Randelbrot Set

Author

Eric W. Weisstein
December 17, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Fractals/RandelbrotSet.nb.

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Figure

V5

DensityPlot[-Length[FixedPointList[#^2+(x+I y)+Random[Complex,.05(I+1){-1,1}]&,x+I y,50,SameTest->(Abs[#2]>2.0&)]],{x,-2.1,0.6},{y,-1.2,1.2},PlotPoints->200,Mesh->False,ColorFunction->Hue,AspectRatio->Automatic,Frame->False]//Timing

V7

DensityPlot[-Length[FixedPointList[#^2+(x+I y)+Random[Complex,.05(I+1){-1,1}]&,x+I y,50,SameTest->(Abs[#2]>2.0&)]],{x,-2.1,0.6},{y,-1.2,1.2},PlotPoints->75,Mesh->False,ColorFunction->Hue,AspectRatio->Automatic,Frame->False]