JACA: Jimmie’s Annihilating Cellular Automata

JACA is a family of two-sided Life-like rules. Cells are positive, negative or empty; each sign grows by its own birth/survival rule; and wherever the two signs touch, they destroy each other. Started from a mixed soup, the two signs sort themselves into territories separated by glowing, shifting fronts, and the fight between them can last thousands of generations. JACA is Jimmie Rodgers’s idea and is introduced in JETCARP.

What it is

Each cell holds one of three values: +1, −1 or 0 (empty), a balanced ternary digit. Every generation is computed from the current state in three steps:

1. Contact. A live cell with at least one neighbour of the opposite sign is a contact cell. Contact cells are destroyed: they are empty next generation.
2. Blast. With a blast radius N greater than 0, every cell within N neighbourhood steps of a contact cell is destroyed too, whatever its sign. With the default blast 0, only the touching cells go.
3. Everything else follows its own sign’s rule. A +1 cell survives if its number of +1 neighbours is in the +1 rule’s survival list; an empty cell is born +1 if its number of +1 neighbours is in the +1 rule’s birth list; and likewise for −1. Each sign counts only neighbours of its own sign. An empty cell that both signs would fill stays empty: the two births cancel.

Two properties make the family easy to reason about. A world that contains only one sign runs that sign’s plain birth/survival rule exactly, so JACA B3/S23 with only +1 cells is Conway’s Life. And the two signs can follow different rules: JACA +B3/S23 -B36/S23 sets Life against HighLife.

What emerges depends on the rules, the tiling and the blast radius. Among the behaviours found so far:

• Territory wars. Seeds-like rules (birth on 2, little survival) in mixed soups form territories that merge and push along their fronts until one sign holds the whole grid, on every tiling tried.
• Rainbow fronts. In rules whose territories go still while their fronts stay active, colouring by age turns every front into a rainbow, as in the figure above.
• Trenches. A blast radius of 1 to 3 leaves a strip of no-man’s-land between territories: bands, beads, ropes, collapsing loops.
• Annealing. With births on 3 or more, fronts become smooth and move to reduce their curvature, like grain boundaries in a cooling metal.
• Two different rules. Bubbles of one rule growing in the other’s still sea, or still crystal against noise, with either side winning.

Where it came from

JACA is Jimmie Rodgers’s idea, from November 2026; it first appeared in JETCARP’s predecessor CART on 8 November 2026. Each of its ingredients has a precedent, and we credit them here:

• Two-player Life. Mark Levene and George Roussos’s two-player game of life (2003) has black and white tokens; opponents weaken each other’s survival through a difference count, and a tie at birth is settled by a coin flip (Levene and Roussos 2003).
• +1, −1 and 0, with cancelled births. The CodinGame bot game “Game of Life or Death”, described on the Unsupervision Blog in November 2025, encodes the two players as 1 and −1; each side treats the other’s cells as dead, and a cell both sides would switch on stays dead (Unsupervision Blog 2025). This is the closest precedent for JACA’s encoding, own-sign counting and cancelled births. Touching cells of opposite sides are not destroyed there.
• Matter and antimatter Life. In September 2018 KittyTac proposed, on the ConwayLife.com forums, a Life with two kinds of cell where contact turns both cells into energy, and wildmyron implemented it as the “Energetic” rule, in which the energy decays into photons (KittyTac and wildmyron 2018; LifeWiki: Rule:Energetic). This is the closest precedent for annihilation on contact. There the products are part of the state and can create cells, and both kinds follow one fixed rule.
• Physics. Opposite particles that annihilate when they meet, A + B → 0, are a classic problem in the physics of diffusion (Toussaint and Wilczek 1983); Chopard and Droz treat such reaction–diffusion processes with cellular automata (Chopard and Droz 1998).

How JETCARP runs it

Notation

The blast radius runs from 0 to 64. Rules with birth on 0 are refused. Counts of 10 or more are written with commas, as in other B/S rules.

On any tiling

JACA uses only neighbour counts and neighbourhood steps, so it runs on every tiling (see How JETCARP generalises automata); the blast radius is measured in steps of the automaton’s own neighbourhood. It runs on the CPU; there is no GPU or HashLife version yet.

Seeds, colours and counts

A JACA field is stored as a three-state field (states 1 and 2 are +1 and −1), so drawing, scenes and scripts treat it like any other multi-state rule. The usual start is a mixed soup ({"signed": {"density": 0.3, "negative": 0.5}}: 30% of cells live, half of them negative); a halves start puts +1 cells on the left and −1 on the right. Each sign has its own palette (palette and palette_neg), coloured by age. Destroyed cells glow briefly and fade; the glow is drawn only and is not part of the state or its hash. The app’s card shows the number of cells of each sign and how many were touching and destroyed; the world status that scripts and the MCP server read also reports cancelled births.

Presets

The Quick Start’s JACA family has 5 named rules and 71 presets. Each preset is a whole scene: tiling, neighbourhood, a rule per sign, blast radius, start and palette pair. Together they cover 24 tilings, from squares and hexagons through the Archimedean and k-uniform tilings to two isohedral tilings, both Penrose tilings, the hat and the spectre. (For a rule, the isohedral IH28 is the Cairo tiling and IH41 the square grid, and the brick, herringbone and Pythagorean presets play on the hexagonal, hexagonal and 4.8.8 graphs; see Isohedral tilings.) They came from a six-hour search over about 130,000 configurations: random rule pairs, mutations and crossovers of the best, and transplants of good pairs to other tilings, scored on balance between the signs, contact along fronts, territory changing hands and activity, then reviewed by eye as contact sheets.

What is new here

Each ingredient of JACA has been published before, as the list above shows, and we do not claim “the first signed Life” or “the first matter–antimatter Life”. To our knowledge, JACA’s particular combination 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 one sign is alone; and all of this on any periodic or aperiodic tiling. The searches behind this statement, and their known gaps (MCell’s weighted rules and parts of the ConwayLife forums were not searched), are described in What is new in JETCARP.

The colouring is not part of the claim: colouring cells by age and fading destroyed cells have precedents in other programs.

Try it

• Quick Start, family JACA: JACA Life, JACA Life vs HighLife, JACA war on the hat tiling, JACA rainbow fronts (Cairo), JACA bead borders (square, blast 1), and the other presets.
• jetcarp run docs/scenes/automata/jaca-hat-war.json --gens 3000 --png hat-war.png
• Try a halves start with two different rules, and watch which front advances.

References

• Levene and Roussos 2003
• Unsupervision Blog 2025
• KittyTac and wildmyron 2018; LifeWiki: Rule:Energetic
• Toussaint and Wilczek 1983; Chopard and Droz 1998