CellularAutomaton
CellularAutomaton[rule,init,t] generates a list representing the evolution of the cellular automaton with the specified rule from initial condition init for t steps.
CellularAutomaton[rule,init] gives the result of evolving init for one step.
CellularAutomaton[rule,init,{tspec,xspec,…}] gives only those parts of the evolution specified by tspec, xspec, etc.
CellularAutomaton[rule,init,{t,All,…}] includes at each step all cells that could be affected over the course of t steps.
CellularAutomaton[rule] is an operator form of CellularAutomaton that represents one step of evolution.
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