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Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 ProbabilisticCellularAutomaton

Source Notebook

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:

In[1]:=
ResourceFunction[ "ProbabilisticCellularAutomaton"][{0.25, 0.75, 0.75, 0.25}, {0, 0, 0, 1, 0, 0, 0}, 3]
Out[1]=

Visualize the evolution of a probabilistic cellular automaton:

In[2]:=
ArrayPlot[ ResourceFunction[ "ProbabilisticCellularAutomaton"][{0, 0.75, 0.75, 0.4}, CenterArray[{1, 0, 1}, 60], 40]]
Out[2]=

Scope (2) 

Give the result of one step of evolution:

In[3]:=
ResourceFunction[ "ProbabilisticCellularAutomaton"][{0.1, 0.3, 0.8, 0.6}, {0, 0, 0, 1, 0, 0, 0}]
Out[3]=

An alternative form:

In[4]:=
ResourceFunction[ "ProbabilisticCellularAutomaton"][{0.1, 0.3, 0.8, 0.6}][{0, 0, 0, 1, 0, 0, 0}]
Out[4]=

Version History

  • 1.0.0 – 31 August 2021

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