Rule 158

Author

Eric W. Weisstein
August 31, 2016

This notebook downloaded from http://mathworld.wolfram.com/notebooks/CellularAutomata/Rule158.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Rule158.html.

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

Initialization

rule=158;

Binary

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

Plot

V5

ElementaryCADiagram[rule]

V6

ElementaryCADiagram[rule]

V11

RulePlot[CellularAutomaton[158]]

RulePlot[CellularAutomaton[158],{{1},0},15,Mesh->True,PlotLegends->"Icon"]

Variants

ElementaryCAVariants[rule]

Triangle of Values

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

StringJoin@@@Map[ToString,t,{2}]

Flatten[t]

Represented in Decimal

ElementaryCATriangle[rule,10]

FromDigits[#,2]&/@ElementaryCATriangle[rule,20]

FindSequenceFunction[%,n]//FullSimplify

LookupFormat[%]

Closed Form

ElementaryCADiagram[rule]

ogf=Factor[-((1+7x+12(x^2)-4(x^3))/(-1-16(x^4)+17(x^2)))]

ogf//TraditionalForm//TeXForm

CoefficientList[Series[ogf,{x,0,20}],x]

<<DiscreteMath`RSolve`

FullSimplify[SeriesTerm[ogf,{x,0,n}],n∈Integers&&n>0]

Table[%,{n,0,20}]