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] > > >
