Cellular automaton simulation programs by supported rulespaces

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This is an incomplete, messy table 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[n 1] range 1[n 1] No ? ? range ?-?[n 2] ? ? ? range 0-?
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
1D range 1[n 1] range 1[n 1] No ? ? range ?-?[n 2] ? ? ? range 0-?[n 2]
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[n 1] range 1[n 1] No ? ? range ?-?[n 2] ? ? ? range 0-?
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Cell Life32 WolframAlpha
1D range 1[n 1] range 1[n 1] No ? ? range ?-?[n 2] ? ? ? range 0-?[n 2]
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-?

{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 3] range 1-500[n 3] range 1[n 4] range 1-? ? range 1-10[n 5] ?[n 6] range 1-2[n 7] range 1-? No
Moore range 1-500[n 3] range 1-500[n 3] range 1-5[n 3]
range 1-7[n 8] 		range 1-? ? range 1-10[n 3][n 5] range 1 range 1-2[n 7] range 1-? No
cross range 1-500 range 1-500 No range 1-? ? No ?[n 6] range 1-2[n 7] ? No
saltire range 1-500 range 1-500 No range 1-? ? No ?[n 6] range 1-2[n 7] ? No
star range 1-500 range 1-500 No range 1-? ? No ?[n 6] range 1-2[n 7] ? No
hash range 1-500 range 1-500 No range 1-? ? No ?[n 6] range 1-2[n 7] ? No
checkerboard range 1-500 range 1-500 No range 1-? ? No ?[n 6] range 1-2[n 7] ? No
L2 range 1-500 range 1-500 No range 1-? ? No ?[n 6] range 1-2[n 7] ? No
circular range 1-500 range 1-500 No range 1-? ? No ?[n 6] range 1-2[n 7] ? 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[n 4] Yes[n 4] Yes[n 4] Yes[n 9] ? Yes[n 9] ? ? ? No
range 1
Moore 		Yes Yes Yes Yes ? Yes[n 9] ? ? ? No
exploded
Moore 		No No C2E1
C1E3 		C2E1
C1E3 		? ? ? ? ? No
range 2
von Neumann 		Multistate emulation only Multistate emulation only Yes Yes ? ? ? ? ? No
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Margolus Multistate emulation only Yes No Yes ? Yes ? ? ? No
range 1
von Neumann 		Yes Yes No Yes[n 9] ? Yes[n 9] ? ? ? No
range 1
Moore 		Yes Yes No Yes[n 9] ? Yes[n 9] ? ? ? No
range 2
von Neumann 		Multistate emulation only Multistate emulation only No Yes[n 9] ? ? ? ? ? No
Custom OT
neighbourhood 		range 1-500 range 1-500 No range 1-? ? No ? range 1-2 ? No
Naive rules Multistate emulation only Multistate emulation only No Yes ? ? ? ? ? No
3-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
BSFKL Yes[n 10] Yes[n 10] Yes Yes[n 10] ? ? ? ? ? No
range 1
Moore 		Yes[n 10] Yes[n 10] Yes[n 10] Yes[n 10] ? ? ? ? ? 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[n 10] Yes[n 10] Yes[n 10] Yes[n 10] ? ? ? ? ? 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[n 10] 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-?[n 11] ? states 2-?[n 11] states 2-50 ? ? No
Extended Generations Yes[n 10] Yes[n 10] states 2-?[n 12] states 2-?[n 11] ? ? ? ? ? No
Deficient Yes[n 10] Yes[n 10] states 2-?[n 12] states 2-?[n 11] ? ? ? ? ? No
Alternating Yes[n 10] rules 2 Yes[n 10] ? ? ? ? ? ? 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-?[n 11] ? Weighted Generations
states 2-?[n 11] 		? ? ? No
Extended Generations Yes[n 10] Yes[n 10] states 2-?[n 12] states 2-?[n 11] ? ? ? ? ? No
Deficient Yes[n 10] Yes[n 10] states 2-?[n 12] states 2-?[n 11] ? ? ? ? ? No
Alternating Yes[n 10] rules 2 Yes[n 10] ? ? ? ? ? ? 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[n 10] Yes[n 10] No ? ? ? ? ? ? No
Deficient Unclear how deficient rules can generalize to non-isotropic rules
Alternating Yes[n 10] 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 3] No ? ? ? ? range 1-2[n 7] ? No
asterisk range 1-500 range 1-500 No ? ? ? ? range 1-2[n 7] ? No
hexagonal range 1-500[n 3] range 1-500[n 3] range 1 ? ? ? range 1 range 1-2[n 7] ? 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[n 9] ? ? ? 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[n 9] ? Yes[n 9] ? ? ? 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-?[n 11] ? states 2-?[n 11] states 2-50 ? ? No
Extended Generations Yes[n 10] Yes[n 10] No ? ? ? ? ? ? No
Deficient Yes[n 10] Yes[n 10] No ? ? ? ? ? ? No
Alternating Yes[n 10] rules 2 Yes[n 10] ? ? ? ? ? ? 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-?[n 11] ? Weighted Generations
states 2-?[n 11] 		? ? ? No
Extended Generations Yes[n 10] Yes[n 10] No ? ? ? ? ? ? No
Deficient Yes[n 10] Yes[n 10] No ? ? ? ? ? ? No
Alternating Yes[n 10] rules 2 Yes[n 10] ? ? ? ? ? ? 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[n 10] Yes[n 10] No ? ? ? ? ? ? No
Deficient Unclear how deficient rules can generalize to non-isotropic rules
Alternating Yes[n 10] 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[n 13] range 1 No range 1 ? ? range 1 ? ? No
inner range 1[n 13] range 1 No range 1 ? ? No ? ? No
outer range 1[n 13] range 1 No range 1 ? ? No ? ? No
vertices range 1[n 13] range 1 No range 1 ? ? No ? ? No
Moore range 1-500 range 1-500[n 3] 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[n 14] No No ? ? ? range 1 No ? No
corners range 1[n 14] No No ? ? ? No No ? No
edges range 1[n 14] No No ? ? ? No No ? No
hexahedral range 1[n 14] No No ? ? ? No No ? No
Moore range 1[n 14] 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

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 As a subset of elementary Wolfram CA
  2. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 Possibly as a subset of other supported 1D rulespaces
  3. ↑ 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 Has a simpler notation for the range-1 case
  4. ↑ 4.0 4.1 4.2 4.3 via Moore isotropic non-totalistic notation
  5. ↑ 5.0 5.1 Consecutive birth/survival transitions (Larger than Life) only for ranges above 2
  6. ↑ 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 "Large Neighborhood Totalistic Cellular Automata" may allow for this - testing needed
  7. ↑ 7.00 7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09 7.10 7.11 For Java Cell applications, neighbourhoods are manually specified and not systematically generated
  8. ↑ Consecutive birth/survival transitions (Larger than Life) only for ranges above 5
  9. ↑ 9.00 9.01 9.02 9.03 9.04 9.05 9.06 9.07 9.08 9.09 9.10 via Weighted Life
  10. ↑ 10.00 10.01 10.02 10.03 10.04 10.05 10.06 10.07 10.08 10.09 10.10 10.11 10.12 10.13 10.14 10.15 10.16 10.17 10.18 10.19 10.20 10.21 10.22 10.23 10.24 10.25 10.26 10.27 10.28 10.29 10.30 10.31 10.32 10.33 10.34 10.35 10.36 10.37 10.38 10.39 10.40 10.41 Requires custom ruletables
  11. ↑ 11.00 11.01 11.02 11.03 11.04 11.05 11.06 11.07 11.08 11.09 11.10 11.11 Extended neighbourhoods unknown
  12. ↑ 12.0 12.1 12.2 12.3 Only range-1 Moore natively supported, and range-1 von Neumann through its notation
  13. ↑ 13.0 13.1 13.2 13.3 Requires the use of a custom CoordCA neighbourhood
  14. ↑ 14.0 14.1 14.2 14.3 14.4 requires 3D.lua
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