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LifeInLife

2026-10-27T13:24:31Z

YanRC: /* LifeInLife */

<big>'''Basic Information'''</big>

Type:Self-simulating cellular automaton construction

Designer:Multiple contributors in the Conway's Life community

Release year:2005 (first documented full implementation)

Dimensions:2D

Outer rule:Conway's Game of Life (B3/S23)

Inner rule:Identical to the outer rule (B3/S23)

<big>'''Overview'''</big>

LifeInLife is a landmark nested simulation construction in Conway's Game of Life, where a complete, functional instance of the B3/S23 cellular automaton is fully implemented using nothing but native Life patterns, signals and interactions. Unlike generic universal computer constructions that can run arbitrary programs, LifeInLife is purpose-built to simulate the exact same rule system that hosts it, creating a self-referential "universe inside a universe" effect that has become one of the most famous demonstrations of emergent complexity in the Life community.

The project was first conceptualized in the early 2000s, after the Life community had fully validated the practicality of building universal computers within Conway's Life. A complete working implementation was first documented in 2005, with subsequent refinements over the following decades drastically reducing its footprint and improving its simulation speed. All modern LifeInLife implementations are fully compatible with standard Life simulation software such as Golly, and can run indefinitely on an unbounded grid without external intervention.

<big>'''Core Design Principles'''</big>

LifeInLife operates on a foundational principle: every element required to run a valid Game of Life simulation can be constructed from existing native Life patterns, with no modifications to the outer B3/S23 rule. The entire system does not rely on any hidden logic, special rules or external processing; every state transition in the inner universe is the natural outcome of standard Life cell updates.

The system is built around three non-negotiable design constraints:

Rule consistency: The inner simulated universe strictly follows the B3/S23 birth/survival rules, with no deviations or simplified logic.

Autonomy: Once initialized, the simulation runs indefinitely on its own, with no manual input or external correction required.

Scalability: The construction can be expanded to simulate an arbitrarily large inner grid, simply by extending the repeating unit cell structure.

<big>'''Unit Cell Specifications'''</big>

The fundamental building block of LifeInLife is the unit cell, a self-contained structure that represents exactly one alive or dead cell in the inner simulated Game of Life.

Standard footprint: The canonical 2020 community-optimized unit cell occupies a 2048 × 2048 block of outer Life grid cells. Earlier 2005 implementations used a far larger 8192 × 8192 footprint, while experimental lightweight versions have compressed this to 1024 × 1024 at the cost of reduced simulation speed.

Internal components: Each unit cell contains three core modules:

A stable still-life based memory bank that stores the current alive/dead state of the inner cell, persisting unchanged across millions of outer generations.

A neighbor signal receiver that collects state data from all 8 adjacent inner unit cells via glider streams.

A native Life logic gate array that counts total living neighbors, calculates the next state according to B3/S23 rules, and updates the memory bank at the end of each inner simulation step.

Temporal Properties

The speed of the inner simulation is fundamentally limited by the overhead of processing millions of glider signals to compute a single inner state update:

The outer Game of Life has a maximum signal speed (the "speed of light in Life", denoted c) of 1 outer grid cell per generation.

A full generation update across the entire inner Life grid requires approximately 4,194,304 (2²²) outer generations to complete.

As a result, the maximum possible movement speed of a glider in the inner Life universe is capped at c/2²², meaning an inner glider takes over 4 million outer generations to move just one single inner grid cell.

This extreme temporal scaling creates a dramatic "time dilation" effect: from the perspective of an observer in the outer Life grid, the inner universe unfolds at a near-geologically slow pace, while hypothetical observers inside the inner simulation would experience their own evolution at a perfectly normal, natural speed.

<big>'''Historical Development'''</big>

The LifeInLife concept evolved alongside the maturation of Life's universal computation ecosystem:

1980s-1990s: After the discovery that Conway's Life is Turing complete, the community began to experiment with simple nested simulation prototypes, but no full, scalable implementation was completed.

2000-2005: Advances in glider logic gate optimization, stable memory cell design and signal routing technology allowed the first complete, working LifeInLife implementation to be assembled and verified in Golly.

2010s-2020s: Community-wide optimization projects reduced the unit cell footprint by over 75%, cut the per-generation simulation overhead, and added support for dynamically resizable inner grids.

Present: LifeInLife remains an active area of research, with ongoing projects to build a LifeInLife implementation that is small enough to fit inside a single large pattern, rather than requiring a custom pre-constructed grid.

Related Patterns and Constructions

Universal constructor: The foundational computational framework that makes nested simulation in Life possible.

Self-replicating constructions: Patterns that can produce exact copies of themselves, sharing conceptual overlap with LifeInLife's recursive properties.

Meta-cell patterns: A broader category of constructions that represent a single cell of an outer cellular automaton using a large, complex pattern, of which LifeInLife is the most famous example.

Gosper glider gun: One of the most critical supporting components, used to generate the steady, reliable streams of gliders that carry state data between LifeInLife unit cells.

Lightweight spaceship

2026-10-27T13:06:15Z

YanRC: /* Tagalong */

{{Spaceship
|name = Lightweight spaceship
|pname = lwss
|family = XWSS
|c = 9
|bx = 5
|by = 4
|fc = 11.2
|dir = Orthogonal
|p = 4
|m = 2
|s = c/2
|z = 2c/4
|h = 11
|symmetry = n-c
|discoverer = John Conway
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B3468/S2378
|isorulemin = B3aij/S2eik3aijnr
|isorulemax = B2kn345-a67e8/S1e234-aw5-jy6-kn78
|synthesis = 3
|synthesisRLE = true
|plaintext = true
|rle = true
|animated = true
|viewerconfig = #C [[ Y 0.5 TRACKLOOP 4 -1/2 0 THUMBSIZE 3 ZOOM 30 GPS 2 ]]
|apgcode = xq4_6frc
|pentadecathlonid = 9P4H2V0.1
|eppsteinid = 1062
}}
The '''lightweight spaceship''' (commonly abbreviated to '''LWSS''') or (rarely) '''small fish'''<ref>{{CiteLexicon|file=lex_s.htm#smallfish|name=Small fish|accessdate=June 10, 2009}}</ref> is the smallest orthogonal [[spaceship]], and the second most common spaceship after the [[glider]]. It moves at speed [[c/2 orthogonal|c/2]] and has {{periodS|4|text=period 4}} (and is therefore often referred to as 2c/4). It was found by [[John Conway]] in {{year|1970}}.

== Tagalong ==
In April {{year|1992}}, [[David Bell]] found a [[tagalong]] for two LWSSs (also works with [[middleweight spaceship(MWSS)]]s or [[heavyweight spaceship(HWSS)]]s replacing either or both LWSS). It can be extended indefinitely by attaching it to the back of itself. Interestingly, a [[hivenudger]] with symmetric rear (that is, both rear spaceships being of same "weight") can pull this tagalong.

{{EmbedViewer
|pname = xwsstagalong
|viewerconfig = #C [[ TRACKLOOP 4 -1/2 0 THUMBSIZE 2 GPS 4 ZOOM 18 HEIGHT 600 ANGLE 90 AUTOSTART ]]
|position = center
|caption = Tagalong for two lightweight spaceships
|style = width:300px;
|apgcode = xq4_8oxvvmxmvvxo8z03b0baksxskab0b3zw224rq8ccc8qr422zy369896zy0uhg9x9ghu
}}

== Construction ==
{{EmbedViewer
|rle = x = 78, y = 45, rule = B3/S23
76bo$75bo$75b3o20$58bobo$59b2o8bobo$59bo9b2o$70bo2$12bo$11bo$o10b3o$b
2o$2o$19bo18bo$20bo15bobo$18b3o16b2o2$53bo$32bo19b2o$12b2o17b2o19bobo$
11b2o18bobo$13bo$41b3o$22b3o18bo$24bo17bo$23bo!
|viewerconfig = #C [[ ZOOM 8 WIDTH 800 HEIGHT 400 THEME Book AUTOSTART GPS 12 T 0 PAUSE 2 T 75 PAUSE 1 LOOP 76 ]]
|position = center
|caption = Four 3G syntheses for the LWSS
|style = width:300px;
}}

A number of different ways to [[Synthesis|construct]] a LWSS can be found in [[Mark Niemiec's database|Mark Niemiec's glider synthesis database]];<ref name="niemiec" /> above are shown [[Three-glider collision|three-glider syntheses]].

A three-object [[one-glider seed]] for the lightweight spaceship, consisting of two [[block]]s and a [[beehive]], is used in the pattern {{filename|Patterns/Life/Breeders/switch-engine-breeder-MR.rle}} included in [[Golly's pattern collection]]. The seed constellation itself can be constructed with four gliders,<ref>{{LinkCatagolue|xs14_696y6oozy5cc|format=pseudo-object|style=nobullet}}</ref> leading to a way of constructing the LWSS using {{gliders|5|text=5 gliders}}.

A different one-glider seed that fits inside a {{times|12|12}} square can be found in the [[octohash database]];<ref>[https://github.com/dvgrn/octohash/ Repository] on GitHub</ref> it is a constellation of a [[blinker]] and an [[eater 1]], itself constructible with four gliders.<ref>{{LinkCatagolue|xp2_354cxs|format=pseudo-object|style=nobullet}}</ref> There are 60 matches in the [[octo3obj database]] which are clean [[one-glider seed]]s for the LWSS.<ref name="post152474" />

{| style="margin:auto;width:400px"
|{{EmbedViewer
|rle = x = 15, y = 18, rule = B3/S23
9bo$8bo$8b3o7$9b2o$9b2o3$13b2o$bo11b2o$obo$obo$bo!
|viewerconfig = #C [[ ZOOM 8 Y 8 THEME Book AUTOSTART GPS 20 T 0 PAUSE 1 T 159 PAUSE 1 LOOP 160 ]]
|position = center
|caption = A three-object 1G seed for the LWSS
}}
|{{EmbedViewer
|rle = x = 11, y = 10, rule = B3/S23
7b2o$8bo$5b3o$3o2bo4$8b2o$8bobo$8bo!
|viewerconfig = #C [[ ZOOM 8 THEME Book AUTOSTART GPS 20 T 0 PAUSE 1 T 63 PAUSE 1 LOOP 64 ]]
|position = center
|caption = A two-object 1G seed for the LWSS
}}
|}

== Occurrence ==
{{related|List of natural spaceships}}
Random soups investigated by Achim Flammenkamp emitted one LWSS for approximately every 615 gliders.<ref>{{cite web|url=http://wwwhomes.uni-bielefeld.de/achim/moving.html |title=Spontaneous appeared Spaceships out of Random Dust |publisher=Achim Flammenkamp |date=December 9, 1995|accessdate=August 18, 2011}}</ref> The LWSS is also the eighteenth most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref>

There are 731 results in the [[octohash database]],<ref group=note name="note_octohash" /> 6563 results in the [[octo3obj database]],<ref group=note name="note_octo3obj" /> and 1009 results in the [[octo3g database]]<ref group=note name="note_octo3g" /> with at least one escaping LWSS.

== See also ==
* [[Fake xWSS]]
* [[Middleweight spaceship]], [[Heavyweight spaceship]], [[LWSS on MWSS 1]], [[LWSS on HWSS 1]]
* [[Lightweight emulator]]
* [[Toaster]]
* [[Infinite LWSS hotel]]
* [[G-to-LWSS]]
* [[LWSS-LWSS bounce]]
* [[LWSS-LWSS deflection]]
* [[LWSS-glider bounce]]

== Notes ==
<references group=note>

<ref name="note_octohash">There are two collisions, each with two escaping LWSSes. One collision (headerless [[RLE]] {{headerlessRLE|8b2o$9bo$b2o6bobo$obo2b2o3b2o$2o2b2o$6bo!}}) has final [[population]] 158. The other collision ({{headerlessRLE|b2o$obo$2o6b2o$9bo$9bobo$10b2o2$12bo$11b2o$11bobo!}}) has final population alternating between 367 and 373.</ref>

<ref name="note_octo3g">There is one collision (headerless RLE {{headerlessRLE|obo$b2o$bo75$75bo$76b2o$75b2o$80bo$79b2o$79bobo!}}) with two escaping lightweight spaceships. The final population is 377.</ref>

<ref name="note_octo3obj">There are 28 results where two lightweight spaceships escape.</ref>

</references>

== References ==
<references>
<ref name="niemiec">{{LinkNiemiec|ss.htm#ss-9|The 1 nine-bit spaceship|rle=ss/9lw.rle|nobullet=nobullet}}</ref>
<ref name="post152474">{{LinkForumThread
|format = ref
|p = 152474
|title = Re: Octohash fingerprints
|author = Dave Greene
|date = October 21, 2022
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_l.htm#lwss|name=LWSS}}
* {{LinkCatagolue|xq4_6frc}}
* {{LinkPentadecathlonObject|9P4H2V0.1|archivedate=20221030044324|patternname=Lightweight Spaceship}}

* {{LinkEppsteinRule|rule=b3s23|rulename=Life (B3/S23)|archivedate=20160309235206}} 
* {{LinkCatagolue|xq4_6frcxcrf6|patternname=LWSS on LWSS|format=pseudo-object}}
* {{LinkCatagolue|xq4_8oxvvmxmvvxo8z03b0baksxskab0b3zw224rq8ccc8qr422zy369896zy0uhg9x9ghu|patternname=xWSS Tagalong}}

[[Category:Polyominoes]]
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