LifeWiki - User contributions [en]

Glider synthesis

2023-05-28T18:00:05Z

Inferno:

{|style="margin-left:16px;margin-bottom:8px;width:300px;float:right;"
|{{EmbedViewer
|pname = loafer_synth
|viewerconfig = #C [[ ZOOM 8 ]]
|position = center
|caption = An 8-glider synthesis of a [[loafer]]
}}
|}
{{Glossary}}
'''Glider synthesis''' (or '''glider construction''') is the construction of an object by means of [[collision]]s of [[glider]]s and glider-constructible [[spaceship]]s. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement (or else it is considered “not fully functional”). [[LWSS]]es, [[MWSS]]es and [[HWSS]]es can also be used in syntheses; these spaceships can themselves be easily synthesized from gliders at any point along their trajectory, so this conversion is often left as an implicit step.

==Features of syntheses==
Four main characterizing features of a synthesis are the ''geometry'', ''construction time'', ''glider cost'', and ''number of stages''.

The '''geometry''' is the number of directions of incoming gliders:
* four-directional: gliders collide from all four directions
* three-directional: gliders collide from all directions but one
* two-directional; further divisible in head-on and 90° syntheses. All two-glider syntheses are necessarily two-directional.
* unidirectional, which assumes the initial presence of a '''target''' (usually a [[still life]] or an [[oscillator]]) to be hit with gliders.
Since gliders are themselves glider-constructible, any multidirectional synthesis can be technically downgraded to a fewer-directional one, usually at the cost of increasing the construction time, cost, and/or number of stages needed for the synthesis. More challenging is finding a two- or three-directional synthesis for a particular object where few or no parts of the synthesis reactions extend outside the final pattern's [[bounding box]] in a particular direction. This is especially important for the synthesis of temporary [[bait]] objects, which will need to be placed sometimes quite close to other components without perturbing them. For especially tight locations, sometimes it will be useful to construct an [[LWSS]] (or another standard c/2 spaceship) some distance away from the synthesis nexus and let that collide with a glider in the final stages; this allows synthesis at a 45° angle, rather than a 90° angle as required for synthesis by gliders from separate directions.

The '''construction time''' is simply the number of [[generation]]s it takes to complete a synthesis. For multi-stage syntheses, each stage has its own construction time.

The '''number of stages''' is a count of how many separate operations a synthesis can be divided into, with pauses of arbitrary length between the stages. Often a particular synthesis operation cannot be achieved by a direct collision of gliders, and a synthesis procedure instead requires first synthesizing a number of [[bait]] objects, and then hitting these with gliders to produce the final result.

The '''cost''' is the number of gliders expended over the course of the synthesis. Similar to the construction time, it can be defined also for individual synthesis stages. A *WSS is considered to cost 3 gliders. The discovery of the [[reverse caber tosser]] in 2018 proved that there is a universal constant upper bound on the cost to synthesise any synthesisable object; currently, the best known upper bound is {{Reverse caber tosser/Lower bound}} gliders.

Of particular interest is [[salvo|slow salvo synthesis]]: unidirectional synthesis where every stage has a glider cost of one. Perhaps surprisingly, anything that is glider synthesizable is also slow salvo synthesizable, a result that crucially depends on the existence of [[universal construction]] [[construction arm|arms]] as well as [[one-time]] [[turner]]s and [[splitter]]s.

An '''incremental synthesis''' is a synthesis with multiple stages. The '''final step''' (final stage, activation step/stage) of an incremental synthesis is the step that converts a previously constructed stationary object or constellation into the target object. Finding the final step of a synthesis is often a nontrivial, complicated process.<ref name="post149546">{{LinkForumThread
|format = ref
|p = 149546
|title = Re: Suggested LifeWiki edits
|author = Dave Greene
|date = August 14, 2022
}}</ref><ref name="post160135">{{LinkForumThread
|format = ref
|p = 160135
|title = Re: Small Spaceship Syntheses
|author = Carson Cheng
|date = April 6, 2023
}}</ref>

==Still life syntheses==
In the 1990s, glider syntheses for all [[still life]]s and known [[oscillator]]s with at most 14 [[cell]]s were found by [[David Buckingham]]. Almost all of these were successfully reduced to a synthesis cost of less than 1 glider per ON cell, or "1 glider per bit".<ref>{{LinkForumThread|p=20597|title=Re: 4 glider syntheses|author=Mark D. Niemiec|date=June 20, 2015|format=ref}}</ref>

A collaborative effort ending in May 2014 completed glider syntheses of all still lifes with 17 or fewer cells.<ref>{{LinkGoLNews|2014/05/constructions_known_for_all_st.html|title=Constructions Known for All Still Lifes up to 17 Bits|author=Dave Greene|date=May 23, 2014|archivedate=20180806063633}}</ref><ref>{{LinkForumThread|f=2|t=1276|title=17-bit SL Syntheses (100% Complete!)|author=Martin Grant|date=January 6, 2014|format=ref}}</ref><ref name="post11972" /> A lengthy project to complete syntheses for all 18-bit still lifes was completed in October 2019.<ref name="post83979" /> The syntheses for 19-bit still lifes were completed in February 2020,<ref name="post89061" /> 20-bit still lifes in March 2021,<ref name="post125259" /> and 21-bit still lifes in November 2022.<ref name="post153564" /> Later optimization projects reduced the maximum cost of construction for 15-bit,<ref>{{LinkForumThread|f=2|t=2441|title=15 in 15: Efficient 15-bit Synthesis Project (DONE!)|author=BlinkerSpawn|date=October 27, 2016|format=ref}}</ref><ref name="post37438" /> 16-bit,<ref>{{LinkForumThread|f=2|t=2642|title=16 in 16: Efficient 16-bit Synthesis Project|author=Bob Shemyakin|date=December 20, 2016|format=ref}}</ref><ref name="post43734" /> and 17-bit<ref name="post82560" /> still lifes to less than one glider per bit, in November 2016, May 2017, and September 2019 respectively.

In September 2020, the 17-glider reverse caber-tosser proved that all synthesizable still lifes could theoretically be constructed with no more than one glider per bit.<ref name="post104484" />

The following table displays statistics about the costs (excluding RCT constructions) for strict and pseudo still lifes with up to 21 cells as of November 15, 2022.<ref>{{CiteCatagolue|page=syntheses|title=Syntheses|accessdate=November 15, 2022}}</ref>

{| class="wikitable" style="text-align:center"
! rowspan=2 | Live cells !! colspan=4 | Strict still lifes !! colspan=3 | Pseudo still lifes
|-
! Count<br>({{OEIS|A019473}}) !! Min. cost !! Avg. cost !! Max. cost !! Count<br>({{OEIS|A056613}}) !! Min. cost !! Max. cost
|-
| 4 || {{A019473|4}} || 2 || 2.500 || 3 || {{A056613|4}} || – || –
|-
| 5 || {{A019473|5}} || 2 || 2.000 || 2 || {{A056613|5}} || – || –
|-
| 6 || {{A019473|6}} || 2 || 3.200 || 4 || {{A056613|6}} || – || –
|-
| 7 || {{A019473|7}} || 2 || 2.750 || 4 || {{A056613|7}} || – || –
|-
| 8 || {{A019473|8}} || 2 || 3.556 || 4 || {{A056613|8}} || 2 || 2
|-
| 9 || {{A019473|9}} || 3 || 4.000 || 5 || {{A056613|9}} || 3 || 3
|-
| 10 || {{A019473|10}} || 4 || 4.360 || 5 || {{A056613|10}} || 3 || 5
|-
| 11 || {{A019473|11}} || 4 || 4.696 || 6 || {{A056613|11}} || 3 || 6
|-
| 12 || {{A019473|12}} || 4 || 5.330 || 7 || {{A056613|12}} || 3 || 9
|-
| 13 || {{A019473|13}} || 4 || 5.971 || 8 || {{A056613|13}} || 4 || 9
|-
| 14 || {{A019473|14}} || 3 || 6.729 || 9 || {{A056613|14}} || 3 || 11
|-
| 15 || {{A019473|15}} || 4 || 7.718 || 11 || {{A056613|15}} || 4 || 12
|-
| 16 || {{A019473|16}} || 3 || 8.715 || 14 || {{A056613|16}} || 4 || style="background-color:#ffff80;" | 23{{refn|group=n|name=RCT}}{{refn|group=n|All but 3 16-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of November 15, 2022.}}
|-
| 17 || {{A019473|17}} || 4 || 9.901 || 16{{refn|group=n|name=RCT}} || {{A056613|17}} || 4 || style="background-color:#ffff80;" | 18{{refn|group=n|name=RCT}}{{refn|group=n|All but 3 17-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of November 15, 2022.}}
|-
| 18 || {{A019473|18}} || 4 || 11.174 || style="background-color:#ffff80;" | 28{{refn|group=n|name=RCT|{{Reverse caber tosser/Lower bound}} gliders using the [[reverse caber-tosser]]}}{{refn|group=n|All but 224 18-bit strict still lifes can be constructed with strictly less than one glider per bit as of May 28, 2023.}} || {{A056613|18}}|| 4 || style="background-color:#ffff80;" | 48{{refn|group=n|name=RCT}}{{refn|group=n|All but 33 18-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of November 15, 2022.}}
|-
| 19 || {{A019473|19}} || 4 || 12.537 || style="background-color:#ffff80;" | 47{{refn|group=n|name=RCT}}{{refn|group=n|All but 1,753 19-bit strict still lifes can be constructed with strictly less than one glider per bit as of May 28, 2023.}} || {{A056613|19}} || 4 || style="background-color:#ffff80;" | 41{{refn|group=n|name=RCT}}{{refn|group=n|All but 71 19-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of November 15, 2022.}}
|-
| 20 || {{A019473|20}} || 4 || 14.071 || style="background-color:#ffff80;" | 115{{refn|group=n|name=RCT}}{{refn|group=n|All but 7,863 20-bit strict still lifes can be constructed with strictly less than one glider per bit as of May 28, 2023.}} || {{A056613|20}} || 4 || style="background-color:#ffff80;" | 73{{refn|group=n|name=RCT}}{{refn|group=n|All but 352 20-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of November 15, 2022.}}
|-
| 21 || {{A019473|21}} || 5 || 15.745 || style="background-color:#ffff80;" | 115{{refn|group=n|name=RCT}}{{refn|group=n|All but 29,411 21-bit strict still lifes can be constructed with strictly less than one glider per bit as of May 28, 2023.}} || {{A056613|21}} || colspan="2" style="background-color:#c0c0c0;" | {{refn|group=n|21-bit pseudo still lifes are currently not fully tabulated on Catagolue.}}
|}

In January 2022, work by [[Ilkka Törmä]] and [[Ville Salo]] demonstrated [[Unique father problem|a still life]] with 306 cells that is impossible to synthesize with gliders.

<references group=n />

== Spaceship syntheses ==
Perhaps the most interesting glider syntheses are those of [[spaceship]]s, because these can be used to create corresponding [[gun]]s and [[rake]]s. Many of the [[c/2]] spaceships that are based on standard spaceships have been synthesized, mostly by [[Mark Niemiec]]. In June {{year|1998}}, [[Stephen Silver]] found syntheses for some of the [[Cordership]]s (although it was not until July {{year|1999}} that [[Jason Summers]] used this to build a Cordership gun). Many larger Corderships also have known glider syntheses, and others could easily be generated using the same techniques. In general, larger Corderships have declined in importance after the discovery of four-, three- and two-engine versions.

In May {{year|2000}}, [[Noam Elkies]] suggested that [[60P5H2V0]], a [[2c/5]] spaceship found by [[Tim Coe]] in May {{year|1996}}, might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March {{year|2003}} that Summers and Elkies managed to find a way to perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in [[Conway's Game of Life|Life]] of a rake which fires spaceships that travel in the same direction as the rake but more slowly.

After the [[loafer]] was discovered and synthesized in 2013, a number of new spaceship syntheses were found during a short period of time in late 2014 and early 2015, including the [[dart]], [[crab]], [[25P3H1V0.2]], [[30P5H2V0]], [[x66]], and [[weekender]]. Most of this was due to the work of [[Martin Grant]].


{| class="wikitable sortable"
! rowspan="2" | Name !! rowspan="2" | Speed !! colspan="2" | First synthesis !! Best current synthesis
|-
! Date !! Discoverer !! Fewest gliders
|-
| [[60P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2003-03-17 || [[Noam Elkies]] || 37
|-
| [[loafer]] || data-sort-value="o 0.142857" | [[c/7 orthogonal]] || 2013-02-17 || [[Adam P. Goucher]] || 8
|-
| [[dart]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2014-12-02 || [[Ivan Fomichev]], [[Mark Niemiec]], [[Martin Grant]], [[Michael Simkin]] || 25
|-
| [[crab]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2014-12-26 || [[Brett Berger]], [[Martin Grant]], [[Tanner Jacobi]] || 14
|-
| [[Parallel HBK]] || data-sort-value="oblique" | [[(6,3)c/245912]] || 2014-12-31 || [[Michael Simkin]] || 38,380
|-
| [[30P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2015-01-01 || [[Martin Grant]], [[Matthias Merzenich]], [[Tanner Jacobi]] || 39
|-
| [[25P3H1V0.1]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2015-01-06 || [[Martin Grant]] || 19
|-
| [[x66]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-01-11 || [[Martin Grant]], [[Tanner Jacobi]] || 12
|-
| [[weekender]] || data-sort-value="o 0.285714" | [[2c/7 orthogonal]] || 2015-01-25 || [[Chris Cain]], [[Martin Grant]], [[Tanner Jacobi]] || 33
|-
| [[pufferfish spaceship]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-02-11 || [[Chris Cain]] || 51
|-
| [[Gemini]] || data-sort-value="oblique" | [[(2560,512)c/16849793]] || 2015-02-16 || [[Dave Greene]] || 173,449
|-
| half-[[x66]] with [[HWSS]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-03-08 || [[Adam P. Goucher]], [[praosylen]], [[Chris Cain]], [[Matthias Merzenich]] || 9
|-
| [[B29]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2015-04-06 || [[Tanner Jacobi]] || 25
|-
| [[Pushalong 1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-06-12 || [[Martin Grant]] || 14
|-
| [[30P4H2V0]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-09-10 || [[Tanner Jacobi]] || 50
|-
| [[0hd Demonoid]] || data-sort-value="d 0.000148114" | [[65c/438852 diagonal]] || 2015-12-06 || [[Chris Cain]] || 12,016
|-
| [[copperhead]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-05 || [[Tanner Jacobi]] || 13
|-
| [[fireship]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-21 || [[Nico Brown]], [[Tanner Jacobi]] || 18
|-
| [[25P3H1V0.2]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2017-12-15 || [[Martin Grant]] || 24
|-
| [[Orthogonoid]] || data-sort-value="o 0.0000736475" | [[16c/217251 orthogonal]] || 2017-12-30 || [[Dave Greene]] || 37,625
|-
| [[2-engine Cordership]] || data-sort-value="d 0.0833" | [[c/12 diagonal]] || 2017-12-31 || [[Dave Greene]] || 9
|-
| [[46P4H1V0]] || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2019-02-04 || [[Martin Grant]], [[Tanner Jacobi]] || 46
|-
| [[spider]] || data-sort-value="o 0.2" | [[c/5 orthogonal]] || 2019-03-07 || [[Martin Grant]] || 233
|-
| [[camelship]] || data-sort-value="oblique" | [[(3,1)c/3948264]] || 2019-05-04 || [[Dave Greene]] || 26,614
|-
| [[wings]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2019-10-28 || [[Goldtiger997]], [[Tanner Jacobi]] || 31
|-
| [[orthogonal loopship]] || data-sort-value="o 0.0499977" | 1000130c/20003511 orthogonal || 2020-01-08 || [[Dave Greene]] || 56,643
|-
| [[56P6H1V0]] || data-sort-value="o 0.167" | [[c/6 orthogonal]] || 2020-03-25 || [[AforAmpere]], [[praosylen]], [[Goldtiger997]], [[Martin Grant]], [[Tanner Jacobi]] || 290
|-
| [[58P5H1V1]] || data-sort-value="d 0.2" | [[c/5 diagonal]] || 2020-04-03 || [[Adam P. Goucher]], [[BlinkerSpawn]], [[Goldtiger997]], [[Peter Naszvadi]], [[Tanner Jacobi]] || 100
|-
| [[31P8H4V0]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2020-04-10 || [[Goldtiger997]] || 36
|-
| [[70P2H1V0.1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2020-07-18 || [[Martin Grant]] || 178
|-
| [[44P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2020-08-29 || [[Goldtiger997]] || 24
|-
| [[55P9H3V0]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2020-09-19 || [[Goldtiger997]] || 231
|-
| [[Speed Demonoid]] || data-sort-value="d 0.1992019" | 1642811c/8246964 diagonal || 2020-09-26 || [[Dave Greene]] || 31,822
|-
| [[57P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2020-11-02 || [[Goldtiger997]] || 391
|-
| [[turtle]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2020-12-04 || [[Goldtiger997]] || 227
|-
| [[doo-dah]] || data-sort-value="o 0.285714" | [[2c/7 orthogonal]] || 2020-12-06 || [[Goldtiger997]] || 39
|-
| [[edge-repair spaceship 1]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2021-01-24 || [[bubblegum]], [[goldenratio]] || 17
|-
| {{LinkCatagolue|xq4_2534uof1u0u1fou4352zy087084048078zx3igi3x3igi3|patternname=72P4H1V0|style=raw}}<ref name="post124810" /> || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2021-03-08 || [[Tanner Jacobi]], [[Goldtiger997]] || 195
|-
| {{LinkCatagolue|xq4_y2oo7t0t7ooz2qgx8t2rgr2t8xgq2z122166y5661221|patternname=61P4H1V0|style=raw}}<ref name="post128012" /> || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2021-04-10 || [[Goldtiger997]] || 89
|-
| [[Canada Grey]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2021-07-01 || [[Goldtiger997]], [[Martin Grant]] || 611
|-
| [[self-synthesizing oblique loopship]] || data-sort-value="oblique" | (16461006,16460963)c/75568091 || 2021-08-02 || [[Goldtiger997]] || 144,221
|-
| [[Orion 2]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2022-01-10 || [[Goldtiger997]] || 58
|-
| [[33P4H1V1]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2022-01-14 || [[Goldtiger997]], [[Mark Niemiec]]<ref name="post140292" /> || 45
|-
| [[70P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2022-01-26 || [[Goldtiger997]] || 221
|-
| [[58P8H4V0]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2022-02-25 || [[Goldtiger997]], [[Mark Niemiec]] || 50
|-
| [[SSGRL]] || data-sort-value="o 0.2419" | 15492980c/72085603 orthogonal || 2022-03-08 || [[Goldtiger997]] || 141,617
|-
| [[30P3H1V0]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2022-06-16 || [[Goldtiger997]] || 24
|-
| [[29P3H1V0]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2022-06-29 || [[Goldtiger997]] || 35
|-
| [[brain]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2022-11-25 || [[Goldtiger997]] || 99
|-
| Infinite families of [[waltz]] stabilisations || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2022-12-09 || [[Goldtiger997]],<ref>https://conwaylife.com/forums/viewtopic.php?f=2&t=1557&start=625#p154625</ref> [[Connor Steppie]]<ref>https://conwaylife.com/forums/viewtopic.php?f=2&t=1557&start=625#p154645</ref> || ≥28
|-
| [https://catagolue.hatsya.com/object/xq5_f930sgy1gs039fz24dcpn03330npcd42zy13iv0vi3/b3s23 66P5H2V0] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2022-12-23 || [[Goldtiger997]] || 57
|-
| [https://catagolue.hatsya.com/object/xq4_y258880638gszwu1w32gkoz34j0ozx11/b3s23 37P4H1V1] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2022-12-28 || [[Goldtiger997]] || 68
|}

==Other syntheses of note==
[[Image:glider_synth_pentadecathlon.png|framed|right|A 3-glider synthesis of a [[pentadecathlon]].]]

A [[Three-glider collision|3-glider synthesis]] of a [[pentadecathlon]] was found in April {{year|1997}} by [[Heinrich Koenig]], which came as a surprise because it was widely assumed that such a small synthesis would already be known.

Along similar lines, a 3-glider synthesis of the [[bi-pond]] was discovered in June {{year|2014}} by [[Bob Shemyakin]]<ref>{{LinkForumThread|p=12276|title=4 glider syntheses|author=Bob Shemyakin|date=June 16, 2014|format=ref}}</ref>, a 3-glider synthesis of a messy [[glider-producing switch engine]] was found in October {{year|2014}} by [[Michael Simkin]]<ref>{{LinkForumThread|p=13988|title=Re: Making switch-engines|author=Michael Simkin|date=October 24, 2014|format=ref}}</ref>, and a 3-glider synthesis of a [[clean]] [[switch engine]] was discovered in March {{year|2017}} by [[Luka Okanishi]].<ref>{{LinkForumThread|p=41557|title=Re: Thread For Your Accidental Discoveries|work=ConwayLife.com forums|author=Luka Okanishi|date=March 12, 2017|format=ref}}</ref>

On March 27, {{year|2022}}, [[dani]] found that two copies of Simkin's GPSE synthesis could be combined to produce a record-breaking 6-glider synthesis<ref name="post143450" /> of a [[breeder]] which had been discovered a week earlier.<ref name="post143132" />

==2-glider syntheses==
{{main|2-glider collision}}

There are 71 distinct 2-glider collisions, of which 28 produce [[nothing]], six produce a [[block]], five produce a [[honey farm]], three produce a [[B-heptomino]], three produce a [[pi-heptomino]], three produce a [[blinker]], three produce a [[traffic light]], two produce a [[glider]], two produce a [[pond]], two produce a [[loaf]] and a [[blinker]], one produces a [[boat]], one produces a [[beehive]], one produces a [[loaf]], one produces an [[eater 1]], one produces [[lumps of muck]], one produces a [[teardrop]], one produces an [[interchange]], one produces a traffic light and a glider, one produces [[Two-glider octomino|an octomino]], one produces a [[bi-block]], one produces four blocks, one produces two blocks, one produces a blinker, loaf, [[tub]] and block, and one produces the so-called [[two-glider mess]], a [[methuselah]] stabilizing after 530 generations and consisting of four gliders, eight blinkers (including a traffic light), four blocks, a beehive and a [[ship]].

All 71 such syntheses can be seen below in a pattern put together by [[Jason Summers]] on January 29, {{year|2005}}:

{{EmbedViewer
|pname = twoglidersyntheses
|position = center
|caption = All 71 distinct 2-glider collisions, arranged by what they synthesize
|viewerconfig = #C [[ WIDTH 1200 HEIGHT 1200 ZOOM 3 ]]
}}

==See also==
* {{CategoryLink|Patterns constructible by a given number of gliders}}
* [[Salvo]]
* [[Tutorials/Glider syntheses]]
* [[Shinjuku]]

==References==
<references>
<ref name="post11972">{{LinkForumThread
|format = ref
|title = Re: 17-bit SL Syntheses
|p = 11972
|author = Martin Grant
|date = May 17, 2014
}}</ref>
<ref name="post82560">{{LinkForumThread
|format = ref
|title = Re: 17 in 17: Efficient 17-bit synthesis project
|p = 82560
|author = Tanner Jacobi
|date = September 9, 2019
}}</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="post83979">{{LinkForumThread
|format = ref
|title = Re: 18-bit SL Syntheses (100% Complete!)
|p = 83979
|author = Ian07
|date = October 9, 2019
}}</ref>
<ref name="post89061">{{LinkForumThread
|format = ref
|title = Re: 19-bit still life syntheses
|p = 89061
|author = Martin Grant
|date = February 8, 2020
}}</ref>
<ref name="post125259">{{LinkForumThread
|format = ref
|title = Re: 20-bit still life syntheses
|p = 125259
|author = Martin Grant
|date = March 12, 2021
}}</ref>
<ref name="post153564">{{LinkForumThread
|format = ref
|title = Re: 21-bit still life syntheses
|p = 153564
|author = May13
|date = November 14, 2022
}}</ref>
<ref name="post37438">{{LinkForumThread
|format = ref
|title = Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain)
|p = 37438
|author = Martin Grant
|date = November 19, 2016
}}</ref>
<ref name="post43734">{{LinkForumThread
|format = ref
|title = Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain)
|p = 43734
|author = Goldtiger997
|date = May 24, 2017
}}</ref>
<ref name="post124810">{{LinkForumThread
|format = ref
|title = Re: Small Spaceship Syntheses
|p = 124810
|author = Goldtiger997
|date = March 8, 2021
}}</ref>
<ref name="post128012">{{LinkForumThread
|format = ref
|title = Re: Small Spaceship Syntheses
|p = 128012
|author = Goldtiger997
|date = April 10, 2021
}}</ref>
<ref name="post140292">{{LinkForumThread
|format = ref
|title = Re: Small Spaceship Syntheses
|p = 140292
|author = Mark Niemiec
|date = January 14, 2022
}}</ref>
<ref name="post143450">{{LinkForumThread
|format = ref
|title = Re: Small Quadratic Growth Patterns
|p = 143450
|author = dani
|date = March 27, 2022
}}</ref>
<ref name="post143132">{{LinkForumThread
|format = ref
|title = Re: Small Quadratic Growth Patterns
|p = 143132
|author = dani
|date = March 20, 2022
}}</ref>
</references>

==External links==
* [https://catagolue.hatsya.com/syntheses Catagolue synthesis database]
* {{LinkNiemiec|lifepage.htm|title=Mark Niemiec's glider synthesis database}}
* [https://conwaylife.com/ref/DRH/life.html Dean Hickerson's Life page] with four pages of glider syntheses
* [https://conwaylife.com/forums/viewtopic.php?p=46552#p46552 Martin Grant's synthesis component database], version 3
* [https://web.archive.org/web/20210716021110/http://pentadecathlon.com/constructions/components/components.php Heinrich Koenig's component catalog] on [[Game of Life News|pentadecathlon.com]]
* {{LinkLexicon|lex_g.htm#glidersynthesis}}
===Forum threads===
* {{LinkForumThread|f=2|t=3267|title=Still Life Synthesis Thread}}
* {{LinkForumThread|f=2|t=1155|title=Synthesising Oscillators}}
* {{LinkForumThread|f=2|t=1557|title=Small Spaceship Syntheses}}
* {{LinkForumThread|f=2|t=3960|title=Soup-based syntheses}}
* {{LinkForumThread|f=2|t=4257|title=Randomly enumerating glider syntheses}}
* {{LinkForumThread|f=2|t=1394|title=4 glider syntheses}}
* {{LinkForumThread|f=2|t=4063|title=Synthesis components}}

[[Category:Synthesis| ]]

Speed Orthogonal Loopship

2022-11-20T04:09:33Z

Inferno: fixed typo

{{stub}}
'''Speed Orthogonal Loopship''' is an [[adjustable spaceship|adjustable]] [[loopship]] constructed on November 11, {{year|2022}} by [[Goldtiger997]]. The [[spaceship]] is [[glide symmetric]], with a speedy of 137457528c/309254024 (or about 4c/9). It can be adjusted to arbitrarily fast velocities by moving the southern-most [[MWSS]] further south by a multiple of 2 [[tick]]s. It is also possible to adjust the speed by modifying the size of the [[snark]] loop, which is done by modifying the size of some of the gaps in the [[recipe]]. The minimum [[population]] is about 1.5 million, much less than [[Speed Orthogonoid]].<ref name="post153452" /> Over the next few days, Goldtiger997 improved the design, and constructed a 7766080c/209071672 spaceship, the first [[SMOS]] made entirely out of [[xWSS]]s.<ref name="post153724" />

==Pattern file==
The original Speed Orthogonal Loopship can be accessed in [[mc]] format with the following link:
[https://conwaylife.com/forums/download/file.php?id=5261 137457528c309254024 spaceship.mc]

==References==
<references>
<ref name="post153452">
{{LinkForumThread
|p = 153452
|format = ref
|title = Re: Make a Spaceship With an Adjustable Slope
|author = Goldtiger997
|date = November 11, 2022
}}
</ref>
<ref name="post153724">
{{LinkForumThread
|p = 153724
|format = ref
|title = Re: Make a Spaceship With an Adjustable Slope
|author = Goldtiger997
|date = November 17, 2022
}}
</ref>
</references>

[[Category:Patterns]]
[[Category:Spaceships]]
[[Category:Adjustable spaceships]]

CatForce

2022-07-06T08:43:17Z

Inferno: added 74p34

{{Software
|name = CatForce
|url = https://github.com/simsim314/CatForce
|purpose = Enumeration of small [[Spartan]] objects
|createdby = [[Michael Simkin]]
|platform = Unix; Windows
}}
'''CatForce''' is an optimized [[search program]] written by [[Michael Simkin]] in {{year|2015}}, using brute-force enumeration of small [[Spartan]] objects in a limited area, instead of a depth-first tree search. One major purpose of CatForce is to find [[glider synthesis|glider-constructible]] completions for [[signal]] [[conduit]]s. An early CatForce discovery was the [[B60]] conduit, which enabled a [[Simkin glider gun|record-breaking new glider gun]].

In May {{year|2022}}, [[mvr]] created a modification of CatForce, both significantly improving speed and adding a [[static symmetry|symmetry]] option.<ref name="post145414" /> This new version of the program was used to find [[p84 honey farm hassler]], [[58P37]], and [[74P34]].

==References==
<references>
<ref name="post145414">{{LinkForumThread
|format = ref
|title = Re: CatForce new catalyst search utility (LifeAPI based)
|p = 145414
|author = mvr
|date = May 10, 2022
}}</ref>
</references>

==External links==
* [https://github.com/simsim314/CatForce CatForce] on Github (original)
* [https://github.com/mvr/CatForce CatForce] on Github (mvr's modification)
{{LinkLexicon|lex_c.htm#catforce}}
{{LinkForumThread|f=9|t=1678|title=CatForce new catalyst search utility (LifeAPI based)}}

Bookend bridge bookend

2022-03-25T22:50:52Z

Inferno:

{{Stilllife
|name = Bookend bridge bookend
|pname = bookendbridgebookend
|c = 14
|bx = 6
|by = 6
|rulemin = B/S23
|rulemax = B3678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S2ae3nry
|isorulemax = B2-ak34-jn5-jq678/S012345678
|fc = 28.9
|synthesis = 6
|plaintext = true
|rle = true
|apgcode = xs14_64lb8ozw11
|pentadecathlonid = 14.561
}}
'''Bookend bridge bookend''' is a {{cells|14}}-[[cell]] strict still life consisting of two mutually stabilising [[bookend]]s. It is one of [[Bookend#As a still life component|six ways in which two bookends can be arranged to create a still life]], and the only one which only has a single [[island]].

It can occur from a rotationally-symmetric collision of two [[lightweight spaceship]]s.

== [[List of common still lifes|Commonness]] ==
Bookend bridge bookend is currently the 603rd most common object on [[Adam P. Goucher]]'s [[Catagolue]], being less common than the unnamed still life xs19_69mgmiczw66, but more common than the unnamed still life xs15_j5q8a6z11.

== [[Glider synthesis]] ==
{{Small constructible periodic object}}

== External links ==
{{LinkPentadecathlonObject|14.561}}
{{LinkCatagolue|xs14_64lb8ozw11}}

{{Symmetry|180degree}}

__NOTOC__

Mathematician

2021-08-05T03:00:18Z

Inferno: Added more information about the synthesis

{{Oscillator
|name = Mathematician
|pname = mathematician
|f1 = Billiard table
|c = 35
|bx = 9
|by = 11
|p = 5
|m = 5
|h = 3.2
|v = 0.20
|discoverer = David Buckingham
|discoveryear = 1972
|rulemin = B3/S23
|rulemax = B38/S0235678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3ijnry/S2-n3-ackn
|isorulemax = B2n34ejkrtwy5ciknq6-i7c8/S01c234-itz5678
|synthesis = 28
|synthesis2 = 24
|plaintext = true
|rle = true
|animated = yes
|viewerconfig = #C [[ GPS 2 THUMBSIZE 2 ]]
|apgcode = xp5_6s1v071c88gz118f0e8311
|apgcode2 = xp5_g25a8cwgzd5hp3ph5dzx343
|pentadecathlonid = 35P5.4
}}
The '''mathematician''' is a {{period|5}} [[oscillator]] that was found in {{year|1972}} by [[David Buckingham]].<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> A variant of it first appeared [[semi-natural]]ly in April {{year|2016}}.<ref name="post29706" />

A 99 [[glider synthesis]] of this oscillator was found by Inferno on August 2 {{year|2021}} based on a final step posted by INoMed.<ref name="post134400" /> Over the next few days, this was reduced by [[iNoMed]], [[wwei23]], [[MathAndCode]], [[Tanner Jacobi]], and [[Martin Grant]] to 28 gliders.<ref name="post134433" /><ref name="post134463" />

==See also==
*[[Chemist]]
*[[Technician]]

==References==
<references>
<ref name="post29706">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 29706
|author = Dongook Lee
|date = April 6, 2016
}}</ref>
<ref name="post134400">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 134400
|author = iNoMed
|date = August 2, 2021
}}</ref>
<ref name="post134433">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 134433
|author = iNoMed
|date = August 3, 2021
}}</ref>
<ref name="post134463">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 134463
|author = Martin Grant
|date = August 4, 2021
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_m.htm#mathematician}}
{{LinkCatagolue|xp5_6s1v071c88gz118f0e8311}}
{{LinkPentadecathlonObject|35P5.4}}