Glossary

The terms this book uses, in alphabetical order, each with the page that explains it.

A

Affects others. An automaton’s setting for sharing a field: on, it acts on the shared field with the other automata of its kind; off, it keeps a private field drawn alongside. On by default for binary rules. See Several automata at once.

Age. The number of generations a cell has been in its current state. Shown by age colouring and included in the state hash.

Agent. An automaton that moves over the tiling instead of updating every cell: an ant or turmite.

Annihilation. In JACA, the destruction of live cells of opposite sign that touch, and of every cell within the blast radius of them.

Aperiodic tiling. A tiling with no translation symmetry: it never repeats. JETCARP has the Penrose kites and darts and rhombs, and the hat and the spectre.

Archimedean tiling. An edge-to-edge tiling by regular polygons in which every corner looks the same, named by its vertex configuration, such as 4.8.8. There are eleven, three of them the regular tilings. See Regular and Archimedean tilings.

Atlas. The selection of confirmed, high-scoring runs from the exploratory search that the Quick Start menu offers, written into the library by jetcarp quickstart publish; its entries are named atlas:….

B

B/S notation. A Life-like rule written as the neighbour counts for birth and survival: B3/S23 is Life. See Rule notation.

B0 rule. A rule in which a dead cell with no live neighbours is born, so empty space switches on. See Life-like rules.

Background. A palette’s colour for empty cells. See also stage.

Blast radius. In JACA, how many neighbour steps around each annihilation are also cleared.

Boundary. What lies past the edge of a finite grid: dead (missing cells, counted as empty), wrap (the grid is a torus) or live (counted as alive). Aperiodic patches have dead edges.

Bounded soup search. Soups run on a finite grid of any tiling. See Search methods.

C

Alias. An old id of a record, kept so that lookups by it still find the record: an id from before a geometry change. See Library format.

Canonical form. A pattern written from its canonical starting phase, in its canonical orientation, at the origin: the form its identity is computed from, so one pattern has one id however it was found or stored. See Library format.

Catalogue (catalog). The SQLite database of verified patterns, ant runs, Quick Start entries and jobs, library.sqlite in the data folder; also called the pattern library. See The pattern library and Library format.

Cell. One tile of the tiling, holding a state.

Census. A run of many rules from the same soups, classifying each rule as died, frozen, oscillating, active or exploded. See Search methods.

Checkpoint. The saved state of a job, written after every step, from which it can be resumed.

Colour by. An automaton’s colouring setting: auto, age, state or row. See Palettes.

Command. One change to a world: add an automaton, paint cells, step, reseed and so on. A scene keeps the log of commands since its start. See Scene file format.

Compound. A “spaceship” that turns out to be two or more smaller ships travelling together. See Findings.

Congruence. Two ships are congruent, and counted as one object, if one rotation, reflection and translation carries the live tiles of one onto the other’s at every generation. See What is new in JETCARP.

Content-addressed file. A file named by the SHA-256 of its bytes, so the same bytes are stored once. The library’s media files are kept this way. See Library format.

Content id. A library record’s id: 32 hexadecimal digits of SHA-256 over its identity text and its tiling’s geometry pin. Its first 8 digits are the short id. See Library format.

Continuous field. A field whose cells hold a value between 0 and 1, as in Lenia.

D

Degree. The number of neighbours a tile has, in the chosen neighbourhood. It varies from tile to tile on mixed and aperiodic tilings. See Tilings as neighbour graphs.

Derivative. A ship that is a smaller ship pulling a passenger along, or a bound pair of gliders.

Displacement. How far a spaceship moves in one period, as a lattice vector.

E

Edge neighbours. Tiles that share a stretch of edge: the von Neumann neighbourhood on squares. Written with a V on a B/S rule. See How JETCARP generalises automata.

Elementary rule. One of Wolfram’s 256 one-dimensional rules, drawn row by row (W30). See Elementary rules.

Explore. JETCARP’s exploratory, quality-diversity search over tilings, rules and starting patterns (jetcarp search explore). See Search methods; its runs are kept as described in Search runs.

F

Family. A kind of rule with its own notation: Life-like, Generations, Larger than Life, turmites, and so on. Also used of tilings (square, hex, spectre, …).

Field. The array of cell values an automaton works on: binary, multi-state, height (sandpile) or continuous. Several automata can share one.

Flag A, Flag B. On the Findings page, spaceship candidates that are most likely already known (A), or need checking before any claim (B).

G

Generation. One step of time, in which every cell’s next state is computed from the current states. Agents and some automata take several steps per generation.

Generations. The family of rules with dying states, written B2/S/C3. See Generations.

Geometry pin. A hash of the geometry a library record ran on: a periodic tiling’s unit cell (its polygons and neighbour offsets), or for an aperiodic family a fixed reference patch (level 4), whatever the record’s level. Every record stores one; when the engine’s pin differs, the record is flagged for re-verification. Not to be confused with the test pins. See Library format.

Glider. A small spaceship. On aperiodic tilings, a pattern that travels with a constant speed and heading although it never repeats exactly.

H

HashLife. An algorithm that jumps a pattern far ahead by remembering how blocks of cells evolve. See HashLife and very long runs.

Highway. A turmite’s endless, repeating, travelling structure, such as the one Langton’s ant builds after 9,977 steps. JETCARP proves highways exactly. See Langton’s ant and turmites.

Host (background host). The part of JETCARP that keeps scenes running with no app window, as a live wallpaper or screensaver. See Wallpapers, screensavers and the background host.

HROT. “Higher-range outer-totalistic”: the Larger than Life notation R5,C2,S33-57,B34-45.

Hunt (soup hunt). The fast search of small random soups on an unbounded plane. See Search methods.

I

Identity text. What a pattern’s content id is the hash of: its cell-state model, neighbourhood, tiling, class, period, displacement and canonical evolution, as lines of text in a fixed form (jetcarp-pattern-v3). See Library format.

Isohedral tiling. A tiling by one tile in which a symmetry carries any tile to any other. Grünbaum and Shephard sorted them into 93 types, IH1 to IH93; JETCARP has the 81 that can be told apart by the tile’s shape alone. See Isohedral tilings.

J

JACA. Jimmie’s Annihilating Cellular Automata: cells of sign +1 and −1, each following its own B/S rule, destroyed where they meet. See JACA.

Job. A search stored in the catalogue with its settings, progress and checkpoint, so that it can be stopped and resumed. See Search methods.

K

k-uniform tiling. An edge-to-edge tiling by regular polygons with exactly k kinds of corner. JETCARP has all 1,248 with k up to 6, from Brian Galebach’s catalogue. See k-uniform tilings.

L

Larger than Life. Life-like rules over a larger range of neighbours. See Larger than Life.

Lattice. The translations that map a periodic tiling onto itself; a lattice step is one of them, the unit in which a spaceship’s speed is given.

Laves tiling. The dual of a uniform tiling. Every isohedral tiling has the neighbour graph of one of the eleven Laves tilings, which is why JETCARP’s 81 isohedral types give rules only eleven worlds. See Findings.

Layer, layered rule. The tiles at one graph distance from a seed; a layered rule writes one layer per generation from the layer before. See Layered rules.

Level. The number of substitution steps used to build an aperiodic patch; higher levels are larger.

Life-like rule. A two-state rule that counts live neighbours, written in B/S notation. See Life-like rules.

M

MAP-Elites. A quality-diversity search method that keeps the best solutions in each niche of a behaviour space; the basis of jetcarp search explore.

MCP. The Model Context Protocol, through which AI assistants can drive JETCARP (jetcarp mcp). See MCP tools.

Mover. A pattern that travels across an aperiodic tiling; it is verified to a distance. See Search methods.

Multi-state field. A field whose cells hold a state number, for rules with more than two states.

My finds. The Quick Start entries you add yourself, from patterns, runs and scenes, named find:<id>.

N

Neighbour graph. A tiling seen as tiles and the links between neighbours, which is all a counting rule sees. See Tilings as neighbour graphs.

Neighbourhood. Which tiles count as a cell’s neighbours: touch or edge.

Niche. In the exploratory search, a combination of rule family, group of tilings and behaviour class; the archive keeps the best few runs of each.

Notation. The text that names a rule, such as B3/S23 or Cyclic 14/1. See Rule notation.

O

Object finder. The part of JETCARP that splits a field into still lifes, oscillators, spaceships and other objects (jetcarp objects).

Onset. The step at which a turmite’s highway begins.

Operation. One of JETCARP’s named actions (scene.run, search.start, jobs.status, …), the same for the command line, scripts, the app and MCP; jetcarp api list lists them.

Oscillator. A pattern that returns to its starting state after a period, without moving.

P

Pack. A planned format for sharing catalogues and search results, not yet in this release. See Packs.

Palette. A list of colour stops with a background and a stage colour. See Palettes.

Patch. A finite piece of an aperiodic tiling, built to some level.

Pattern library. See catalogue.

Period. The number of generations after which an oscillator, spaceship or highway repeats.

Periodic tiling. A tiling that repeats in two directions: it has a lattice of translations.

Pins. Recorded hashes that JETCARP’s tests compare against: geometry pins for every tiling and dynamics pins for every built-in Quick Start entry. See Reproducibility.

Provenance. A library record’s history: how it was found or imported, by whom, by which search, on which engine and geometry, and when it was checked again. See Library format.

Priority table. James Edmond’s rule family: ordered rows of conditions on neighbour counts, the first matching row deciding the next state. See Priority rules.

Profile (screensaver profile). A named, complete setup for the screensaver: what to show (a scene or a Quick Start entry), and optionally its palette, colouring, reseeding, cell size and speed. See Wallpapers, screensavers and the background host.

Q

Quick Start. The app’s menu of ready-to-run scenes: the built-in classics, entries from packs, the atlas and My finds, all in one table of the library, each named by a handle such as life, atlas:… or find:… (see Quick Start entries).

R

Receipt. A planned record of a verification check on a pack, not yet in this release. See Reproducibility.

Reseed. Putting new cells into a world that has settled, by hand or by an automatic policy. See Reseeding.

Rhai. The scripting language JETCARP runs (jetcarp script). See Scripting (Rhai) API.

Ring. One step of edge-neighbour distance from a starting tile; distances on aperiodic tilings are counted in rings.

Rotation. What a wallpaper or screensaver shows over time: a list of profiles, scenes or Quick Start entries, each with the conditions that end it. See Rotations.

Rule. How a cell’s next state follows from its own state and its neighbours’.

Rule range. Every Life-like or Generations rule in which a pattern runs through exactly the same phases, stored with each catalogued pattern. See Search methods.

Rule-semantics version. The version of what a rule family’s rules mean, raised whenever that meaning changes; every family is at 1 in JETCARP 0.4.0. Every pattern stores its family’s version, and a pattern verified under another version is flagged for re-verification. See Library format.

Rule table. A rule written as a list of explicit transitions. See Rule tables.

Run segment. One of an exploratory search’s Parquet files of run records (runs/part-000001.parquet), a million runs each, written when the runs are sealed and never changed after. See Search runs.

S

Scene. A JSON file that holds a run: tiling, automata, random state and command log. See Scene file format.

Score sidecar. A Parquet file of new scores (scores-<n>/) that rescoring writes beside a run segment instead of rewriting it. See Search runs.

Seed. What an automaton puts on its field at the start: a random soup, one cell, ants, a pile of grains and so on. Also the number that starts a random-number generator.

Settled. A run that has stopped changing, or repeats.

Short id. The first 8 hexadecimal digits of a content id, accepted by commands wherever an id is, when no other record starts with them.

Sighting. A record that a job saw a catalogued pattern.

Sliding window. The few tiles of an infinite aperiodic tiling kept around a moving pattern, rebuilt as it travels.

Soup. A random starting pattern, usually a small square of random cells.

Spaceship. A pattern that returns to its starting shape after a period, moved by a lattice vector. Its speed is written as a fraction of one lattice step per generation, such as c/4, and its direction in the lattice’s own terms: orthogonal along one of the lattice’s shortest steps (on a rectangular lattice, one of its two mirror axes), diagonal halfway between two of them (square and hexagonal lattices only), and oblique otherwise. A lattice with no mirror axes gets no word. The fraction counts steps in the lattice’s basis: the larger of the displacement’s two coordinates, over the period. On a hexagonal lattice, whose basis vectors are 60° apart, that is the convention Golly’s hexagonal rules use, so (1, 1), halfway between two shortest steps, also counts as one step.

Stage. A palette’s colour for the area outside the tiling.

State. The value a cell holds: dead or alive, a number, a height or a level.

State hash. A 64-bit hash of everything that determines a world’s future. Equal hashes mean equal states, in practice. See Reproducibility.

Still life. A pattern that does not change.

Strategy. A kind of search run as a job (hunt, bounded, census, ants, mover, pile, collide, evolve, explore, and reverify, which checks library records again).

Supertile. A cluster of tiles that the substitution rules of an aperiodic tiling treat as one larger tile.

T

Tiling. A covering of the plane by tiles without gaps or overlaps. See the tiling catalogue.

Touch neighbours. Tiles that share an edge or just a corner: the Moore neighbourhood on squares.

Turmite. A Turing-machine-like agent that reads a cell’s colour, writes a new one, turns and steps. Langton’s ant is the simplest. See Langton’s ant and turmites.

Turn string. A one-state turmite written as one turn per colour, such as RL or LLRR.

V

Verified. Of a pattern: run again alone and compared cell by cell with its stored phases for several periods before it is catalogued. Of a mover: verified to a distance, the number of rings it was followed without changing. See Search methods.

Vertex configuration. The polygons around a corner of a tiling by regular polygons, in order: 4.8.8 is a square and two octagons.