What is new in JETCARP

Draft. This page is a first draft of JETCARP’s contributions, written for the v0.4.0 release and the paper that will follow. Each claim below is limited to what our prior-art search supports. The spaceship claims have been through the checks described in How we checked, but not yet past the ConwayLife community, whom we will ask; see Checks still to do at the end. If you know of earlier work that we have missed, please open an issue. We will correct the page and credit it.

JETCARP stands on a great deal of earlier work, credited on every page of this encyclopedia and collected in the bibliography. This page lists the few things that, as far as we can tell, are new, says how we looked, and lists the things we have decided not to claim.

How we searched

In November 2026 we audited each candidate contribution against the literature and the hobbyist record: web and arXiv searches, Crossref records for every paper cited, the authors’ own pages and repositories, and LifeWiki. Every search query and fetched page is logged with its date in our research notes, and each source was checked against its primary record before being listed in the bibliography. The verdicts used three levels: prior art found, related work only, and nothing found after search. Only the last two can support a claim, and we word such claims “to our knowledge”.

The search has known weaknesses:

• Forums. The ConwayLife.com site refuses automated reading, so LifeWiki and the forums were read through a mirror, and forum coverage is the weakest part of the search. A second pass over the forum boards, Code Golf Stack Exchange and code hosts in November 2026 found EricG’s 2013 exploration of Life-like rules on the Archimedean tilings, which changed the spaceship claims below; its pattern files are no longer online. A third pass, aimed at the claim about Life on the 2- and 3-uniform tilings, searched for “2-uniform”, “3-uniform”, “k-uniform”, “demiregular” and the tilings’ other names on the forums, LifeWiki, Stack Exchange, GitHub, arXiv, YouTube and Hacker News. It found other rules run on one 2-uniform tiling, and no report of Life on any 2- or 3-uniform tiling but k2-007 (see below). Reddit, Discord, the contents of videos, and the tile sets of closed programs such as Visions of Chaos could not be searched. Hobbyists may well have found other things below without publishing them in papers.
• Unread full texts. For a few papers only abstracts or search excerpts could be read; where a statement rests on an excerpt, the page that makes it says so.
• A fast-moving field. Several closely related works appeared between August and October 2026 (Guttesen’s paper on Life on Archimedean lattices, whose results first appeared as Code Golf answers in 2024, and Edmond’s monotile gliders). We will re-run the key searches just before publication.

Contributions

1. JACA, an annihilating two-sided family of Life-like rules

Claim (to our knowledge). The particular combination in JACA is new: an independent birth/survival rule for each sign, counting only same-sign neighbours; destruction of every live cell that touches the other sign; a blast radius measured in neighbourhood steps; cancelled double births; an exact reduction to the plain rule when only one sign is present; and use on any periodic or aperiodic tiling. JACA is Jimmie Rodgers’s idea (November 2026).

Evidence. Each ingredient has a precedent, and all are credited: two-player Life with a coin flip for tied births (Levene and Roussos 2003); the +1/−1/0 encoding, own-sign counting and cancelled births of the “Game of Life or Death” (Unsupervision Blog 2025); matter–antimatter Life whose touching cells turn into energy (KittyTac and wildmyron 2018; LifeWiki: Rule:Energetic); and A + B → 0 annihilation in physics (Toussaint and Wilczek 1983; Chopard and Droz 1998). No source combined them. Not searched: MCell’s weighted rules with negative weights, Golly’s rule-table collection, and most of the ConwayLife rule-request thread.

Not claimed. “The first signed or ternary Life”, “the first matter–antimatter Life”, and anything about JACA’s colouring.

2. Layered rules on any tiling

Claim (to our knowledge). Layered rules, Wolfram-style totalistic rules whose rows are the graph-distance layers around a seed so that they run unchanged on any tiling, including aperiodic ones, are a construction we have not seen published. They are Jimmie Rodgers’s (2026).

Evidence. The closest work embeds one-dimensional rules in hyperbolic tilings along a chosen line (Margenstern 2010) or draws elementary rules on the fixed rows of hexagon and pentagon lattices (Kerekrety 2020). Dalai’s “Layered Cellular Automata” is unrelated despite the name (Dalai 2023). The idea is simple, so it may exist in unpublished code or in work on rules over graphs that our search did not reach; Wolfram’s work on network systems was not checked in detail.

3. Presenting and cataloguing the three-parent hexagon rules

Claim (to our knowledge). JETCARP is the first to present the three-parent hexagon rules (HexT, HexT3) as a family of hexagon pictures with a Wolfram-style numbering of all 256 binary and 3²⁷ three-state rules, totalistic and symmetric subsets, and an automatic classification of all binary and totalistic rules. The claim is to the presentation and catalogue only: the underlying rules are standard second-order one-dimensional automata.

Evidence. Second-order rules and staggered neighbourhoods are in Wolfram 2002 and the Wolfram Language; no source numbered or catalogued this family as hexagon rules.

Not claimed. The two-parent rules HexW and HexW3, which are Wolfram’s two-cell rules (Wolfram 2002, p. 885) and are also drawn by Kerekrety 2020.

4. Spaceships on non-square tilings

Claim (to our knowledge). JETCARP’s soup searches have found particular spaceships in Life-like rules on Archimedean and k-uniform tilings that we have not found reported before. Spaceships on these tilings are not new in themselves: EricG found ships in Life-like rules on every Archimedean tiling in 2013 (EricG 2013), and Martin Büttner found one on a tiling of hexagons, squares and triangles in 2014 (Code Golf 2014). Of 72 candidates, 60 distinct objects survived the checks in the box below. We claim, to our knowledge, only the 25 of them that are single ships, carry no flag, and run in none of the rules in which EricG reported ships: six on Archimedean tilings (3.4.6.4, 3.3.3.4.4 and 3.3.3.3.6), thirteen on 2-uniform tilings and six on 3-uniform tilings. Every one is listed, with its rule range, in Findings. Each runs the same way in a whole range of rules; none of these 25 runs in Life itself. Life’s own spaceships on these tilings are a separate claim, below.

The other 35 are described, not claimed:

• Flagged, 28. Eleven are flagged as most likely already known: eight small ships that turn up often in soups and run in many rules on an Archimedean tiling (on 4.8.8, 3.12.12, 4.6.12, 3.6.3.6 and 3.3.3.4.4), and three built on Guttesen’s gliders. Seventeen are flagged to check before claiming: they run in a well-known rule (HighLife, Pedestrian Life, or B2/S34 on 4.8.8), contain a phase of one of Guttesen’s gliders, were very common in their search, or run on 4.8.8 or 3.12.12 in the B2 and B26 rules where EricG reported many ships in 2013 without listing them. We found no earlier report of any of them, but others may well have seen them.
• Derivative, 13, six of them also flagged. A smaller ship that pulls a passenger along unchanged, or a bound pair of gliders. They are kept as distinct objects with the core named, as Life catalogues keep tag-alongs, but they are not counted as discoveries.

The strongest candidates, single ships with no flag that the checks confirmed on every count (the fourth, on 4.8.8, is now flagged):

One ship that was among the strongest before the congruence test shows how far that test reaches:

Evidence. Gliders on triangles, hexagons and Cairo pentagons go back to Carter Bays (Bays 1994; Bays 2005; Kerekrety 2020), and hexagonal Life (B2/S34H) has known spaceships (drc, Hickerson and wildmyron 2016).

The closest earlier work is EricG’s, posted on the ConwayLife forums on 12 June 2013 (EricG 2013; pentagonal tilings in EricG 2013). EricG emulated the eight composite Archimedean tilings and their eight duals in Golly, with the same neighbours as JETCARP’s (cells sharing an edge or a vertex: octagons 8 and squares 4 on 4.8.8, squares 12 and triangles 9 on 3.3.3.4.4), and found spaceships in Life-like rules on 14 of the 16, among them every Archimedean tiling. EricG named the rules but not the ships: on 4.8.8, “many of the B2 rules” and B2/S346; on 3.12.12, B2/S2 (“generates lots of spaceships”) and B26/S3569 and its variants; on 4.6.12, B2/S2; on 3.4.6.4, B3468/S239 and B346/S239; on 3.3.3.4.4, B3/S23 and other B3 rules, B36/S23 and B3/S2489; on 3.3.3.3.6, rules such as B37/S247,10; and on 3.6.3.6 and 3.3.4.3.4, Life itself. EricG’s pattern files were shared from a Google Drive folder that no longer opens. JETCARP’s six claimed Archimedean ships run in none of the named rules: the 3.4.6.4 ship needs S5 and cannot have B4 or B6, the 3.3.3.4.4 ships need births on 4 and the named ones are all B3 rules, and the 3.3.3.3.6 ship needs S5 and S6 and cannot have S4. The 4.8.8 and 3.12.12 ships do run in the B2 and B26 rules EricG describes, so they are flagged.

In 2014 a Code Golf challenge asked for Life (B3/S23) on any grid but a regular one, with vertex-sharing neighbours (Code Golf 2014). Peter Taylor found only oscillators on 3.4.6.4. Kevin L ran a tiling of hexagons, squares and triangles whose repeating unit, by its code, is one hexagon, two squares and two triangles, as in the 2-uniform tiling [3.4².6; 3.6.3.6], and posted a period-20 spaceship found by Martin Büttner. The page does not name the tiling, and its rule is stated only in a comment copied from an earlier answer, but the challenge asked for Life. A JETCARP hunt of 500,000 Life soups on each of the two tilings of that type found no ship on k2-006 and, on k2-007, a period-20 spaceship of 8 cells moving one lattice step per period (c/20) in about one soup in nine, so Büttner’s tiling was very likely k2-007 and Büttner’s ship very likely this one. It is the earliest spaceship on a k-uniform tiling (k of 2 or more) that we know of. JETCARP’s claimed ships on k2-006 and k2-007 are of other periods and run in other rules.

H. S. Guttesen studied Life (B3/S23) on six Archimedean lattices and found no gliders on 4.8.8, 4.6.12, 3.12.12 or 3.3.3.3.6 (Guttesen 2026); JETCARP’s ships there are in other rules. We found no other report of Life-like spaceships on k-uniform tilings.

Claim (to our knowledge): Life on the 2- and 3-uniform tilings. In November 2026 JETCARP ran a census of Life itself (B3/S23, touching neighbours) on all 92 Archimedean, 2-uniform and 3-uniform tilings, 50,000 random soups on each (Findings). By the searches above, Life has not been reported on any 3-uniform tiling before, nor on any 2-uniform tiling but k2-007, where Büttner’s ship was very likely found. Other rules have been run on one 2-uniform tiling, k2-001 ([3.4.6.4; 4.6.12]): a 2017 program described as “Conway’s Game of Life on a k-uniform tiling”, which counts only edge neighbours and scales its thresholds to each tile’s number of sides, so is not B3/S23 (Gillespie and Kobayashi 2017), and 2024 videos in B26789/S2345 and in rules not stated (Tessellation Automata 2024). Neither reports a spaceship there, and the census found no Life ship on k2-001. The census finds Life spaceships on 19 of the 61 3-uniform tilings and 5 of the 20 2-uniform ones. After the same checks as the candidates above, 26 of its objects are single ships with no flag, on 2 of the 2-uniform and 8 of the 3-uniform tilings, and to our knowledge they have not been reported before; 13 of them are large ships of k3-055 that may share a common engine. Twelve more passed the same checks but are flagged: ten are so common on their tiling that anyone who ran Life there would see them at once, although we know of no one who has, and two lie on tilings where others have run Life (3.3.4.3.4 and k2-007). Everything else the census found is a known ship, two or more smaller ships flying together, or a smaller ship with a passenger.

Not claimed.

• Guttesen’s gliders. EricG reported spaceships in Life on the kagome (3.6.3.6) and snub square tilings in 2013 (EricG 2013) without describing them. Guttesen described the small gliders themselves and built a kagome glider gun, first in Code Golf answers in November 2024 and then in a paper (Guttesen 2024; Guttesen 2026), and we call them Guttesen’s gliders after that description. In May 2024 a YouTube channel had also shown Life gliders on the snub square tiling (Tessellation Automata 2024); we have not compared them with Guttesen’s. JETCARP’s searches found both independently: its kagome ship is exactly Guttesen’s glider g, and its snub-square ship matches Guttesen’s figure. Ten catalogue entries turned out to be pairs of ships flying side by side without touching: eight pairs of Guttesen’s glider g, one pair of the snub-square glider and one pair of a 3.6.3.6 ship. All Life candidates on 3.6.3.6 were such pairs. In Life on 3.3.4.3.4, JETCARP also found two larger ships built around Guttesen’s glider, of periods 16 and 24; we found no earlier report of them, but they are that glider’s relatives and flagged as such.
• Ships on isohedral tilings. The 81 isohedral types have only 11 neighbour graphs, those of the Laves tilings (see Findings): 57 types are the square, hexagonal or triangular grid in another drawing, and IH27–IH29 are the Cairo tiling. Among the drawn families, the brick, herringbone and lizard tilings likewise behave as hexagons, the quadrilateral, glide and four-fold tilings as squares, and the Pythagorean tiling as 4.8.8. Every ship JETCARP found on an isohedral type is a known ship of the square or triangular grid, such as Conway’s glider, and results on an isohedral type are presented as results on its Laves tiling.
• Ships of simpler tilings. Eight ships found on 3-uniform tilings run unchanged on a 2-uniform tiling or on 3.6.3.6, and eight more, among them five found in strips of squares and triangles, run with the same live tiles on 3.3.3.4.4 or on a 2-uniform tiling; each is claimed only on the simplest tiling it runs on.
• The same ship catalogued twice. 388daffd is d8692b4b, and cf8efa2e is 1a403313: the same live tiles at every generation, at positions with other neighbour counts around them.
• The known Life ships of the census. Conway’s glider and spaceships; Guttesen’s two gliders, also in the kagome corridors of three 3-uniform tilings; the period-2 ship on 3.3.3.4.4, the only Life ship the census found there, which is probably the “common spaceship (although it only travels horizontally)” EricG reported in 2013; and the period-20 ship on k2-007, very likely Büttner’s. Neither of the last two could be compared cell for cell, since EricG’s patterns are offline and Büttner’s animation could not be read. The lightweight spaceship also runs in the strips of squares of k3-010, and the census found it there too.

The full list is in Findings. See also Life-like rules and Regular and Archimedean tilings.

5. Sandpiles on the monotiles and across the tiling catalogues

Claim (to our knowledge). JETCARP is the first to show sandpile identities and large single-source sandpiles on the hat and spectre monotiles, on the k-uniform tilings with k of 2 or more, and on the eight Laves tilings that are not regular grids. The last are what JETCARP’s 81 isohedral types amount to: a sandpile sees only the neighbour graph, and the isohedral types have only the 11 graphs of the Laves tilings (see Findings), so a result on, say, IH21 is a result on the floret pentagonal tiling.

Evidence. Identities have been computed on triangular, hexagonal and Penrose grids (Fersula, Noûs and Perrot 2020); single-source piles have a long literature on the square grid (Ostojic 2003; Pegden and Smart 2013). No sandpile work on the hat or spectre was found at all. Identities on the hexagonal and 4.8.8 grids also appear in Eli T. Johnson’s 2019 master’s thesis at the University of Washington (Johnson 2019), so 4.8.8 is excluded.

Not claimed. The doubling method JETCARP uses for very large piles, which follows directly from the abelian property and is presumably known. See The Abelian sandpile.

6. Tilings as a dimension of an exploratory search

Claim (to our knowledge). JETCARP’s exploratory search is the first to treat the tiling itself as a search dimension: it explores tiling, rule family, rule and starting pattern together, over about 1,200 periodic and aperiodic tilings and 22 rule families in one archive. (Fewer of the tilings are distinct as neighbour graphs: the 81 isohedral types among them have only 11.) Its first full run covered about 15 million runs.

Evidence. The method’s parts are established. The archive keeps the best few runs per niche, in the manner of MAP-Elites quality-diversity search (Mouret and Clune 2015), which Faldor and Cully applied to Lenia (Faldor and Cully 2024). Its score is a small model fitted to human keep/maybe/drop ratings of animated clips, the general technique of learning from human preferences (Christiano et al. 2017); in Picbreeder people chose directly, with no model in between (Secretan et al. 2008; 2011). Jimmie Rodgers and Emily Teich rated the first two rounds together and Jimmie Rodgers the last two, so both their eyes for what is beautiful are built into the score. Other automated discovery in artificial life uses learned goal spaces (Reinke, Etcheverry and Oudeyer 2020) or foundation models in place of human judgement (Kumar et al. 2025). Earlier cellular automaton searches of this kind work on one substrate, such as Lenia (Chan 2019); searches over several tilings had fixed goals, such as gliders on three aperiodic tilings (Edmond 2026) or Life on six Archimedean lattices (Guttesen 2026).

The search will be described in full in Search methods.

7. One engine for every family on every tiling

Claim (to our knowledge). No earlier program runs as many cellular automaton families (Life-like, Generations, Larger than Life, JACA, layered, turmites, WireWorld, cyclic, Greenberg–Hastings, rock-paper-scissors, Hodgepodge, forest fire, Lenia, sandpiles, priority tables and rule tables) on as many classes of tiling (lattices, 1,248 k-uniform tilings, 81 isohedral types with their 11 Laves neighbour graphs, drawn tiles, and the Penrose, hat and spectre tilings) with one neighbour model, tested for agreement across thread counts and between CPU and GPU.

Evidence. Breadth is the contribution, not any one family on any one tiling: Ready runs arbitrary rules on meshes (Ready); HatLife ran Life-like, Larger than Life-style and WireWorld rules on the hat (Trevorrow 2023); Edmond ran Generations and priority-table rules on the hat and spectre (Edmond 2026); Life has long been studied on Penrose tilings (Owens and Stepney 2010). Our search found no aperiodic-tiling version of the cyclic, Greenberg–Hastings, rock-paper-scissors, Hodgepodge or forest-fire rules, and no turmites on the hat or spectre, but these are direct applications of known rules to known graphs, and we do not count them as discoveries. See How JETCARP generalises automata.

What we do not claim

• Age colouring, including colouring cells by how long they have been alive and fading destroyed cells: Chris Rowett’s LifeViewer and other programs did this first (LifeWiki: LifeViewer; Rowett: LifeViewer).
• The two-parent hexagon rules (HexW, HexW3): Wolfram’s (Wolfram 2002).
• Life gliders on the kagome and snub square tilings, and the pairs of them that JETCARP’s catalogue first listed as ships: reported by EricG in 2013 and described by Guttesen in 2026 (EricG 2013; Guttesen 2026).
• Spaceships on Archimedean tilings as such: EricG found them on every Archimedean tiling in 2013. Only particular ships are claimed.
• Spaceships on isohedral tilings: all are known ships of the square or triangular grid.
• The hat glider: it is James Edmond’s hat glider B in another table. With B’s states renamed, the two tables give the same evolution cell for cell; JETCARP’s search found it again, and JETCARP’s only addition is a check that it travels a million rings of tiles on a sliding window, where Edmond’s certificates already prove it immortal (Edmond 2026; see Priority rules and Findings).
• “The first cellular automata on aperiodic tilings”: Life on Penrose tilings was studied from 2005, and Goucher found the first aperiodic glider in 2012 (Goucher 2012).
• “The first matter–antimatter Life”: see JACA above.

Checks still to do

Done in November 2026: the re-verification on the release engine, the lattice-equivalence, compound and cross-tiling checks, the comparison of JETCARP’s kagome and snub-square ships with Guttesen’s figures, and the side-by-side run of the hat glider and Edmond’s glider B (see Findings). Before the claims above are final, and before the paper:

• Ask on the ConwayLife forums, when the results are posted there, whether any of the spaceship candidates have been seen before, and ask EricG whether the 2013 Tiling Project patterns can be shared again, so the flagged 4.8.8 and 3.12.12 ships, and the claimed Archimedean ones, can be compared with EricG’s.
• Find Martin Büttner’s 2014 period-20 ship, confirm its tiling and rule, and compare it cell for cell with the census’s period-20 ship on k2-007, which is very likely Büttner’s.
• Compare the census’s 3.3.3.4.4 ship with EricG’s, and look more closely at the large Life ships of k3-055, which may share a common engine.
• Compare the kagome and snub-square ships with Guttesen’s configurations cell for cell, once they are published.
• Extend the equivalence survey to the k-uniform tilings with k from 4 to 6.
• Re-run the key searches just before publication.

Credits

These findings were made with JETCARP by Jimmie Rodgers. The evolutionary glider search is James Edmond’s method, reimplemented. Emily Teich and Jimmie Rodgers rated the clips that taught the exploratory search what to show.