Mandelbrot

• To: mathgroup at smc.vnet.net
• Subject: [mg13595] Mandelbrot
• From: Jon Prudhomme <prudhomj at elwha.evergreen.edu>
• Date: Mon, 3 Aug 1998 03:53:54 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```	Hello

I was just curious if anyone had found a decent way to plot the
Mandelbrot or Julia sets with Mathematica yet.  I have been able to do
it with DensityPlot and ListDensityPlot, but I can't help but wonder if
there is an easier way than either of these:

iterations=200;
pointColor[c_]:=Module[{i,p},
For[i=1;p=0,i<=iterations&&Sqrt[Re[p]^2+Im[p]^2]<=2,i++,p=p^2+c];i]

DensityPlot[pointColor[Complex[x,y]],{x,-2.5,1.5},{y,-1.5,1.5},Mesh->False,

ColorFunction->Hue,AspectRatio->Automatic,PlotPoints->1000]

(* or this for a ListDensityPlot... *)

manSet=Table[pointColor[Complex[x,y]],{y,-1.5,1.5,.01},{x,-2.5,1.5,.01}];
ListDensityPlot[manSet,Mesh->False,ColorFunction->Hue,AspectRatio->Automatic]

Anyone got any other ideas?

Jon Prudhomme
The Evergreen State College
prudhomj at elwha.evergreen.edu

PS - The algorithm for the Mandelbrot set is z[[n]]=z[[n-1]]^2+c where
z[[0]]=0 and c is the point on the complex plain being tested as a
member of the set.  If after an arbitrary number of iterations the
point is not 2 units away from the origin on the complex plain, the
point c is a member of the set.  Colors of non-member points are based
on the iteration number that them as excluded from the set.

```

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