Complex Newton Iteration for a Cubic Polynomial

Quiet[regions=(Floor[(3/2) (1+((Arg[#1])/π))]&)[NestList[Map[#1-((((#1)^3)-1)/(3 ((#1)^2)))&,#1,{2}]&,Table[x+I y,{y,1,-1,-(1/(2.^6))},{x,-1,1,(1/(2.^6))}],7]]/.Interval[_]|Indeterminate->0;];

Manipulate[ArrayPlot[(1/3) Take[regions[[n+1]],{1,-1,(2^r)},{1,-1,(2^r)}],ColorFunction -> "BlueGreenYellow",ImageSize->{500,400},Frame->False],{{n,3,"number of iterations"},0,7,1},{{r,3,"resolution"},6,0,-1},SaveDefinitions->True]

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Complex Newton Iteration for a Cubic Polynomial" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ComplexNewtonIterationForACubicPolynomial/

Contributed by: Eric Rowland

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