Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 CellularAutomatonFromNumber

Source Notebook

Convert numbers specifying a cellular automaton into an explicit list of rules

Contributed by: Wolfram Physics Project Team

ResourceFunction["CellularAutomatonFromNumber"][n]

converts a cellular automaton specified with elementary rule number n into an equivalent list of rules.

ResourceFunction["CellularAutomatonFromNumber"][n,k]

converts a k-color cellular automaton with general nearest‐neighbor rule number n into an equivalent list of rules.

ResourceFunction["CellularAutomatonFromNumber"][n,k,r]

converts a cellular automaton specified with general rule number n,k colors and range r into an equivalent list of rules.

Details and Options

The number of possible cellular automaton rules is as follows:
elementary rules256
1D general ruleskk2r+1

Examples

Basic Examples (2) 

Generate the list of rules corresponding to rule 30:

In[1]:=
ResourceFunction["CellularAutomatonFromNumber"][30]
Out[1]=

Show that the two specifications are equivalent:

In[2]:=
{RulePlot[CellularAutomaton[30], {{1}, 0}, 10], ArrayPlot[ CellularAutomaton[ ResourceFunction["CellularAutomatonFromNumber"][30], {{1}, 0}, 10]]}
Out[2]=

Scope (2) 

Generate the rule representation of 3-color rule 679458:

In[3]:=
ResourceFunction["CellularAutomatonFromNumber"][679458, 3]
Out[3]=

Generate the rule representation of a general range-r=2 rule:

In[4]:=
ResourceFunction["CellularAutomatonFromNumber"][39421042, 2, 2]
Out[4]=

Version History

  • 1.0.0 – 12 August 2020

Related Resources

License Information