Three-Color Cellular Automaton Rules that Double Their Input

A list of rules for k=3 cellular automata that eventually double a block of gray input cells

A collection of these rules originally appears on page 833 of "A New Kind of Science" (Wolfram, 2002)

(199 elements)

Examples

Basic Examples

Retrieve the ResourceObject:

In[1]:=
ResourceObject["Three-Color Cellular Automaton Rules that Double \
Their Input"]
Out[1]=

View part of the data:

In[2]:=
Take[ResourceData[
  "Three-Color Cellular Automaton Rules that Double Their Input"], 10]
Out[2]=

Visualization

See how the first 10 rules act on inputs of length 10:

In[3]:=
ArrayPlot[
   CellularAutomaton[{#, 3}, {Append[Table[1, 10], 2], 0}, 100]] & /@ 
 Take[ResourceData[
   "Three-Color Cellular Automaton Rules that Double Their Input"], 
  10]
Out[3]=

See that this holds when input length and evaluation steps are doubled:

In[4]:=
ArrayPlot[
   CellularAutomaton[{#, 3}, {Append[Table[1, 20], 2], 0}, 200]] & /@ 
 Take[ResourceData[
   "Three-Color Cellular Automaton Rules that Double Their Input"], 
  10]
Out[4]=

Wolfram Research, "Three-Color Cellular Automaton Rules that Double Their Input" from the Wolfram Data Repository. (2017) https://doi.org/10.24097/wolfram.07085.data

License Information

CC BY-SA 4.0

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