Cellular automaton simulation programs by supported rulespaces

From LifeWiki
Jump to navigation Jump to search

This is an set of tables of multiple cellular automaton simulator programs with the rulespaces they natively support.

Grids

Euclidean regular

{∞}

One-dimensional cellular automata, run on the cells of an apeirogon.

2-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
1D range 1[subset 1] range 1[subset 1] No ? ? range ?-?[verify 1] ? ? ? range 0-?
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
1D range 1[subset 1] range 1[subset 1] No ? ? range ?-?[verify 1] ? ? ? range 0-?[verify 1]
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
1D range 1 range 1 No ? ? range ?-? ? ? ? range 0-?
n-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
1D range 1[subset 2] range 1[subset 2] No ? ? range ?-?[verify 1] ? ? ? range 0-?
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
1D range 1[subset 2] range 1[subset 2] No ? ? range ?-?[verify 1] ? ? ? range 0-?[verify 1]
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
1D range 1[subset 2] range 1[subset 2] No ? ? range ?-? ? ? ? range 0-?

{4,4}

Two-dimensional cellular automata, run on the cells of a square grid.

2-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
von Neumann range 1-500[n 1] range 1-500[n 1] range 1[subset 3] range 1-? ? range 1-10[exclude 1] ?[verify 2] range 1-2[subset 4] range 1 No
Moore range 1-500[n 1] range 1-500[n 1] range 1-5[n 1]
range 1-7[exclude 2] 		range 1-? ? range 1-10[n 1][exclude 1] range 1 range 1-2[subset 4] range 1 No
cross range 1-500 range 1-500 No range 1-? ? No ?[verify 2] range 1-2[subset 4] No No
saltire range 1-500 range 1-500 No range 1-? ? No ?[verify 2] range 1-2[subset 4] No No
star range 1-500 range 1-500 No range 1-? ? No ?[verify 2] range 1-2[subset 4] No No
hash range 1-500 range 1-500 No range 1-? ? No ?[verify 2] range 1-2[subset 4] No No
checkerboard range 1-500 range 1-500 No range 1-? ? No ?[verify 2] range 1-2[subset 4] No No
L2 range 1-500 range 1-500 No range 1-? ? No ?[verify 2] range 1-2[subset 4] No No
circular range 1-500 range 1-500 No range 1-? ? No ?[verify 2] range 1-2[subset 4] No No
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
range 1
von Neumann 		Yes[subset 3] Yes[subset 3] Yes[subset 3] Yes[subset 5] ? Yes[subset 5] ? ? Yes[subset 3] No
range 1
Moore 		Yes Yes Yes Yes ? Yes[subset 5] ? ? Yes No
exploded
Moore 		No No C2E1
C1E3 		C2E1
C1E3 		? ? ? ? No No
range 2
von Neumann 		No[emulate 1] No[emulate 1] Yes Yes ? ? ? ? No No
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Margolus No[emulate 1] Yes[exclude 3] No Yes ? Yes ? ? No No
range 1
von Neumann 		Yes Yes No Yes[subset 5] ? Yes[subset 5] ? ? No No
range 1
Moore 		Yes Yes No Yes[subset 5] ? Yes[subset 5] ? ? No No
range 2
von Neumann 		No[emulate 1] No[emulate 1] No Yes[subset 5] ? ? ? ? No No
Custom OT
neighbourhood 		range 1-500 range 1-500 No range 1-? ? No ? range 1-2 No No
Naive rules No[emulate 1] No[emulate 1] No Yes ? ? ? ? No No
3-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
BSFKL Yes[subset 2] Yes[subset 2] Yes Yes[subset 2] ? ? ? ? ? No
range 1
Moore 		Yes[subset 2] Yes[subset 2] Yes[subset 2] Yes[subset 2] ? ? ? ? ? No
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
range 1
Moore 		Yes[subset 2] Yes[subset 2] Yes[subset 2] Yes[subset 2] ? ? ? ? ? No
16-state
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Partitioned cellular automata Yes[subset 2] Yes No No ? ? ? ? ? No
n-state
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Cyclic No No No No ? range 1-10
states ?-? 		range ?-?
states ?-? 		? ? No
Rock-paper-scissors No No No No ? ? range ?-?
states ?-? 		? ? No
n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Generations states 2-255 states 2-255 states 2-? states 2-?[verify 3] ? states 2-?[verify 3] states 2-50 ? ? No
Extended Generations Yes[subset 2] Yes[subset 2] states 2-?[exclude 4] states 2-?[verify 3] ? ? ? ? ? No
Deficient Yes[subset 2] Yes[subset 2] states 2-?[exclude 4] states 2-?[verify 3] ? ? ? ? ? No
Alternating Yes[subset 2] rules 2 Yes[subset 2] ? ? ? ? ? ? No
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Generations states 2-255 states 2-255 states 2-? states 2-?[verify 3] ? Weighted Generations
states 2-?[verify 3] 		? ? ? No
Extended Generations Yes[subset 2] Yes[subset 2] states 2-?[exclude 4] states 2-?[verify 3] ? ? ? ? ? No
Deficient Yes[subset 2] Yes[subset 2] states 2-?[exclude 4] states 2-?[verify 3] ? ? ? ? ? No
Alternating Yes[subset 2] rules 2 Yes[subset 2] ? ? ? ? ? ? No
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Generations states 2-255 states 2-255 No ? ? ? ? ? ? No
Extended Generations Yes[subset 2] Yes[subset 2] No ? ? ? ? ? ? No
Deficient Unclear how deficient rules can generalize to non-isotropic rules
Alternating Yes[subset 2] rules 2 No ? ? ? ? ? ? No

{6,3}

Two-dimensional cellular automata, run on the cells of a hexagonal grid.

2-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Hexagonal Cell Life32 WolframAlpha
tripod range 1-500 range 1-500[n 1] No ? ? ? ? range 1-2[subset 4] ? No
asterisk range 1-500 range 1-500 No ? ? ? ? range 1-2[subset 4] ? No
hexagonal range 1-500[n 1] range 1-500[n 1] range 1 ? ? ? range 1 range 1-2[subset 4] ? No
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Hexagonal Cell Life32 WolframAlpha
range 1
hexagonal 		Via MAP strings Yes Yes Yes ? Yes[subset 5] ? ? ? No
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Hexagonal Cell Life32 WolframAlpha
range 1
hexagonal 		Yes Yes No Yes[subset 5] ? Yes[subset 5] ? ? ? No
Custom OT
neighbourhood 		range 1-500 range 1-500 No range 1-? ? No ? range 1-2 ? No
n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Hexagonal Cell Life32 WolframAlpha
Generations states 2-255 states 2-255 states 2-? states 2-?[verify 3] ? states 2-?[verify 3] states 2-50 ? ? No
Extended Generations Yes[subset 2] Yes[subset 2] No ? ? ? ? ? ? No
Deficient Yes[subset 2] Yes[subset 2] No ? ? ? ? ? ? No
Alternating Yes[subset 2] rules 2 Yes[subset 2] ? ? ? ? ? ? No
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Hexagonal Cell Life32 WolframAlpha
Generations states 2-255 states 2-255 states 2-? states 2-?[verify 3] ? Weighted Generations
states 2-?[verify 3] 		? ? ? No
Extended Generations Yes[subset 2] Yes[subset 2] No ? ? ? ? ? ? No
Deficient Yes[subset 2] Yes[subset 2] No ? ? ? ? ? ? No
Alternating Yes[subset 2] rules 2 Yes[subset 2] ? ? ? ? ? ? No
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Hexagonal Cell Life32 WolframAlpha
Generations states 2-255 states 2-255 No ? ? ? ? ? ? No
Extended Generations Yes[subset 2] Yes[subset 2] No ? ? ? ? ? ? No
Deficient Unclear how deficient rules can generalize to non-isotropic rules
Alternating Yes[subset 2] rules 2 No ? ? ? ? ? ? No

{3,6}

Two-dimensional cellular automata, run on the cells of a triangular grid.

2-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Triangular Cell Life32 WolframAlpha
edges range 1[subset 6] range 1 No range 1 ? ? range 1 ? ? No
inner range 1[subset 6] range 1 No range 1 ? ? No ? ? No
outer range 1[subset 6] range 1 No range 1 ? ? No ? ? No
vertices range 1[subset 6] range 1 No range 1 ? ? No ? ? No
Moore range 1-500 range 1-500[n 1] No range 1-? ? ? range 1 ? ? No
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Triangular Cell Life32 WolframAlpha
Custom OT
neighbourhood 		range 1-500 range 1-500 No range 1-? ? No ? ? ? No
n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Triangular Cell Life32 WolframAlpha
Generations states 2-255 states 2-255 No ? ? ? states 2-50 ? ? No
Extended Generations No No No ? ? ? ? ? ? No
Deficient No No No ? ? ? ? ? ? No
Alternating No rules 2 No ? ? ? ? ? ? No
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Triangular Cell Life32 WolframAlpha
Generations states 2-255 states 2-255 No ? ? ? ? ? ? No
Extended Generations No No No ? ? ? ? ? ? No
Deficient Unclear how deficient rules can generalize to non-isotropic rules
Alternating No rules 2 No ? ? ? ? ? ? No

{4,3,4}

Three-dimensional cellular automata, run on the cells of a cubic grid.

2-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
von Neumann range 1[emulate 2] No No ? ? ? range 1 No ? No
corners range 1[emulate 2] No No ? ? ? No No ? No
edges range 1[emulate 2] No No ? ? ? No No ? No
hexahedral range 1[emulate 2] No No ? ? ? No No ? No
Moore range 1[emulate 2] No No ? ? ? range 1 No ? No
n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
Generations No No No No No No states 2-10 No No No

{4,3,3,4}

Four-dimensional cellular automata, run on the cells of a tesseractic grid.

2-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
Moore No No No No No No range 1 No No No
n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
Generations No No No No No No states 2-10 No No No

{3,4,3,3}

Four-dimensional cellular automata, run on the cells of a 24-cell grid.

{3,3,4,3}

Four-dimensional cellular automata, run on the cells of a 16-cell grid.

{4,3,3,3,4}

Five-dimensional cellular automata, run on the cells of a penteractic grid.

2-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
Moore No No No No No No range 1 No No No
n-state extensions of 2-state

All of the cases that are supported for 2-state also support extensions (if both the cases and extensions are themselves natively supported) unless mentioned otherwise.

Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
Generations No No No No No No states 2-10 No No No

Notation extensions

Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
[Rule]History Yes Yes No Yes ? ? ? ? ? No
[Rule]Super Yes Yes No No ? ? ? ? ? No

Rulespaces to investigate

The following rulespaces should be investigated to see if they match up with (or can be considered a subset of) existing rulespaces which are not mentioned, or if they are new rulespaces in their own right and can be added as new table rows.

  • Mirek's Cellebration
    • 1D totalistic
    • 1D binary
    • General binary
    • Neumann binary
    • Rules tables
    • Special rules
    • User DLLs
  • Visions of Chaos
    • 1D Cellular Automata
    • 1D Cellular Automata 2
    • 1D Totalistic Cellular Automata
    • Cascade Cellular Automata
    • Combinations Cellular Automata
    • Extended Neighbourhood Cellular Automata
    • Next Nearest Neighbourhood Cellular Auromata
    • Traffic Cellular Automata
    • Two Steps Back Cellular Automata
    • Two Steps Back Extended Cellular Automata
    • 2D Totalistic Cellular Automata
    • Accretor Cellular Automata
    • Alternating Neighbourhoods Cellular Automata
    • Alternating Neighbourhoods Cellular Automata 2
    • Alternating Neighbourhoods Cyclic Cellular Automata
    • Alternating Neighbourhoods Cyclic Cellular Automata 2
    • Archean Cellular Automata
    • Block Cellular Automata
    • Coupled Cellular Automata
    • Coupled Cellular Automata 2
    • Digital Inkblot
    • History Dependent Cellular Automata
    • History Dependent Cellular Automata 2
    • Hodgepodge Machine
    • Indexed Totalistic Cellular Automata
    • Indexed Totalistic Cellular Automata 2
    • Large Neighbourhood Totalistic Cellular Automata
    • Liquid Crystal Cellular Automata
    • Majority Rule Cellular Automata
    • MergeLife Cellular Automata
    • Multiple Neighbourhoods Cellular Automata
    • Multiple Neighbourhoods Cellular Automata 2
    • Multiple Rules Cellular Automata
    • Nonlinear Voter Model
    • Pinwheels Cellular Automata
    • Rock Paper Scissors Image Cellular Automata
    • Sandpile Automata
    • Self Replicating Loops
    • Smooth Life Cellular Automata
    • Stepping Stone Cellular Automata
    • Stochastic Cellular Automata
    • Tiled Cellular Automata
    • Yin Yang Fire Cellular Automata
    • Zhang Cellular Automata
    • 3D Accretor Cellular Automata
    • 3D Cyclic Cellular Automata
    • 3D Hexagonal Generations Cellular Automata
    • 3D History Dependent Cellular Automata
    • 3D Hodgepodge Machine
    • 3D Rock Paper Scissors Cellular Automata
    • 3D Rule Table Cellular Automata
    • 3D Stochastic Cellular Automata
    • 3D Voxel Automata Terrain
    • 4D Accretor Cellular Automata
    • 4D Cyclic Cellular Automata
    • 4D Hodgepodge Machine
    • 4D Rock Paper Scissors Cellular Automata
  • Misc.
    • "Second-order cellular automata"

Notes

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 Has a simpler notation for the range-1 case

Emulation via script or custom rule

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Can be emulated by a multistate ruletable
  2. ↑ 2.0 2.1 2.2 2.3 2.4 requires 3D.lua

Emulation via generated rule


Excluded subsets

  1. ↑ 1.0 1.1 Consecutive birth/survival transitions (Larger than Life) only for ranges above 2
  2. ↑ Consecutive birth/survival transitions (Larger than Life) only for ranges above 5
  3. ↑ Rules where 0000 becomes something that is not 0000 are disallowed, except in the case where 0000 becomes 1111 and 1111 becomes 0000, where they are instead replaced with an alternating rule
  4. ↑ 4.0 4.1 4.2 4.3 Only range-1 Moore natively supported, and range-1 von Neumann through its notation

As subsets

  1. ↑ 1.0 1.1 1.2 1.3 As a subset of elementary Wolfram CA
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 Requires custom ruletables
  3. ↑ 3.0 3.1 3.2 3.3 3.4 via Moore isotropic non-totalistic notation
  4. ↑ 4.00 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10 4.11 For Java Cell applications, neighbourhoods are manually specified and not systematically generated
  5. ↑ 5.00 5.01 5.02 5.03 5.04 5.05 5.06 5.07 5.08 5.09 5.10 via Weighted Life
  6. ↑ 6.0 6.1 6.2 6.3 Requires the use of a custom CoordCA neighbourhood

Needs verification

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 Possibly as a subset of other supported 1D rulespaces
  2. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 "Large Neighborhood Totalistic Cellular Automata" may allow for this - testing needed
  3. ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 Extended neighbourhoods unknown
Retrieved from "https://conwaylife.com/w/index.php?title=Cellular_automaton_simulation_programs_by_supported_rulespaces&oldid=79559"