Examples for

Cellular Automata

A simple model capable of complex behavior, a cellular automaton is a computational system where many identical cells on a lattice update their color according to a local and constant rule of evolution. Cellular automata have been shown to exhibit diverse behaviors, including chaos and complexity. Wolfram|Alpha can help you investigate any of trillions of rules or an entire rule space; compute transition diagrams, Boolean forms and algebraic forms; and visualize the evolution of these rules from simple and random initial conditions.

Elementary Cellular Automata

Perform computations with elementary cellular automata, including rule 30 and rule 110, and learn about their properties.

Compute properties of an elementary cellular automaton:

rule 110

Specify random initial conditions:

rule 30, random ic

Compute a property of an elementary cellular automaton:

eca rule 60 transition diagrams

Totalistic Cellular Automata

See totalistic cellular automata evolve, get information about them, and see their transition diagrams.

Specify a totalistic cellular automaton:

3-color code 1086
code 506119 k=4
CA 3-color, range 2, totalistic code 5050

General 1D Cellular Automata

Specify, simulate and analyze any one-dimensional cellular automaton by its rule number, its number of neighbors (or range) and the number of colors.

Specify the number of colors:

rule 7,110,222,193,934 k=3

Specify the range:

rule 1,388,968,789 r=2

Specify the number of colors and range:

CA 3-color, range 1, rule 4594122302107
CA k=3 r=2 rule 914752986721674989234787899872473589234512347899

Specify a half-integer range:

radius 3/2 rule 1235
radius 3/2 rule 6681

RELATED EXAMPLES

  • Computational Complexity
  • Fractals
  • Substitution Systems
  • Turing Machines
  • Wolfram Language