Rule 28

Author

Eric W. Weisstein
August 31, 2016

This notebook downloaded from http://mathworld.wolfram.com/notebooks/CellularAutomata/Rule28.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Rule28.html.

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

Initialization

rule=28;

Binary

StringJoin@@(ToString/@IntegerDigits[rule,2,8])

Plot

V5

ElementaryCADiagram[rule]

V6

ElementaryCADiagram[rule]

V11

RulePlot[CellularAutomaton[28]]

RulePlot[CellularAutomaton[28],{{1},0},10,Mesh->True,PlotLegends->"Icon"]

Variants

ElementaryCAVariants[rule]

FromDigits[#,2]&/@Cases[IntegerDigits[Range[0,255],2,8],{_,0,0,1,1,1,0,0}]

ElementaryCAVariants[156]

Evolution

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

Triangle of Values

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

Flatten[t]

Flatten[IntegerDigits[#,2]&/@(FromDigits[#,2]&/@t)]

Represented in Decimal

ElementaryCATriangle[rule,10]

FromDigits[#,2]&/@%

FindSequenceFunction[%,n]

FullSimplify[%]

Table[(1/3)((2^(n+2))-(((-1))^n)),{n,0,10}]