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Block Simulation Network of Elementary Cellular Automata

A network showing how one elementary cellular automaton can emulate another if its states contain only particular blocks

Originator: Stephen Wolfram

All the 88 inequivalent elementary rules are included. This network originally appeared on page 702 of Stephen Wolfram's A New Kind of Science.

(88 rows)

Examples

Basic Examples

Retrieve the default content:

In[1]:=
ResourceData["Block Simulation Network of Elementary Cellular Automata"]
Out[1]=

Find which rules can be emulated by rule 22:

In[2]:=
ResourceData[ "Block Simulation Network of Elementary Cellular Automata"][ Key[22], All, "Rule"]
Out[2]=

Find the details of the emulation of rule 90 by rule 22:

In[3]:=
ResourceData[ "Block Simulation Network of Elementary Cellular Automata"][Key[22], Select[#Rule == 90 &]]
Out[3]=

Get the blocks:

In[4]:=
ResourceData[ "Block Simulation Network of Elementary Cellular Automata"][ Key[22], Select[#Rule == 90 &], "Blocks"] // Values
Out[4]=

Plot them:

In[5]:=
ArrayPlot[CellularAutomaton[22, {{1, 0, 0, 0}, {0, 0, 0, 0}}, 40]]
Out[5]=

Look at every 4th step:

In[6]:=
ArrayPlot[ CellularAutomaton[22, {{1, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 40, 4}}]]
Out[6]=

Convert the blocks to 0 and 1 respectively:

In[7]:=
Reverse /@ Normal[Normal[ First[ResourceData[ "Block Simulation Network of Elementary Cellular Automata"][ Key[22], Select[#Rule == 90 &], "Blocks"]]]]
Out[7]=
In[8]:=
ArrayPlot[(Partition[#, 4] /. {{0, 0, 0, 0} -> 0, {1, 0, 0, 0} -> 1}) & /@ CellularAutomaton[22, {{1, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 40, 4}}]]
Out[8]=

Plot the entire simulation network

In[9]:=
Graph[Flatten[Normal[KeyValueMap[Thread[#1 -> #2] &, ResourceData[ "Block Simulation Network of Elementary Cellular Automata"][All, All, "Rule"]]]], VertexLabels -> Automatic]
Out[9]=
In[10]:=

Wolfram Research, "Block Simulation Network of Elementary Cellular Automata" from the Wolfram Data Repository (2017)   https://doi.org/10.24097/wolfram.05827.data

Data Resource History

  • Date Created:

Source Metadata

  • Source: http://www.wolframscience.com/nksonline/page-702
  • Citation: Stephen Wolfram "A New Kind of Science" (2002)

Publisher Information

  • Prepared for the Wolfram Data Repository By: Stephen Wolfram
  • Publisher of Record: Wolfram Research