Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 DynamicCellularAutomaton

Source Notebook

Generate a cellular automaton evolution with initial conditions chosen by a click

Contributed by: Wolfram Staff

ResourceFunction["DynamicCellularAutomaton"][rule,t]

generates an array plot of the evolution of the cellular automaton with specified rule from zero initial condition for t steps and allows the choice of different initial conditions with a click.

ResourceFunction["DynamicCellularAutomaton"][rule,{t,x}]

allows offsets up to x on on the left and on the right.

Details and Options

A click in the array plot created by ResourceFunction["DynamicCellularAutomaton"][…] sets up the evolution to start from the point in the top row in the column pointed to by the click.
Clicks at several points set up more complex initial conditions.
A second click on the same column removes that part of the evolution.
ResourceFunction["DynamicCellularAutomaton"][rule] is equivalent to ResourceFunction["DynamicCellularAutomaton"][rule,20].
ResourceFunction["DynamicCellularAutomaton"][rule,…] accepts the rule specification in the same form that is allowed in CellularAutomation[rule].
ResourceFunction["DynamicCellularAutomaton"] accepts the options of ArrayPlot.

Examples

Basic Examples (2) 

Create a rule 30 evolution by evaluating the input and clicking in the graphics:

In[1]:=
ResourceFunction["DynamicCellularAutomaton"][30]
Out[1]=
Image

Click several times to use more complex initial conditions:

In[2]:=
ResourceFunction["DynamicCellularAutomaton"][30]
Out[2]=
Image

Scope (4) 

Specify a rule by number:

In[3]:=
ResourceFunction["DynamicCellularAutomaton"][110]
Out[3]=
Image

Specify the rule as a string:

In[4]:=
ResourceFunction["DynamicCellularAutomaton"]["Rule30"]
Out[4]=
Image

Specify the number of steps:

In[5]:=
ResourceFunction["DynamicCellularAutomaton"][30, 10]
Out[5]=
Image

Alternatively:

In[6]:=
ResourceFunction["DynamicCellularAutomaton"][30, {10}]
Out[6]=
Image

Create a wider canvas to specify more complex initial conditions:

In[7]:=
ResourceFunction["DynamicCellularAutomaton"][30, {10, 30}]
Out[7]=
Image

Options (3) 

Use options of ArrayPlot:

In[8]:=
ResourceFunction["DynamicCellularAutomaton"][30, ColorRules -> {1 -> Pink, 0 -> Yellow}]
Out[8]=
Image

Turn off the mesh:

In[9]:=
ResourceFunction["DynamicCellularAutomaton"][30, Mesh -> False]
Out[9]=
Image

Specify the image size:

In[10]:=
ResourceFunction["DynamicCellularAutomaton"][30, ImageSize -> Small]
Out[10]=
Image

Version History

  • 2.0.0 – 30 December 2019
  • 1.0.0 – 06 November 2019

License Information