Rule 102

Author

Eric W. Weisstein
August 31, 2016

This notebook downloaded from http://mathworld.wolfram.com/notebooks/CellularAutomata/Rule102.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Rule102.html.

©2016 Wolfram Research, Inc. except for portions noted otherwise

Initialization

rule=102;

Plot

V5

ElementaryCADiagram[rule]

V6

ElementaryCADiagram[rule]

V11

RulePlot[CellularAutomaton[102]]

RulePlot[CellularAutomaton[102],{{1},0},15,Mesh->True,PlotLegends->"Icon"]

Variants

ElementaryCAVariants[rule]

Evolution

ArrayPlot[ElementaryCellularAutomaton[rule,250],Frame->False,PixelConstrained->True,ImageSize->1000]

Additive Animation

<<GIF`

Export[gifs<>"rule"<>ToString[rule]<>".gif",movie=Show/@With[{g=32},
Table[
RasterGraphics[
CellularAutomaton[rule,{
ReplacePart[
Table[0,{2g+1}],1,{{g+1},{s+g+1}}
],0},g,{All,{0,2g+1}}
],
Mesh->False
],
{s,-g,g}]
]]//Timing

Show[GraphicsArray[Partition[Take[movie,9],3]]]

Triangle of Values

ColumnForm[t=ElementaryCATriangle[rule,5],Center]

Flatten[t]

Represented in Decimal

ElementaryCATriangle[rule,15]

FromDigits[#,2]&/@%

FindSequenceFunction[%,n]

FromDigits[#,2]&/@With[{n=10},MapIndexed[Take[#1,n+#2[[1]]{-1,1}+{2,0}]&,ElementaryCellularAutomaton[102,n]]]

FromDigits[#,2]&/@With[{n=40},MapIndexed[Take[#1,n+#2[[1]]{-1,0}+{2,1}]&,ElementaryCellularAutomaton[rule,n]]]

IntegerDigits[#,2]&/@Take[%,20]