Persistent Structures in the Code 20 Cellular Automaton

The known persistent structures in the k=2, r=2 totalistic code 20 cellular automaton

These structures were given on page 284 of A New Kind of Science (Wolfram, 2002)

(4 columns, 20 rows)

Examples

Basic Examples

Retrieve the resource:

In[1]:=
ResourceObject["Persistent Structures in the Code 20 Cellular \
Automaton"]
Out[1]=

Retrieve the default content:

In[2]:=
ResourceData["Persistent Structures in the Code 20 Cellular \
Automaton"]
Out[2]=

Visualization

Plot the first 100 steps in evolution for the first 10 structures:

In[3]:=
ArrayPlot[CellularAutomaton[{20, {2, 1}, 2}, {#Cells, 0}, 100], 
   ImageSize -> {Automatic, 200}] & /@ 
 Normal[Take[
   ResourceData[
    "Persistent Structures in the Code 20 Cellular Automaton"], 10]]
Out[3]=

Reproduce the images on page 284 of A New Kind of Science:

In[4]:=
Map[
 If[#Shift == 0,
   ArrayPlot[
    Flatten@{Table[0, 3], #, Table[0, 3]} & /@
     
     CellularAutomaton[
      {20, {2, 1}, 2},
      {#Cells, 0},
      200
      ],
    ImageSize -> {Automatic, 200}],
   ArrayPlot[
    Flatten@{Table[0, 3], #, Table[0, 3]} & /@
     
     CellularAutomaton[
      {20, {2, 1}, 2},
      {#Cells, 0},
      {200, 40}
      ], ImageSize -> {Automatic, 200}]
   ] &,
 Normal[Take[
    ResourceData[
     "Persistent Structures in the Code 20 Cellular Automaton"], 13][
   Select[#Shift >= 0 &]]]
 ]
Out[4]=

Wolfram Research, "Persistent Structures in the Code 20 Cellular Automaton" from the Wolfram Data Repository. (2017) https://doi.org/10.24097/wolfram.39328.data

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