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
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
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
range 1 range 1 No ? ? range ?-? ? ? ? range 0-?
n-state

{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] ? range 1-? range 1-? ?
Moore range 1-500[n 3] range 1-500[n 3] range 1-5[n 3]
range 1-7[n 6] 		range 1-? ? range 1-10[n 3][n 5] ? range 1-? range 1-? ?
cross range 1-500 range 1-500 No range 1-? ? No ? range 1-? ? ?
saltire range 1-500 range 1-500 No range 1-? ? No ? range 1-? ? ?
star range 1-500 range 1-500 No range 1-? ? No ? range 1-? ? ?
hash range 1-500 range 1-500 No range 1-? ? No ? ? ? ?
checkerboard range 1-500 range 1-500 No range 1-? ? No ? ? ? ?
L2 range 1-500 range 1-500 No range 1-? ? No ? ? ? ?
circular range 1-500 range 1-500 No range 1-? ? 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 7] ? Yes[n 7] ? ? ? ?
range 1
Moore 		Yes Yes Yes Yes ? Yes[n 7] ? ? ? ?
exploded
Moore 		No No C2E1
C1E3 		C2E1
C1E3 		? ? ? ? ? ?
range 2
von Neumann 		Multistate emulation only Multistate emulation only Yes Yes ? ? ? ? ? ?
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 ? ? ? ?
range 1
von Neumann 		Yes Yes No Yes[n 7] ? Yes[n 7] ? ? ? ?
range 1
Moore 		Yes Yes No Yes[n 7] ? Yes[n 7] ? ? ? ?
range 2
von Neumann 		Multistate emulation only Multistate emulation only No Yes[n 7] ? ? ? ? ? ?
Custom OT
neighbourhood 		range 1-500 range 1-500 No range 1-? ? No ? ? ? ?
Naive rules Multistate emulation only Multistate emulation only No Yes ? ? ? ? ? ?
3-state
Outer-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
BSFKL Ruletables only Ruletables only Yes Ruletables only ? ? ? ? ? ?
range 1
Moore 		Ruletables only Ruletables only Ruletables only Ruletables only ? ? ? ? ? ?
Isotropic non-totalistic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
range 1
Moore 		Ruletables only Ruletables only Ruletables only Ruletables only ? ? ? ? ? ?
16-state
Non-isotropic
Rulespace Golly LifeViewer lifelib CAViewer Caterer Mirek's Cellebration Visions of Chaos Java Square Cell Life32 WolframAlpha
Partitioned cellular automata Ruletables only Yes 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 ?-? 		? ? ? ?
Rock-paper-scissors No No No No ? ? Yes ? ? ?
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 8] ? states 2-?[n 8] ? ? ? ?
Extended Generations Ruletables only Ruletables only states 2-?[n 9] states 2-?[n 8] ? ? ? ? ? ?
Deficient rules Ruletables only Ruletables only states 2-?[n 9] states 2-?[n 8] ? ? ? ? ? ?
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 8] ? Weighted Generations
states 2-?[n 8] 		? ? ? ?
Extended Generations Ruletables only Ruletables only states 2-?[n 9] states 2-?[n 8] ? ? ? ? ? ?
Deficient rules Ruletables only Ruletables only states 2-?[n 9] states 2-?[n 8] ? ? ? ? ? ?
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 ? ? ? ? ? ? ?
Extended Generations Ruletables only Ruletables only No ? ? ? ? ? ? ?
Deficient rules Unclear how deficient rules can generalize to non-isotropic rules

{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 ? ? ? ? ? ? ?
asterisk range 1-500[n 3] range 1-500[n 3] range 1 ? ? ? ? ? ? ?
hexagonal range 1-500[n 3] range 1-500[n 3] range 1 ? ? ? ? ? ? ?
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 7] ? ? ? ?
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 7] ? Yes[n 7] ? ? ? ?
Custom OT
neighbourhood 		range 1-500 range 1-500 No range 1-? ? 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 8] ? states 2-?[n 8] ? ? ? ?
Extended Generations Ruletables only Ruletables only No ? ? ? ? ? ? ?
Deficient rules Ruletables only Ruletables only 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 8] ? Weighted Generations
states 2-?[n 8] 		? ? ? ?
Extended Generations Ruletables only Ruletables only No ? ? ? ? ? ? ?
Deficient rules Ruletables only Ruletables only 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 ? ? ? ? ? ? ?
Extended Generations Ruletables only Ruletables only No ? ? ? ? ? ? ?
Deficient rules Unclear how deficient rules can generalize to non-isotropic rules

{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 10] range 1 No range 1 ? ? ? ? ? ?
inner range 1[n 10] range 1 No range 1 ? ? ? ? ? ?
outer range 1[n 10] range 1 No range 1 ? ? ? ? ? ?
vertices range 1[n 10] range 1 No range 1 ? ? ? ? ? ?
Moore range 1-500 range 1-500[n 3] No range 1-? ? ? ? ? ? ?
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 ? ? ? ?
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 ? ? ? ? ? ? ?
Extended Generations No No No ? ? ? ? ? ? ?
Deficient rules No 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 ? ? ? ? ? ? ?
Extended Generations No No No ? ? ? ? ? ? ?
Deficient rules Unclear how deficient rules can generalize to non-isotropic rules

{4,3,4}

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

{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 Square Cell Life32 WolframAlpha
Cyclic 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 Square Cell Life32 WolframAlpha
Cyclic No No No No No No states 2-? 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 Square Cell Life32 WolframAlpha
Cyclic 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 Square Cell Life32 WolframAlpha
Cyclic No No No No No No states 2-? 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 ? ? ? ? ? ?
[Rule]Super Yes Yes 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 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 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. ↑ Consecutive birth/survival transitions (Larger than Life) only for ranges above 5
  7. ↑ 7.00 7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09 7.10 via Weighted Life
  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 Extended neighbourhoods unknown
  9. ↑ 9.0 9.1 9.2 9.3 Only range-1 Moore natively supported, and range-1 von Neumann through its notation
  10. ↑ 10.0 10.1 10.2 10.3 Requires the use of a custom CoordCA neighbourhood
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