{{CiteDiscord
|author = Alex Greason
|date = February 15, 2020
|channel = cgol
|id = 678458385414488064
}}</ref>
<ref name="message678530168649678850">{{CiteDiscord
|author = Adam P. Goucher
|date = February 16, 2020
|channel = cgol
|id = 678530168649678850
}}</ref>
<ref name="message700361705988816907">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 16, 2020
|channel = cgol
|id = 700361705988816907
}}</ref>
<ref name="message700583344085139496">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 17, 2020
|channel = cgol
|id = 700583344085139496
}}</ref>
<ref name="post137788">{{LinkForumThread
|format = ref
|title = Small Spacefillers
|p = 137788
|author = Rocknlol
|date = November 17, 2021
}}</ref>
<ref name="post155354">{{LinkForumThread
|format = ref
|title = Re: Small Spacefillers
|p = 155354
|author = iNoMed
|date = December 29, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_s.htm#spacefiller}}

{{Symmetry|180degree}}
[[Category:Infinite growth]]
[[Category:Breeders]]

__NOTOC__

Max

2023-01-06T17:02:14Z

Ch91:

{{Pattern
|name = Max
|pname = max
|type = Spacefiller
|c = 187
|bx = 27
|by = 27
|discoverer = Tim Coe
|discoveryear = 1995
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-c/S23
|isorulemax = B34q5k6e7e8/S234eqt5ack6cei7e8
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
}}
'''Max''' is a [[spacefiller]] that was found by [[Tim Coe]]<ref>{{LinkCallahan|patterns/sf/sfiller.html|patternname=Coe's improvements on the spacefiller}}</ref> in October {{year|1995}} that fills the plane with [[zebra stripes]]. In terms of its 187 [[cell]]s, it was formerly tied with [[spacefiller 2]] as the smallest known spacefiller, and in terms of its {{times|27|27}} [[bounding box]] it was the outright smallest for many years.<ref>Spacefiller.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>

In February {{year|2020}}, [[Alex Greason]] and [[Adam P. Goucher]] found {{times|26|26}} and {{times|25|25}} [[predecessor]]s to Max that improved on the bounding box at the cost of increased [[population]].<ref name="message678458385414488064" /><ref name="message678530168649678850" /> In April, [[Mateusz Naściszewski]] found a {{times|25|25}} predecessor with a population of only 215,<ref name="message700361705988816907" /> as well as a Max variant with a {{times|27|27}} bounding box but a population of only 183 cells.<ref name="message700583344085139496" /> In November {{year|2021}}, [[Rocknlol]] found several new patterns with [[LogicLifeSearch]] which separately break the records for smallest population (151) and bounding box ({{times|23|23}}) of known Max predecessors.<ref name="post137788" /> In December 2022, iNoMed constructed a 127-cell {{times|27|23}} variant of Rocknlol's 151-cell pattern<ref name="post155354" />,l; a few days later Rocknlol found a 134-cell {{times|21|21}} variation as well as a 110-cell {{times|27|23}} variation.

{|style="margin:auto;width:300px;"
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = maxpredecessor25x25
|caption = A smaller but higher-population grandparent of the Max spacefiller, by [[Mateusz Naściszewski]]
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max183
|caption = 183-cell Max variant, by [[Mateusz Naściszewski]]
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max151
|caption = 151-cell {{times|27|23}} predecessor, by [[Rocknlol]]
|position = center
}}
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max155
|caption = 155-cell {{times|25|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max161
|caption = 161-cell {{times|25|21}} predecessor, by Rocknlol
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max189
|caption = 189-cell {{times|23|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max127
|caption = 127-cell {{times|27|23}} spacefiller, by iNoMed
|position = center
}}
|}

Alternatively, the term '''Max''' may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{CiteLexicon|file=lex_m.htm#max|name=Max|accessdate=May 24, 2009}}</ref>

==Image gallery==
{|
|-
|[[Image:Max_gen50.png|framed|left|Max at [[generation]] 50]]
|}

==See also==
*[[Halfmax]]
*[[Quartermax]]
*[[Spacefiller 1]]

==References==
<references>
<ref name="message678458385414488064">{{CiteDiscord
|author = Alex Greason
|date = February 15, 2020
|channel = cgol
|id = 678458385414488064
}}</ref>
<ref name="message678530168649678850">{{CiteDiscord
|author = Adam P. Goucher
|date = February 16, 2020
|channel = cgol
|id = 678530168649678850
}}</ref>
<ref name="message700361705988816907">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 16, 2020
|channel = cgol
|id = 700361705988816907
}}</ref>
<ref name="message700583344085139496">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 17, 2020
|channel = cgol
|id = 700583344085139496
}}</ref>
<ref name="post137788">{{LinkForumThread
|format = ref
|title = Small Spacefillers
|p = 137788
|author = Rocknlol
|date = November 17, 2021
}}</ref>
<ref name="post155354">{{LinkForumThread
|format = ref
|title = Re: Small Spacefillers
|p = 155354
|author = iNoMed
|date = December 29, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_s.htm#spacefiller}}

{{Symmetry|180degree}}
[[Category:Infinite growth]]
[[Category:Breeders]]

__NOTOC__

Max

2023-01-06T17:01:41Z

Ch91:

{{Pattern
|name = Max
|pname = max
|type = Spacefiller
|c = 187
|bx = 27
|by = 27
|discoverer = Tim Coe
|discoveryear = 1995
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-c/S23
|isorulemax = B34q5k6e7e8/S234eqt5ack6cei7e8
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
}}
'''Max''' is a [[spacefiller]] that was found by [[Tim Coe]]<ref>{{LinkCallahan|patterns/sf/sfiller.html|patternname=Coe's improvements on the spacefiller}}</ref> in October {{year|1995}} that fills the plane with [[zebra stripes]]. In terms of its 187 [[cell]]s, it was formerly tied with [[spacefiller 2]] as the smallest known spacefiller, and in terms of its {{times|27|27}} [[bounding box]] it was the outright smallest for many years.<ref>Spacefiller.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>

In February {{year|2020}}, [[Alex Greason]] and [[Adam P. Goucher]] found {{times|26|26}} and {{times|25|25}} [[predecessor]]s to Max that improved on the bounding box at the cost of increased [[population]].<ref name="message678458385414488064" /><ref name="message678530168649678850" /> In April, [[Mateusz Naściszewski]] found a {{times|25|25}} predecessor with a population of only 215,<ref name="message700361705988816907" /> as well as a Max variant with a {{times|27|27}} bounding box but a population of only 183 cells.<ref name="message700583344085139496" /> In November {{year|2021}}, [[Rocknlol]] found several new patterns with [[LogicLifeSearch]] which separately break the records for smallest population (151) and bounding box ({{times|23|23}}) of known Max predecessors.<ref name="post137788" /> In December 2022, iNoMed constructed a 127-cell {{times|27|23}} variant of Rocknlol's 151-cell pattern<ref name="post155354" />,l; a few days later Rocknlol found a 134-cell {{times|21|21}} variation as well as a 110-cell {{27|23}} variation.

{|style="margin:auto;width:300px;"
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = maxpredecessor25x25
|caption = A smaller but higher-population grandparent of the Max spacefiller, by [[Mateusz Naściszewski]]
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max183
|caption = 183-cell Max variant, by [[Mateusz Naściszewski]]
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max151
|caption = 151-cell {{times|27|23}} predecessor, by [[Rocknlol]]
|position = center
}}
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max155
|caption = 155-cell {{times|25|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max161
|caption = 161-cell {{times|25|21}} predecessor, by Rocknlol
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max189
|caption = 189-cell {{times|23|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max127
|caption = 127-cell {{times|27|23}} spacefiller, by iNoMed
|position = center
}}
|}

Alternatively, the term '''Max''' may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{CiteLexicon|file=lex_m.htm#max|name=Max|accessdate=May 24, 2009}}</ref>

==Image gallery==
{|
|-
|[[Image:Max_gen50.png|framed|left|Max at [[generation]] 50]]
|}

==See also==
*[[Halfmax]]
*[[Quartermax]]
*[[Spacefiller 1]]

==References==
<references>
<ref name="message678458385414488064">{{CiteDiscord
|author = Alex Greason
|date = February 15, 2020
|channel = cgol
|id = 678458385414488064
}}</ref>
<ref name="message678530168649678850">{{CiteDiscord
|author = Adam P. Goucher
|date = February 16, 2020
|channel = cgol
|id = 678530168649678850
}}</ref>
<ref name="message700361705988816907">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 16, 2020
|channel = cgol
|id = 700361705988816907
}}</ref>
<ref name="message700583344085139496">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 17, 2020
|channel = cgol
|id = 700583344085139496
}}</ref>
<ref name="post137788">{{LinkForumThread
|format = ref
|title = Small Spacefillers
|p = 137788
|author = Rocknlol
|date = November 17, 2021
}}</ref>
<ref name="post155354">{{LinkForumThread
|format = ref
|title = Re: Small Spacefillers
|p = 155354
|author = iNoMed
|date = December 29, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_s.htm#spacefiller}}

{{Symmetry|180degree}}
[[Category:Infinite growth]]
[[Category:Breeders]]

__NOTOC__

Max

2023-01-06T16:58:20Z

Ch91:

{{Pattern
|name = Max
|pname = max
|type = Spacefiller
|c = 187
|bx = 27
|by = 27
|discoverer = Tim Coe
|discoveryear = 1995
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-c/S23
|isorulemax = B34q5k6e7e8/S234eqt5ack6cei7e8
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
}}
'''Max''' is a [[spacefiller]] that was found by [[Tim Coe]]<ref>{{LinkCallahan|patterns/sf/sfiller.html|patternname=Coe's improvements on the spacefiller}}</ref> in October {{year|1995}} that fills the plane with [[zebra stripes]]. In terms of its 187 [[cell]]s, it was formerly tied with [[spacefiller 2]] as the smallest known spacefiller, and in terms of its {{times|27|27}} [[bounding box]] it was the outright smallest for many years.<ref>Spacefiller.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>

In February {{year|2020}}, [[Alex Greason]] and [[Adam P. Goucher]] found {{times|26|26}} and {{times|25|25}} [[predecessor]]s to Max that improved on the bounding box at the cost of increased [[population]].<ref name="message678458385414488064" /><ref name="message678530168649678850" /> In April, [[Mateusz Naściszewski]] found a {{times|25|25}} predecessor with a population of only 215,<ref name="message700361705988816907" /> as well as a Max variant with a {{times|27|27}} bounding box but a population of only 183 cells.<ref name="message700583344085139496" /> In November {{year|2021}}, [[Rocknlol]] found several new patterns with [[LogicLifeSearch]] which separately break the records for smallest population (151) and bounding box ({{times|23|23}}) of known Max predecessors.<ref name="post137788" /> In December 2022, iNoMed constructed a 127-cell {{times|27|23}} variant of Rocknlol's 151-cell pattern<ref name="post155354" />, which Rocknlol further reduced to a 110- cell predecessor.

{|style="margin:auto;width:300px;"
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = maxpredecessor25x25
|caption = A smaller but higher-population grandparent of the Max spacefiller, by [[Mateusz Naściszewski]]
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max183
|caption = 183-cell Max variant, by [[Mateusz Naściszewski]]
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max151
|caption = 151-cell {{times|27|23}} predecessor, by [[Rocknlol]]
|position = center
}}
| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max155
|caption = 155-cell {{times|25|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max161
|caption = 161-cell {{times|25|21}} predecessor, by Rocknlol
|position = center
}}
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max189
|caption = 189-cell {{times|23|23}} predecessor, by Rocknlol
|position = center
}}
|-
|| {{EmbedViewer
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|pname = max127
|caption = 127-cell {{times|27|23}} spacefiller, by iNoMed
|position = center
}}
|}

Alternatively, the term '''Max''' may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{CiteLexicon|file=lex_m.htm#max|name=Max|accessdate=May 24, 2009}}</ref>

==Image gallery==
{|
|-
|[[Image:Max_gen50.png|framed|left|Max at [[generation]] 50]]
|}

==See also==
*[[Halfmax]]
*[[Quartermax]]
*[[Spacefiller 1]]

==References==
<references>
<ref name="message678458385414488064">{{CiteDiscord
|author = Alex Greason
|date = February 15, 2020
|channel = cgol
|id = 678458385414488064
}}</ref>
<ref name="message678530168649678850">{{CiteDiscord
|author = Adam P. Goucher
|date = February 16, 2020
|channel = cgol
|id = 678530168649678850
}}</ref>
<ref name="message700361705988816907">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 16, 2020
|channel = cgol
|id = 700361705988816907
}}</ref>
<ref name="message700583344085139496">{{CiteDiscord
|author = Mateusz Naściszewski
|date = April 17, 2020
|channel = cgol
|id = 700583344085139496
}}</ref>
<ref name="post137788">{{LinkForumThread
|format = ref
|title = Small Spacefillers
|p = 137788
|author = Rocknlol
|date = November 17, 2021
}}</ref>
<ref name="post155354">{{LinkForumThread
|format = ref
|title = Re: Small Spacefillers
|p = 155354
|author = iNoMed
|date = December 29, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_s.htm#spacefiller}}

{{Symmetry|180degree}}
[[Category:Infinite growth]]
[[Category:Breeders]]

__NOTOC__

Reverse caber-tosser

2022-11-16T01:00:18Z

Ch91: /* Terminology */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 15-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations, and it will include a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-11-16T00:59:59Z

Ch91: /* MathAndCode's RCT */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations, and it will include a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities due to the sheer size of its bounding box.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-11-16T00:58:58Z

Ch91: /* MathAndCode's RCT */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations, and it will include a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost of the RCT down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for the RCT15 was completed three days later.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-11-16T00:58:23Z

Ch91: /* MathAndCode's RCT */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations, and it will include a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost down to 15 gliders was proposed on November 12,<ref>{{LinkForumThread|format=ref|p=153465|title=Re: RCT remaining tasks|author=Pavel Grankovskiy|date=November 12, 2022}}</ref> and a demonstration pattern for it was completed three days later.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-11-13T04:14:07Z

Ch91: /* MathAndCode's RCT */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicentre''': The area of interest where all of the gliders from the glider-producing switch engines collide to perform initial construction work.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicentre.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BRG''': Bit-Reading Glider. This is a glider used to read a bit from the construction [[recipe]] encoded in the position of the southeastern [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. The current best candidate for a practical implementation of a DBCA is the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup. The name was originally "Binary Storage and Retrieval Device", and the planned implementation was a stable diagonal tape with storage and retrieval mechanisms. However, it turned out to be much cheaper to store the required data in a simple pair of very long glider loops.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, it is much cheaper to construct because its recipe is encoded in DBCA operations, and it will include a self-destruct mechanism that can be activated by a single glider. The ECCA is responsible for shooting down DBCA circuitry and producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{LinkForumThread|f=2|t=3347|p=60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018|format=ref}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately {{times|5.23|10615}} generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{LinkForumThread|f=2|t=3347|p=60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018|format=ref}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{LinkForumThread|f=12|t=1596|p=16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015|format=ref}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{LinkForumThread|f=2|t=3347|p=61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{LinkForumThread|f=2|t=3347|p=61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018|format=ref}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion by [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{LinkForumThread|p=61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018|format=ref}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{LinkForumThread|f=2|t=4415|p=100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020|format=ref}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, MathAndCode was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{LinkForumThread|p=144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022|format=ref}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

On 9 November 2022, [[Pavel Grankovskiy]] completed the final subtask needed to construct a [https://conwaylife.com/forums/viewtopic.php?p=153348#p153348 complete demonstration pattern] for an RCT-based construction of [https://conwaylife.com/forums/viewtopic.php?p=147825#p147825 Alan Hensel's 1994 decimal counter], using [[Adam P. Goucher]]'s script-generation code to compile an associated RCT viewer script at the same time, showing how the various stages of construction and destruction work in detail.<ref>{{cite web|url=https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html|title=In Conway's Life, Sixteen Gliders Can Build Anything|author=Dave Greene|date=November 10, 2022}}</ref>

Grankovskiy also compiled a true 16-glider version of the RCT pattern at the same time in [[macrocell]] format. It turned out to be possible to [https://discord.com/channels/357922255553953794/370571014654001154/1040222390950576128 open the resulting 140MB file in Golly], but running it for any length of time appeared to be beyond Golly's current design capacities.

Several dozen subproblems had to be solved to complete the RCT16 example patterns. Contributors included [[Daniel Vargas]], [[Adam P. Goucher]], [[Simon Ekström]], [[Dave Greene]], [https://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=2896 Lucas de la Paz], and [[Pavel Grankovskiy]].

A modification that would bring the cost down to 15 gliders has been proposed, but a demonstration pattern for it has not yet been completed.

==External links==
* {{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at ... 16|author=Dave Greene|date=June 13, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
* {{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
* {{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
* {{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-07-08T03:57:28Z

Ch91: /* Terminology */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicenter''': The area of interest where all of the gliders will collide.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicenter.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BS/AS''': Before Singularity/After Singularity.
*'''BRG''': Bit-Reading Glider-a glider used to read a bit from the construction [[recipe]] encoded in the position of the [[glider-producing switch engine]].
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. It is based on the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': Bit Storage and Retrieval Device, a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup.
*'''ECCA''': Extreme Compression Construction Arm, a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, its recipe length is cheaper and it will include a self-destruct mechanism that can be activated by a single glider. The ECCT is responsible for producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately 5.23×10615 generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=12&t=1596&hilit=caterpillar#p16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion of [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=61666#p61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=4415&start=25#p100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, the author was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=144533#p144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

==External links==
*{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at 35|author=Dave Greene|date=June 13, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
*{{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-07-07T20:57:28Z

Ch91: /* Terminology */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicenter''': The area of interest where all of the gliders will collide.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicenter.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BS/AS''': Before Singularity/After Singularity.
*'''BRG''': Bit-Reading Glider.
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. It is based on the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': [[Bit Storage and Retrieval Device]], a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup.
*'''ECCA''': [[Extreme Compression Construction Arm]], a secondary construction arm built by the DBCA to further increase construction efficiency; while approximately as complex as the DBCA, its recipe length is cheaper and it will include a self-destruct mechanism. The ECCT is responsible for producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately 5.23×10615 generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=12&t=1596&hilit=caterpillar#p16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion of [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=61666#p61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=4415&start=25#p100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, the author was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=144533#p144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

==External links==
*{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at 35|author=Dave Greene|date=June 13, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
*{{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-07-07T20:56:02Z

Ch91: /* External links */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicenter''': The area of interest where all of the gliders will collide.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicenter.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BS/AS''': Before Singularity/After Singularity.
*'''BRG''': Bit-Reading Glider.
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. It is based on the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': [[Bit Storage and Retrieval Device]], a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup.
*'''ECCA''': [[Extreme Compression Construction Arm]], a secondary construction arm built by the DBCA with similar functions to the DBCA; while approximately as complex as the DBCA, its recipe length is cheaper and it will include a self-destruct mechanism that further reduces the difficulty of cleanup. The ECCT is responsible for producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately 5.23×10615 generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=12&t=1596&hilit=caterpillar#p16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion of [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=61666#p61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=4415&start=25#p100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, the author was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=144533#p144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

==External links==
*{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at 35|author=Dave Greene|date=June 13, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/07/current-rct-technology-part-3-extreme.html|title=Current RCT Technology, Part 3: the ECCA (Extreme Compression Construction Arm)|author=Dave Greene|date=July 5, 2022}}
*{{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-07-07T20:54:48Z

Ch91: /* Terminology */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicenter''': The area of interest where all of the gliders will collide.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicenter.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BS/AS''': Before Singularity/After Singularity.
*'''BRG''': Bit-Reading Glider.
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. It is based on the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': [[Bit Storage and Retrieval Device]], a method of delaying construction and rerouting input RCT data from the DBCA into the ECCA until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup.
*'''ECCA''': [[Extreme Compression Construction Arm]], a secondary construction arm built by the DBCA with similar functions to the DBCA; while approximately as complex as the DBCA, its recipe length is cheaper and it will include a self-destruct mechanism that further reduces the difficulty of cleanup. The ECCT is responsible for producing the one-glider seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately 5.23×10615 generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=12&t=1596&hilit=caterpillar#p16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion of [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=61666#p61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=4415&start=25#p100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, the author was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=144533#p144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

==External links==
*{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at 35|author=Dave Greene|date=June 13, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html?m=1|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
*{{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-07-07T20:46:02Z

Ch91: Please change if this is incorrect.

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicenter''': The area of interest where all of the gliders will collide.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicenter.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BS/AS''': Before Singularity/After Singularity.
*'''BRG''': Bit-Reading Glider.
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. It is based on the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': [[Bit Storage and Retrieval Device]], a method of delaying construction until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup.
*'''ECCA''': [[Extreme Compression Construction Arm]], a secondary construction arm built by the DBCA with similar functions to the DBCA; while approximately as complex as the DBCA, its recipe length is cheaper and it includes a self-destruct mechanism that further reduces the difficulty of cleanup. The self-destruction will also activate the seed for the ATBC.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately 5.23×10615 generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=12&t=1596&hilit=caterpillar#p16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion of [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=61666#p61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=4415&start=25#p100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, the author was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=144533#p144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

==External links==
*{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at 35|author=Dave Greene|date=June 13, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html?m=1|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
*{{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Orthogonoid

2022-06-15T02:08:03Z

Ch91: /* Fast Orthogonoids */

{{Spaceship
|name = Orthogonoid
|pname = orthogonoid
|c = 467746
|bx = 868856
|by = 707
|dir = Orthogonal
|p = 3476016
|m = 1738008
|s = 16c/217251
|z = 256c/3476016
|discoverer = Dave Greene
|discoveryear = 2017
|mc = true
|synthesis = 37625
|synthesisRLE = true
}}
The '''Orthogonoid''' is a [[self-constructing]] [[spaceship]] analogous to the [[Demonoid]]s, with a slow [[orthogonal]] direction of travel. The first example was completed by [[Dave Greene]] on 29 June {{year|2017}}, with a top [[speed]] of 16[[speed of light|c]]/217251 (this is just 256c/3476016 in lowest terms).<ref name="post45486" />

The [[construction recipe]] is a stream of [[MWSS]]es, with the [[recovery time]] limited to 90 [[tick]]s by the [[Lx200]] [[dependent conduit]] that follows the initial [[syringe]] [[converter]]. The design is [[hashlife]]-friendly, meaning that the spaceship can be trivially adjusted so that spatial and temporal offsets are exact powers of two; [[period]] 4194304 and period 8388608 versions have been constructed, with speeds of c/16384 and c/32768 respectively. A script is available that can build any other sufficiently large Orthogonoid period.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=&p=56072#p56072 |author=Dave Greene |title=Re: Orthogonoid spaceship -- completed!|date=February 3, 2018|accessdate=February 3, 2018}}</ref>

The MWSSes are converted to [[Herschel]]s, which produce a standard [[single-channel]] [[glider stream]] that runs the Orthogonoid's single [[construction arm]]. After the child [[circuitry]] is complete, a previously constructed [[Snark]] in the parent is removed from the construction arm [[lane]], converting it to a "[[destruction arm]]" that efficiently shoots down the previous [[constructor]]/[[reflector]] in the series as soon as it is no longer needed.

==Fast Orthogonoids==

In October 2018, Dave Greene and [[Adam P. Goucher]] built sparse, fast, [[HashLife]]-friendly Orthogonoids with speeds of c/128, c/64 and c/16. Greene noticed that the last of these could be accelerated to 65536c/951573, which is only marginally slower than the theoretical upper bound of c/12 (limited by the [[2-engine Cordership]] and [[3-engine Cordership]]).<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=&p=65106#p65106 |author=Dave Greene |title=Re: Orthogonoid spaceship -- completed!|date=October 28, 2018|accessdate=November 25, 2018}}</ref>

The construction of this, together with a [[Demonoid]] and [[loopship]], made extensive use of [[slmake]].<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/11/new-tools-for-self-construction.html |author=Dave Greene |title=New Tools for Self-Construction|date=November 10, 2018|accessdate=November 25, 2018}}</ref>

On April 1, 2022, Goldtiger997 designed the [[Speed Orthogonoid]], which can travel at any speed below c/2.

== References ==
<references>
<ref name="post45486">{{LinkForumThread
|format = ref
|title = Re: Orthogonoid working notes
|p = 45486
|author = Dave Greene
|date = June 29, 2017
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_o.htm#orthogonoid}}
{{LinkForumThread|f=2|t=2212|title=Orthogonoid spaceship -- completed!}}

Reverse caber-tosser

2022-06-08T15:07:03Z

Ch91: /* Terminology */

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicenter''': The area of interest where all of the gliders will collide.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicenter.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BS/AS''': Before Singularity/After Singularity.
*'''BRG''': Bit-Reading Glider.
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. It is based on the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': [[Bit Storage and Retrieval Device]], a method of delaying construction until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup.
*'''ATBC''': [[Actual Thing Being Constructed]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately 5.23×10615 generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=12&t=1596&hilit=caterpillar#p16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion of [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=61666#p61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=4415&start=25#p100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, the author was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=144533#p144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

==External links==
*{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at 35|author=Dave Greene|date=June 13, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html?m=1|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
*{{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-06-08T15:06:46Z

Ch91: Preparation for a possible expansion, not necessarily by myself, as well as adding links to relevant terms.

A '''reverse caber-tosser''' (RCT) is a universal constructor with a small bounded population, where a recipe is encoded in the distance between an approaching [[c/12 diagonal]] object (such as a Cordership or puffer) and the origin. One or more [[glider]]s shuttle between the Cordership and the fixed circuitry, causing the times between collisions to repeatedly halve. The pattern is named by analogy with the [[caber tosser]] which behaves as a time-reversed version thereof. Each iteration, the least significant bit of the recipe is consumed by the circuitry and typically routed to a universal construction arm.

{{POTY|name=The reverse caber-tosser|year=2018|rank=3|behind=the [[0E0P metacell]] and [[Sir Robin]]}}

There have been three fundamentally different reverse caber tosser designs, which follow the same general principle but differ in the implementation details.

==Terminology==
Due to its specialized functions, a handful of distinctive terms are needed when discussing the reverse caber tosser's mechanisms. All of these refer to the 16-glider version of the RCT, as it is the most advanced version of the constructor thus far:

*'''Epicenter''': The area of interest where all of the gliders will collide.
*'''Parsec''': The distance between the construction site of the southeastern [[glider-producing switch engine]] and the epicenter.
*'''Aeon''': The time it takes for a lightspeed diagonal signal to traverse a parsec. This measure is not fixed, as it is based on the length of the RCT recipe.
*'''Singularity''': The moment when all construction bits have been read.
*'''BS/AS''': Before Singularity/After Singularity.
*'''BRG''': Bit-Reading Glider.
*'''DBCA''': [[Decoder and Better Construction Arm]], an optional stage of the RCT that allows building much more complex objects with the same number of bits encoded in the RCT distance. It is based on the [[Goucher-Grankowskiy construction arm]] design.
*'''BSRD''': [[Bit Storage and Retrieval Device]], a method of delaying construction until all glider streams have been absorbed and all the GPSEs have been stabilized into ash trails in order to minimize difficulty with cleanup.
*'''ATBC''': [[Actual Thing Being Constructed]]], the pattern that the RCT will eventually produce, with the rest of the Life universe being empty after the RCT has run to completion.

==Applications==

The binary output stream can be connected to a [[construction arm]] capable of [[universal construction]]. In doing so, a bounded-[[population]] initial setup can construct an arbitrary glider-constructible pattern. Since the reverse caber-tosser (together with the attached construction arm) is itself [[synthesis]]able, this implies the existence of some fixed integer N such that any glider-constructible pattern can be synthesised in at most N gliders. In combination with a [[universal computer]], this implies the existence of arbitrarily slow spaceships<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60820|title=Re: Building a reverse caber-tosser|author=Dave Greene|date=June 8, 2018}}</ref> which, in one phase, consist only of N gliders.

Currently, the best upper bound on N is {{Reverse caber tosser/Lower bound}} gliders.

The application is mostly theoretical rather than practical: it takes a number of generations exponential in the recipe length to construct a given glider synthesis, thereby cancelling out any potential speedup from [[Hashlife]]. Even though it is straightforward to calculate the positions of the initial gliders needed to create a given recipe, it is impractical to run all but the simplest of constructions. On April 16, {{year|2022}}, Goucher published an example pattern with a 2-kilobit recipe, along with a Python script to assist with running it in [[Golly]], which produces a [[shillelagh]] (along with a massive amount of additional debris) after approximately 5.23×10615 generations.<ref name="post144315" /> As this takes two hours to run, and the total wall-clock runtime appears to be cubic in the recipe length, it is infeasible to directly run significantly more complicated constructions. However, modifying the design to incorporate the creation of a new construction arm dubbed the [[DBCA]] have been shown to drastically improve the efficiency of the RCT mechanism while also opening up the potential for further improvements.

==History==

===Original 329-glider design===

The pattern<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=75#p60865|title=Re: Building a reverse caber-tosser|author=Adam P. Goucher|date=June 10, 2018}}</ref> was built in 2018 by [[Adam P. Goucher]] and [[Dave Greene]] using a glider-pair reflection reaction found by [[Martin Grant]]. The circuitry involves [[Herschel track]]s, period-8 [[reflector]]s and [[bumper]]s, and a receding [[block-laying switch engine]] to produce an inexhaustible source of [[block]]s to act as [[elbow]]s for the construction arm.

The assembly was later synthesised by [[Goldtiger997]], providing the explicit upper bound of N <= 329. This settled a 2015 conjecture by Gustavo Ramos Rehermann<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=12&t=1596&hilit=caterpillar#p16509|title=
Re: Game-of-Life-related Secret project leaked - GOL-SSRP|author=Gustavo Ramos Rehermann|date=February 4, 2015}}</ref> that the [[Caterpillar]] can be built in fewer than 386 gliders, assuming that it can be constructed at all (which is strongly believed to be the case).

Three days later, Dave Greene wrote a blog post<ref>{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Meaning of Life is 42 -- But the Cost of Living is Capped at 329|author=Dave Greene|date=June 13, 2018}}</ref> announcing this discovery.

===Pure switch-engine designs===

[[Adam P. Goucher]] observed that the glider stream produced by a [[glider-producing switch engine]] is identical to that of a period-256 [[glider gun]], but much cheaper to synthesise. [[Chris Cain]] proceeded to redesign the reverse caber-tosser to replace all of the fixed circuitry with just 12 glider-producing switch engines, and exhibited a suitable 4-glider synthesis for a glider-producing switch engine. Moreover, he noticed that one of the emitted gliders could be used to stabilise the synthesis of the block-laying switch-engine, eliminating a further glider.

On the 28th June 2018, Chris Cain completed<ref>{{cite web|url=
https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61433|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref> a 59-glider synthesis of this reverse caber-tosser, demonstrating both the PULL and DFIRE operations and improving the upper bound on N from 329 to 59. The minimum population attained is 278, which implies the existence of an extremely high-period [[knightship]] with a smaller population than the 282-cell [[Sir Robin]] (which was discovered earlier in the same year).

Later that same day, Chris Cain replaced the [[2-engine Cordership]] with a slightly cheaper [[boat]] [[puffer]], reducing the total number of gliders from 59 to 58.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=3347&start=125#p61439|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=June 28, 2018}}</ref>

On 2nd July 2018, Chris Cain proceeded to optimise this to 44 gliders, and a suggestion of [[Dave Greene]] reduced this further to 43.

On 5th July 2018, Adam P. Goucher and Chris Cain reduced this further to just 35 gliders, by using a 2-lane [[shotgun]] instead of a 4-lane shotgun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=61666#p61666|title=Re: Building a reverse caber-tosser|author=Chris Cain|date=July 6, 2018}}</ref> Instead of PULL and DFIRE, one glider stream is used for [[crystal]]lisation and decay, and the other glider stream introduces perturbations capable of emitting sideways gliders.

On 13th April 2020, Chris Cain found a universal set of slow salvo operations. This removed the dependence on a [[block-laying switch engine]], allowing a further two gliders to be saved, reducing the total cost to 33 gliders while also greatly simplifying the cleanup process for the synthesis.<ref name="post94346" />

On 21st July 2020, Adam P. Goucher was able to remove a glider by modifying the Sakapuffer<ref name="post145196" /> synthesis, reducing the total cost to 32 gliders.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=4415&start=25#p100871|title=Binary slow salvos|author=Adam P. Goucher|date=July 21, 2020}}</ref>

===MathAndCode's RCT===

During September 2020, [[MathAndCode]] proposed a major design change to the reverse caber tosser. Firstly, the Sakapuffer<ref name="post145196" /> is replaced with a cheaper [[GPSE]]. Secondly, the circuitry that detects whether the approaching glider is at time 0 or 128 (modulo 256) is eliminated, relying on the fact that a GPSE can perform this task itself. In doing so, the author was able to use 4 GPSEs instead of 6 GPSEs, a Sakapuffer, and a block, saving a total of 15 gliders. The complete pattern was posted on 19th September in a series of forum post edits by MathAndCode, and the universality of the construction arm was demonstrated by [[Adam P. Goucher]] later that day. The result is that universal construction can be performed with 17 gliders: 4 for each of the 4 GPSEs, and a final glider to create the construction arm.<ref name="post104484" /> Because all [[still life]]s up to 17 bits have explicit constructions with no more than 16 gliders, this discovery had the side effect of proving that all constructible still lifes can be synthesized with no more than one glider per bit.

On 21st April 2022, [[dani]] improved this to 16 gliders, by finding a 7 glider synthesis for two GPSEs together that had previously been made from 4 gliders each.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=144533#p144533|title=Binary slow salvos|author=Oscar Cunningham|date=April 21, 2022}}</ref> This also released some 'dirty' gliders, but [[Oscar Cunningham]] and [[Adam P. Goucher]] showed that these could be used in the creation of the construction arm at no extra cost.

==External links==
*{{cite web|url=http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html|title=The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at 35|author=Dave Greene|date=June 13, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html|title=Fixed Cost Glider Construction, Part II|author=Dave Greene|date=June 16, 2018}}
*{{cite web|url=https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html|title=Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)|author=Dave Greene|date=April 25, 2022}}
*{{cite web|url=http://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html?m=1|title=Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)|author=Dave Greene|date=May 29, 2022}}
*{{LinkLexicon|lex_r.htm#reversecabertosser}}

==References==
<references>
<ref name="post144315">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 144315
|author = Adam P. Goucher
|date = April 16, 2022
}}</ref>
<ref name="post94346">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 94346
|author = Chris Cain
|date = April 13, 2020
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post145196">{{LinkForumThread
|format = ref
|title = Re: Thread for Basic Questions
|p = 145196
|author = GUYTU6J
|date = May 6, 2022
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found in 2018]]
[[Category:Patterns found by Adam P. Goucher]]
[[Category:Patterns found by Dave Greene]]

Reverse caber-tosser

2022-06-08T14:47:05Z

Ch91: /* Applications */

Reverse caber-tosser

2022-06-06T15:11:15Z

Ch91: Made a mistake with the citation. Replacement would be appreciated.

Reverse caber-tosser

2022-06-06T15:02:17Z

Ch91:

Reverse caber-tosser

2022-06-06T15:00:35Z

Ch91: Please check the ref formatting for me, and add more detail on how the arm works to improve the RCT.

IceNine

2022-03-23T14:36:51Z

Ch91:

{{Glossary}}
'''IceNine'''{{refn|group=note|The name is a reference to the [http://en.wikipedia.org/wiki/Ice-nine chemical of the same name] in the novel ''[http://en.wikipedia.org/wiki/Cat's_Cradle Cat's Cradle]'' by [http://en.wikipedia.org/wiki/Kurt_Vonnegut Kurt Vonnegut], with similar properties to the hypothetical pattern. It is not related to [https://en.wikipedia.org/wiki/Ice_IX Ice IX], a metastable form of solid water.}} is [[Dave Greene]]'s name for a hypothetical unstoppable [[quadratic growth]] pattern that expands outward through random [[ash]] at speed [[c]]/137, described as follows in a tongue-in-cheek post in February {{year|2008}}:

{{Cquote|Aha! You and your intuition have clearly not been exposed to the IceNine Agar, found recently with an alternate-universe oscilloscope:

<pre>#C IceNine seed -- currently this is the smallest sample
#C for which no external conditions have yet been found
#C that prevent long-term quadratic growth
x = 2718, y = 4669, rule = B3/S23
<<<Server notice from fermat.yahoo.com:
11.9MB nonstandard text removed from message
Please notify sender of potential virus threat>>></pre>

Every sufficiently large and ancient B3/S23 universe observed so far turns out to be full of this weird agar, which expands in all directions through random ash at c/137. IceNine seems to absorb blocks and blinkers particularly well, due to a complicated froth of sparks at its front lines -- not generated by glider collisions, but by a lucky accident of the agar's internal structure.

When the expanding front touches an active pattern that it can't immediately annihilate, the pattern "dies back" a short distance at near lightspeed, leaving behind a protective scattering of blocks; behind the blocks the front stabilizes and starts expanding again. Converging IceNine fronts usually cause small diebacks that stabilize as small defects in an apparent quasicrystalline structure.

And before you all ask, my alternate-universe oscilloscope was repossessed by the Outsiders the other day, so unfortunately I can't lend it out. But there didn't seem to be anything but IceNine out there anyway --}}

He went on to further characterize IceNine as follows:

{{Cquote|The IceNine I tried to describe doesn't have a memory per se, any more than a cell's DNA knows the position of every lipid molecule in its cell wall. It's an active, growing agar with lots of edge sparks that just happen to annihilate nearby gliders and still lifes unusually efficiently. Along with several other utterly improbable properties. Basically it's the spacefiller that wins the Survival of the Fittest Award in an infinite Life universe, and it's about as likely as the proverbial tornado in a junkyard building a jumbo jet.}}

It is generally agreed that a pattern exhibiting the characteristics of IceNine cannot exist in [[Conway's Game of Life]], but a formal proof remains elusive. However, mechanisms that a replicator could implement to clear random ash fields with a similar "dying back" process to the one described by Greene to act as a failsafe have been proposed and have been demonstrated to work with greater than 50% odds of success.<ref name="post136948" />

==Notes==
<references group="note" />

==References==
<references>
<ref name="post136948">{{LinkForumThread
|format = ref
|title = Re: Clearing Ash
|p = 136948
|author = mscibing
|date = October 23, 2021
}}</ref>
</references>

==External links==
{{LinkForumThread|p=293|title=Re: Stable Life?|author=Adam P. Goucher|date=June 13, 2009}}

[[Category:Jokes]]

IceNine

2022-03-22T16:57:00Z

Ch91:

{{Glossary}}
'''IceNine'''{{refn|group=note|The name is a reference to the [http://en.wikipedia.org/wiki/Ice-nine chemical of the same name] in the novel ''[http://en.wikipedia.org/wiki/Cat's_Cradle Cat's Cradle]'' by [http://en.wikipedia.org/wiki/Kurt_Vonnegut Kurt Vonnegut], with similar properties to the hypothetical pattern. It is not related to [https://en.wikipedia.org/wiki/Ice_IX Ice IX], a metastable form of solid water.}} is [[Dave Greene]]'s name for a hypothetical unstoppable [[quadratic growth]] pattern that expands outward through random [[ash]] at speed [[c]]/137, described as follows in a tongue-in-cheek post in February {{year|2008}}:

{{Cquote|Aha! You and your intuition have clearly not been exposed to the IceNine Agar, found recently with an alternate-universe oscilloscope:

<pre>#C IceNine seed -- currently this is the smallest sample
#C for which no external conditions have yet been found
#C that prevent long-term quadratic growth
x = 2718, y = 4669, rule = B3/S23
<<<Server notice from fermat.yahoo.com:
11.9MB nonstandard text removed from message
Please notify sender of potential virus threat>>></pre>

Every sufficiently large and ancient B3/S23 universe observed so far turns out to be full of this weird agar, which expands in all directions through random ash at c/137. IceNine seems to absorb blocks and blinkers particularly well, due to a complicated froth of sparks at its front lines -- not generated by glider collisions, but by a lucky accident of the agar's internal structure.

When the expanding front touches an active pattern that it can't immediately annihilate, the pattern "dies back" a short distance at near lightspeed, leaving behind a protective scattering of blocks; behind the blocks the front stabilizes and starts expanding again. Converging IceNine fronts usually cause small diebacks that stabilize as small defects in an apparent quasicrystalline structure.

And before you all ask, my alternate-universe oscilloscope was repossessed by the Outsiders the other day, so unfortunately I can't lend it out. But there didn't seem to be anything but IceNine out there anyway --}}

He went on to further characterize IceNine as follows:

{{Cquote|The IceNine I tried to describe doesn't have a memory per se, any more than a cell's DNA knows the position of every lipid molecule in its cell wall. It's an active, growing agar with lots of edge sparks that just happen to annihilate nearby gliders and still lifes unusually efficiently. Along with several other utterly improbable properties. Basically it's the spacefiller that wins the Survival of the Fittest Award in an infinite Life universe, and it's about as likely as the proverbial tornado in a junkyard building a jumbo jet.}}

It is generally agreed that a pattern exhibiting the characteristics of IceNine cannot exist in [[Conway's Game of Life]], but a formal proof remains elusive. However, mechanisms that a replicator could implement to remove enough nearby ash to make space for future copies have been proposed and and have been proven to function on small scales.<ref name="post136948" />

==Notes==
<references group="note" />

==References==
<references>
<ref name="post136948">{{LinkForumThread
|format = ref
|title = Re: Clearing Ash
|p = 136948
|author = mscibing
|date = October 23, 2021
}}</ref>
</references>

==External links==
{{LinkForumThread|p=293|title=Re: Stable Life?|author=Adam P. Goucher|date=June 13, 2009}}

[[Category:Jokes]]

IceNine

2022-03-18T03:39:07Z

Ch91: Blanking on how to add a reference, but it should be https://conwaylife.com/forums/viewtopic.php?p=136948#p136948

{{Glossary}}
'''IceNine'''{{refn|group=note|The name is a reference to the [http://en.wikipedia.org/wiki/Ice-nine chemical of the same name] in the novel ''[http://en.wikipedia.org/wiki/Cat's_Cradle Cat's Cradle]'' by [http://en.wikipedia.org/wiki/Kurt_Vonnegut Kurt Vonnegut], with similar properties to the hypothetical pattern. It is not related to [https://en.wikipedia.org/wiki/Ice_IX Ice IX], a metastable form of solid water.}} is [[Dave Greene]]'s name for a hypothetical unstoppable [[quadratic growth]] pattern that expands outward through random [[ash]] at speed [[c]]/137, described as follows in a tongue-in-cheek post in February {{year|2008}}:

{{Cquote|Aha! You and your intuition have clearly not been exposed to the IceNine Agar, found recently with an alternate-universe oscilloscope:

<pre>#C IceNine seed -- currently this is the smallest sample
#C for which no external conditions have yet been found
#C that prevent long-term quadratic growth
x = 2718, y = 4669, rule = B3/S23
<<<Server notice from fermat.yahoo.com:
11.9MB nonstandard text removed from message
Please notify sender of potential virus threat>>></pre>

Every sufficiently large and ancient B3/S23 universe observed so far turns out to be full of this weird agar, which expands in all directions through random ash at c/137. IceNine seems to absorb blocks and blinkers particularly well, due to a complicated froth of sparks at its front lines -- not generated by glider collisions, but by a lucky accident of the agar's internal structure.

When the expanding front touches an active pattern that it can't immediately annihilate, the pattern "dies back" a short distance at near lightspeed, leaving behind a protective scattering of blocks; behind the blocks the front stabilizes and starts expanding again. Converging IceNine fronts usually cause small diebacks that stabilize as small defects in an apparent quasicrystalline structure.

And before you all ask, my alternate-universe oscilloscope was repossessed by the Outsiders the other day, so unfortunately I can't lend it out. But there didn't seem to be anything but IceNine out there anyway --}}

He went on to further characterize IceNine as follows:

{{Cquote|The IceNine I tried to describe doesn't have a memory per se, any more than a cell's DNA knows the position of every lipid molecule in its cell wall. It's an active, growing agar with lots of edge sparks that just happen to annihilate nearby gliders and still lifes unusually efficiently. Along with several other utterly improbable properties. Basically it's the spacefiller that wins the Survival of the Fittest Award in an infinite Life universe, and it's about as likely as the proverbial tornado in a junkyard building a jumbo jet.}}

It is generally agreed that a pattern exhibiting the characteristics of IceNine cannot exist in [[Conway's Game of Life]], but a formal proof remains elusive. However, mechanisms that a replicator could implement to remove enough nearby ash to make space for future copies have been proposed and and have been proven to function on small scales.

==Notes==
<references group="note" />

==External links==
{{LinkForumThread|p=293|title=Re: Stable Life?|author=Adam P. Goucher|date=June 13, 2009}}

[[Category:Jokes]]

Crab

2022-03-13T15:53:33Z

Ch91: /* Use as a tubstretcher */

{{Spaceship
|name = Crab
|pname = crab
|type = Tagalong
|c = 25
|bx = 13
|by = 12
|dir = Diagonal
|p = 4
|m = 2
|s = c/4
|z = c/4
|h = 22.0
|discoverer = Jason Summers
|discoveryear = 2000
|rulemin = B3/S23
|rulemax = B3678/S23678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-cey/S2-in3ajnqr
|isorulemax = B2i34-ajkr5-knq678/S234-akrw5-jq678
|synthesis = 14
|synthesisRLE = true
|plaintext = true
|rle = true
|animated = true
|viewerconfig = #C [[ TRACKLOOP 4 -1/4 -1/4 THUMBSIZE 2 GPS 4 ]]
|apgcode = xq4_go217z1b6koox84szy323
|pentadecathlonid = 25P4H1V1.1
}}
'''Crab''' (or '''quarter'''<ref>{{CiteLexicon|lex_q.htm#quarter|name=quarter}}</ref>) is a [[c/4 diagonal]] [[spaceship]] that was found by [[Jason Summers]] in September {{year|2000}}. It is the smallest known diagonal spaceship other than the [[glider]] and it consists of two gliders pulling a [[tagalong]].

== Use as a tubstretcher ==
It was noticed by [[Nicolay Beluchenko]] in August {{year|2005}} that it can be converted into a small [[tubstretcher]], as shown below.<ref>{{cite web|url=http://pentadecathlon.com/lifeNews/2005/08/new_c4_diagonal_tubstretcher_1.html|title=New c/4 Diagonal Tubstretcher|publisher=Game of Life News|author=H. Koenig|accessdate=May 9, 2009|date=August 5, 2005}}</ref> This tubstretcher is the basis for the [[one per generation]] pattern.

Due to the diagonal glide symmetry and by simple inspection, the spaceship can easily be made to stretch two tub wicks simultaneously, via a [[domino]] [[spark]] repeatedly adding units to a tub or long^N [[barge]]. Additional non-stretching variants are possible by adding [[tubeater|tub-eating]] c/4 spaceships at the back of the chain(s), at any distance. Such a double wickstretcher was used as the basis for the [[Speed Demonoid]] and the [[self-synthesizing oblique loopship]].

{{EmbedViewer
|pname = crabtubstretcher
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 2 ]]
|caption = The crab as a tubstretcher 
}}

== [[List of common spaceships|Commonness]] ==
At 25 cells, the crab is one of the three smallest spaceships yet to appear from soup, alongside [[25P3H1V0.1]] and [[25P3H1V0.2]].

== [[Glider synthesis]] ==
[[Martin Grant]] found a synthesis for crab with the help of Tanner Jacobi and Brett Berger on December 26, {{year|2014}}.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1533#p15243|title=Re: How about a crab synthesis?|author=Martin Grant|date=December 26, 2014 |accessdate=December 26, 2014}}</ref> The cost has since been reduced several times, most recently to 14 gliders by [[Tanner Jacobi]] on August 16, {{year|2020}}.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=102367#p102367|title=Re: One Glider Seeds|author=Tanner Jacobi|date=August 16, 2020 |accessdate=August 16, 2020}}</ref>

== See also ==
* [[Canada goose]]
* [[Orion]]
* [[Wings]]

== References ==
<references />

== External links ==
{{LinkLexicon|lex_q.htm#quarter|name=Quarter}}
{{LinkPentadecathlonObject|25P4H1V1.1}}
{{LinkCatagolue|xq4_go217z1b6koox84szy323}}

[[Category:Glide symmetric spaceships]]

Knightship

2022-02-18T04:33:13Z

Ch91: /* History */

{{Glossary}}
[[File:Sirrobin tiny.png|framed|right|[[Sir Robin]], the first elementary knightship to be found. {{JavaRLE|sirrobin}}]]
A '''knightship''' is a spaceship of type (2''m'',''m'')/''n'' (that is, a spaceship that moves two [[cell]]s horizontally for every one cell it moves vertically).

Alternatively and in a looser sense, 'knightship' is colloquially used to refer to any [[oblique spaceship]]; we refrain from using this broader definition here.

Knightships must be asymmetric and their period must be at least 6, which makes searching for them using programs like [[lifesrc]] very difficult.

==History==
An elementary would-be knightship, dubbed "[[almost knightship]]" was found by [[Eugene Langvagen]] on March 23, {{year|2004}}, which would be a period-6 knightship if it weren't for two cells that are incorrect in its sixth generation.<ref>{{cite web|url=http://plife.sourceforge.net/|title=PLife Home Page|accessdate=May 22, 2009}}</ref>

The first true knightship in Life was constructed by [[Dave Greene]] in June {{year|2010}}; based on [[Gemini]], it travels at a velocity of (4096,8192)c/35567490.<ref name="post2578" />

A knightship based on a different principle, dubbed [[half-baked knightship]], was built by a joint effort in July {{year|2014}}. This was optimised by [[Chris Cain]] to yield the much smaller [[parallel HBK]].

The first elementary knightship, [[Sir Robin]], was discovered on March 6, {{year|2018}} by [[Adam P. Goucher]], using a partial found by [[Tomas Rokicki]]. A second elementary knightship, [[sprayer]], was discovered on May 9, {{year|2021}}.

==Also see==
* [[Oblique spaceship]]
* [[Types of spaceships]]

==References==
<references>
<ref name="post2578">{{LinkForumThread
|format = ref
|f = 2
|t = 40
|p = 2578
|title = Re: Shrinking Gemini: Four Ideas
|author = [[Dave Greene]]
|date = June 13, 2010
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_k.htm#knightship}}

__NOTOC__

8-bit programmable computer

2022-02-16T17:36:55Z

Ch91:

{{Pattern
|name = 8-bit programmable computer
|pname = 8bitcomputer
|c = 1571767
|bx = 311607
|by = 303995
|discoverer = Nicolas Loizeau
|discoveryear = 2016
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|mc = true
}}
'''8-bit programmable computer''' is an implementation of an 8-bit [[universal computer|computer]] in [[Conway's Game of Life]] designed and built in {{year|2016}} by [[Nicolas Loizeau]].<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=37428#p37428|title=Programmable computer|author=Nicolas Loizeau|date=19 November 2016|accessdate=30 October 2019}}</ref>

An improved scalable version of the design with optimized circuitry, a 32x32 pixel display, and instructions to handle arrays was created in 2021.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=5432|title=New scalable programmable computer|author=Nicolas Loizeau|date=October 12, 2021|accessdate=14 October 2021}}</ref>

==Architecture==
The computer supports eight variables and 13 instructions -- '''write''', '''goto''', '''move''', '''jumpif''', '''print''', '''add''', '''or''', '''and''', '''xor''', '''not''', '''flat''', '''sign''', and '''increment'''. The computer is programmed by changing the arrangement of structures in its Program area.

The improved version possesses two more instructions, '''shift''' and '''rotate''', as well as a display that uses '''disp''' and '''erase''' instructions.

==Comparison with other computer patterns==
* The 8-bit programmable computer is considerably simpler than the [[Spartan universal computer-constructor]], in large part because it does not contain a universal-construction component.
* It is easy to program with the help of the associated Python utility script, assembly.py, and associated resources which can be found in the project's GitHub repository.<ref>{{cite web|url=https://github.com/nicolasloizeau/gol-computer|title=GOL computer|author=Nicolas Loizeau|date=18 November 2018|accessdate=30 October 2019}}</ref><ref>{{cite web|url=https://github.com/nicolasloizeau/scalable-gol-computer|title= Scalable GOL computer|author=Nicolas Loizeau|date=12 October 2021|accessdate=14 October 2021}}</ref>
* It is capable of performing standard 8-bit AND, OR, XOR, and NOT operations using any of its eight variables. The improved version can process up to 128 variables, which can be 8-bit, 16-bit, or 32-bit. Additionally, the improved version can use its variables as addresses that can be read from or written to.

==References==
<references />

8-bit programmable computer

2022-02-16T17:30:53Z

Ch91: /* Comparison with other computer patterns */

{{Pattern
|name = 8-bit programmable computer
|pname = 8bitcomputer
|c = 1571767
|bx = 311607
|by = 303995
|discoverer = Nicolas Loizeau
|discoveryear = 2016
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|mc = true
}}
'''8-bit programmable computer''' is an implementation of an 8-bit [[universal computer|computer]] in [[Conway's Game of Life]] designed and built in {{year|2016}} by [[Nicolas Loizeau]].<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=37428#p37428|title=Programmable computer|author=Nicolas Loizeau|date=19 November 2016|accessdate=30 October 2019}}</ref>

An improved scalable version of the design with optimized circuitry, a 32x32 display, and instructions to handle arrays was created in 2021.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=5432|title=New scalable programmable computer|author=Nicolas Loizeau|date=October 12, 2021|accessdate=14 October 2021}}</ref>

==Architecture==
The computer supports eight variables and 13 instructions -- '''write''', '''goto''', '''move''', '''jumpif''', '''print''', '''add''', '''or''', '''and''', '''xor''', '''not''', '''flat''', '''sign''', and '''increment'''. The computer is programmed by changing the arrangement of structures in its Program area.

The improved version possesses two more instructions, '''shift''' and '''rotate''', as well as a display that uses '''disp''' and '''erase''' instructions.

==Comparison with other computer patterns==
* The 8-bit programmable computer is considerably simpler than the [[Spartan universal computer-constructor]], in large part because it does not contain a universal-construction component.
* It is easy to program with the help of the associated Python utility script, assembly.py, and associated resources which can be found in the project's GitHub repository.<ref>{{cite web|url=https://github.com/nicolasloizeau/gol-computer|title=GOL computer|author=Nicolas Loizeau|date=18 November 2018|accessdate=30 October 2019}}</ref><ref>{{cite web|url=https://github.com/nicolasloizeau/scalable-gol-computer|title= Scalable GOL computer|author=Nicolas Loizeau|date=12 October 2021|accessdate=14 October 2021}}</ref>
* It is capable of performing standard 8-bit AND, OR, XOR, and NOT operations using any of its eight variables. The improved version can process up to 128 variables, which can be 8-bit, 16-bit, or 32-bit. Additionally, the improved version can use its variables as addresses that can be read from or written to.

==References==
<references />

8-bit programmable computer

2022-02-16T17:29:03Z

Ch91: /* Architecture */

{{Pattern
|name = 8-bit programmable computer
|pname = 8bitcomputer
|c = 1571767
|bx = 311607
|by = 303995
|discoverer = Nicolas Loizeau
|discoveryear = 2016
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|mc = true
}}
'''8-bit programmable computer''' is an implementation of an 8-bit [[universal computer|computer]] in [[Conway's Game of Life]] designed and built in {{year|2016}} by [[Nicolas Loizeau]].<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=37428#p37428|title=Programmable computer|author=Nicolas Loizeau|date=19 November 2016|accessdate=30 October 2019}}</ref>

An improved scalable version of the design with optimized circuitry, a 32x32 display, and instructions to handle arrays was created in 2021.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=5432|title=New scalable programmable computer|author=Nicolas Loizeau|date=October 12, 2021|accessdate=14 October 2021}}</ref>

==Architecture==
The computer supports eight variables and 13 instructions -- '''write''', '''goto''', '''move''', '''jumpif''', '''print''', '''add''', '''or''', '''and''', '''xor''', '''not''', '''flat''', '''sign''', and '''increment'''. The computer is programmed by changing the arrangement of structures in its Program area.

The improved version possesses two more instructions, '''shift''' and '''rotate''', as well as a display that uses '''disp''' and '''erase''' instructions.

==Comparison with other computer patterns==
* The 8-bit programmable computer is considerably simpler than the [[Spartan universal computer-constructor]], in large part because it does not contain a universal-construction component.
* It is easy to program with the help of the associated Python utility script, assembly.py, and associated resources which can be found in the project's GitHub repository.<ref>{{cite web|url=https://github.com/nicolasloizeau/gol-computer|title=GOL computer|author=Nicolas Loizeau|date=18 November 2018|accessdate=30 October 2019}}</ref><ref>{{cite web|url=https://github.com/nicolasloizeau/scalable-gol-computer|title= Scalable GOL computer|author=Nicolas Loizeau|date=12 October 2021|accessdate=14 October 2021}}</ref>
* It is capable of performing standard 8-bit AND, OR, XOR, and NOT operations using any of its eight variables. The improved version can process up to 128 variables, each of which can be 8-bit, 16-bit, or 32-bit. Additionally, the improved version can use its variables as addresses that can be read from or written to.

==References==
<references />