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 3] range 1[n 3] 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 3] range 1[n 3] 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[n 3] range 1[n 3] 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 4] range 1-500[n 4] range 1[n 5] range 1-? ? range 1-10[n 6] ?[n 7] range 1-2[n 8] range 1-? No
Moore range 1-500[n 4] range 1-500[n 4] range 1-5[n 4]
range 1-7[n 9] 		range 1-? ? range 1-10[n 4][n 6] range 1 range 1-2[n 8] range 1-? No
cross range 1-500 range 1-500 No range 1-? ? No ?[n 7] range 1-2[n 8] ? No
saltire range 1-500 range 1-500 No range 1-? ? No ?[n 7] range 1-2[n 8] ? No
star range 1-500 range 1-500 No range 1-? ? No ?[n 7] range 1-2[n 8] ? No
hash range 1-500 range 1-500 No range 1-? ? No ?[n 7] range 1-2[n 8] ? No
checkerboard range 1-500 range 1-500 No range 1-? ? No ?[n 7] range 1-2[n 8] ? No
L2 range 1-500 range 1-500 No range 1-? ? No ?[n 7] range 1-2[n 8] ? No
circular range 1-500 range 1-500 No range 1-? ? No ?[n 7] range 1-2[n 8] ? 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 5] Yes[n 5] Yes[n 5] Yes[n 10] ? Yes[n 10] ? ? ? No
range 1
Moore 		Yes Yes Yes Yes ? Yes[n 10] ? ? ? No
exploded
Moore 		No No C2E1
C1E3 		C2E1
C1E3 		? ? ? ? ? No
range 2
von Neumann 		No[n 11] No[n 11] Yes Yes ? ? ? ? ? No
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Margolus No[n 11] Yes No Yes ? Yes ? ? ? No
range 1
von Neumann 		Yes Yes No Yes[n 10] ? Yes[n 10] ? ? ? No
range 1
Moore 		Yes Yes No Yes[n 10] ? Yes[n 10] ? ? ? No
range 2
von Neumann 		No[n 11] No[n 11] No Yes[n 10] ? ? ? ? ? No
Custom OT
neighbourhood 		range 1-500 range 1-500 No range 1-? ? No ? range 1-2 ? No
Naive rules No[n 11] No[n 11] 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 3] Yes[n 3] Yes Yes[n 3] ? ? ? ? ? No
range 1
Moore 		Yes[n 3] Yes[n 3] Yes[n 3] Yes[n 3] ? ? ? ? ? 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 3] Yes[n 3] Yes[n 3] Yes[n 3] ? ? ? ? ? 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 3] 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 12] ? states 2-?[n 12] states 2-50 ? ? No
Extended Generations Yes[n 3] Yes[n 3] states 2-?[n 13] states 2-?[n 12] ? ? ? ? ? No
Deficient Yes[n 3] Yes[n 3] states 2-?[n 13] states 2-?[n 12] ? ? ? ? ? No
Alternating Yes[n 3] rules 2 Yes[n 3] ? ? ? ? ? ? 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 12] ? Weighted Generations
states 2-?[n 12] 		? ? ? No
Extended Generations Yes[n 3] Yes[n 3] states 2-?[n 13] states 2-?[n 12] ? ? ? ? ? No
Deficient Yes[n 3] Yes[n 3] states 2-?[n 13] states 2-?[n 12] ? ? ? ? ? No
Alternating Yes[n 3] rules 2 Yes[n 3] ? ? ? ? ? ? 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 3] Yes[n 3] No ? ? ? ? ? ? No
Deficient Unclear how deficient rules can generalize to non-isotropic rules
Alternating Yes[n 3] 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 4] No ? ? ? ? range 1-2[n 8] ? No
asterisk range 1-500 range 1-500 No ? ? ? ? range 1-2[n 8] ? No
hexagonal range 1-500[n 4] range 1-500[n 4] range 1 ? ? ? range 1 range 1-2[n 8] ? 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 10] ? ? ? 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 10] ? Yes[n 10] ? ? ? 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 12] ? states 2-?[n 12] states 2-50 ? ? No
Extended Generations Yes[n 3] Yes[n 3] No ? ? ? ? ? ? No
Deficient Yes[n 3] Yes[n 3] No ? ? ? ? ? ? No
Alternating Yes[n 3] rules 2 Yes[n 3] ? ? ? ? ? ? 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 12] ? Weighted Generations
states 2-?[n 12] 		? ? ? No
Extended Generations Yes[n 3] Yes[n 3] No ? ? ? ? ? ? No
Deficient Yes[n 3] Yes[n 3] No ? ? ? ? ? ? No
Alternating Yes[n 3] rules 2 Yes[n 3] ? ? ? ? ? ? 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 3] Yes[n 3] No ? ? ? ? ? ? No
Deficient Unclear how deficient rules can generalize to non-isotropic rules
Alternating Yes[n 3] 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 14] range 1 No range 1 ? ? range 1 ? ? No
inner range 1[n 14] range 1 No range 1 ? ? No ? ? No
outer range 1[n 14] range 1 No range 1 ? ? No ? ? No
vertices range 1[n 14] range 1 No range 1 ? ? No ? ? No
Moore range 1-500 range 1-500[n 4] 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 15] No No ? ? ? range 1 No ? No
corners range 1[n 15] No No ? ? ? No No ? No
edges range 1[n 15] No No ? ? ? No No ? No
hexahedral range 1[n 15] No No ? ? ? No No ? No
Moore range 1[n 15] 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 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. ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 3.42 3.43 3.44 3.45 3.46 3.47 Requires custom ruletables
  4. ↑ 4.00 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 Has a simpler notation for the range-1 case
  5. ↑ 5.0 5.1 5.2 5.3 via Moore isotropic non-totalistic notation
  6. ↑ 6.0 6.1 Consecutive birth/survival transitions (Larger than Life) only for ranges above 2
  7. ↑ 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 "Large Neighborhood Totalistic Cellular Automata" may allow for this - testing needed
  8. ↑ 8.00 8.01 8.02 8.03 8.04 8.05 8.06 8.07 8.08 8.09 8.10 8.11 For Java Cell applications, neighbourhoods are manually specified and not systematically generated
  9. ↑ Consecutive birth/survival transitions (Larger than Life) only for ranges above 5
  10. ↑ 10.00 10.01 10.02 10.03 10.04 10.05 10.06 10.07 10.08 10.09 10.10 via Weighted Life
  11. ↑ 11.0 11.1 11.2 11.3 11.4 11.5 11.6 Can be emulated by a multistate ruletable
  12. ↑ 12.00 12.01 12.02 12.03 12.04 12.05 12.06 12.07 12.08 12.09 12.10 12.11 Extended neighbourhoods unknown
  13. ↑ 13.0 13.1 13.2 13.3 Only range-1 Moore natively supported, and range-1 von Neumann through its notation
  14. ↑ 14.0 14.1 14.2 14.3 Requires the use of a custom CoordCA neighbourhood
  15. ↑ 15.0 15.1 15.2 15.3 15.4 requires 3D.lua
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