Function Repository Resource:

# ProbabilisticCellularAutomaton

Generate the evolution of a probabilistic cellular automaton

Contributed by: Wolfram Staff
 ResourceFunction["ProbabilisticCellularAutomaton"][{p1,p2,…},init,t] generates a list representing the evolution of the probabilistic cellular automaton with probabilities pi from initial condition init for t steps. ResourceFunction["ProbabilisticCellularAutomaton"][probs,init] gives the result of evolving init for one step. ResourceFunction["ProbabilisticCellularAutomaton"][probs] is an operator form of ResourceFunction["ProbabilisticCellularAutomaton"] that represents one step of evolution.

## Details

The probabilities pi are taken to be real numbers between 0 and 1.
init is taken to be a list with elements equal to 0 or 1.
The initial condition is considered to be at step 0.
ResourceFunction["ProbabilisticCellularAutomaton"][rule][init] is equivalent to ResourceFunction["ProbabilisticCellularAutomaton"][rule,init].

## Examples

### Basic Examples (2)

Run a probabilistic cellular automaton for three steps:

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Visualize the evolution of a probabilistic cellular automaton:

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### Scope (2)

Give the result of one step of evolution:

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An alternative form:

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## Version History

• 1.0.0 – 31 August 2021