fractal_teardrops.gif (GIF Image, 658x1009 pixels) - Scaled (90%)

• To: mathgroup at smc.vnet.net
• Subject: [mg101558] fractal_teardrops.gif (GIF Image, 658x1009 pixels) - Scaled (90%)
• From: Roger Bagula <rlbagula at sbcglobal.net>
• Date: Fri, 10 Jul 2009 06:44:05 -0400 (EDT)
• References: <h2fe37\$ppu\$1@smc.vnet.net> <h340hn\$gcn\$1@smc.vnet.net>

```http://www.geocities.com/rlbagulatftn/fractal_teardrops.gif
I was wondering if I could do the self-similar trick with othher figures
besides ellipses and circles and
I remembered the teardrop or piriform shape:
Clear[f, dlst, pt, cr, ptlst, x, y]
RandomSeed[];
dlst = Table[ Random[Integer, {1, 2}], {n, 250000}];
f[1, {x_,
y_}] := N[ {((
x^2 - y^2)/(y^2 + x^2))^2*2*x*y/(x^2 + y^2) , (x^2 - y^2)/(
y^2 + x^2)}];
f[2, {x_, y_}] := N[{7/24 - x/2 - y/2, x/2 - y/2}];
pt = {0.5, 0.75};
cr[n_] := If[n - 2 == 0, RGBColor[0, 0, 1], If[n - 3 == 0, RGBColor[0, 1,
0], If[n - 1 == 0, RGBColor[1, 0, 0], RGBColor[0, 0, 0]]]]
ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]},
{j, Length[dlst]}];
Show[Graphics[Join[{PointSize[.001]}, ptlst]], AspectRatio ->
Automatic, PlotRange -> All]

>
>
>

```

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