`CellularAutomaton`¶

Generates a cellular automaton evolution.

$ wo 'CellularAutomaton[90, {{1}, 0}, 2]'
{{0, 0, 1, 0, 0}, {0, 1, 0, 1, 0}, {1, 0, 0, 0, 1}}

The step specification {{t}} returns just the state at step t, wrapped in a list ({t} behaves like the bare t form, giving all steps 0 through t):

$ wo 'CellularAutomaton[30, {{1}, 0}, {{3}}]'
{{1, 1, 0, 1, 1, 1, 1}}

Two-dimensional rules take a weight matrix and a range specification. {{t1, t2, dt}} selects the states at steps t1 through t2 in increments of dt:

$ wo 'ArrayPlot /@ CellularAutomaton[{942, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, {{10, 30, 10}}]'
{-Graphics-, -Graphics-, -Graphics-}

A second element in the step specification restricts the cells returned. All keeps every affected cell, while {x1, x2} names offsets relative to the first cell of the initial condition:

$ wo 'CellularAutomaton[90, {{1}, 0}, {3, {-2, 2}}]'
{{0, 0, 1, 0, 0}, {0, 1, 0, 1, 0}, {1, 0, 0, 0, 1}, {0, 1, 0, 1, 0}}

Without a step count only one step runs, and just the new state comes back — as a {cells, {background}} pair when the initial condition has a background:

$ wo 'CellularAutomaton[30, {{1}, 0}]'
{{1, 1, 1}, {0}}

The operator form does the same:

$ wo 'CellularAutomaton[30][{0, 0, 1, 0, 0}]'
{0, 1, 1, 1, 0}

$ wo 'CellularAutomaton[x, {{1}, 0}, 3]'

CellularAutomaton::nspecnl: Rule specification x should be an Integer, a List, a pure Boolean function, a String or an Association.
CellularAutomaton[x, {{1}, 0}, 3]

CellularAutomaton¶

`CellularAutomaton`¶