Re: eyeofra_ifs.gif (GIF Image, 1044x1044 pixels) - Scaled (87%)
- To: mathgroup at smc.vnet.net
- Subject: [mg101418] Re: [mg101388] eyeofra_ifs.gif (GIF Image, 1044x1044 pixels) - Scaled (87%)
- From: John Fultz <jfultz at wolfram.com>
- Date: Sun, 5 Jul 2009 23:17:42 -0400 (EDT)
- Reply-to: jfultz at wolfram.com
On Sat, 4 Jul 2009 06:43:42 -0400 (EDT), Roger Bagula wrote: > http://www.geocities.com/rlbagulatftn/eyeofra_ifs.gif > > The Eye of Ra fractal > by doing an affine inside the > kiss ellipse with reduced the number of transforms in > Mathematica: > Clear[f, dlst, pt, cr, ptlst, x, y] > RandomSeed[]; > dlst = Table[ Random[Integer, {1, 2}], {n, 100000}]; > f[1, {x_, y_}] := N[ {2*x*y/(x^2 + y^2) , (y^2 - x^2)/(y^2 + x^2)}]; > f[2, {x_, y_}] := N[ {(2*((x - y)/ > Sqrt[2]) - (x + y)/Sqrt[2])/( > 2.83), (2*((x - y)/Sqrt[2]) + (x + y)/Sqrt[2])/(2.83)}]; > 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] New to version 7, when doing lists of multi-color points, it's much better to use a multi-Point primitive with the VertexColors option. Here's an example of your code refactored (also used FoldList rather than your history-remembering global variable, which also adds a small speedup). I think you'll find this rendering significantly faster. Clear[f, dlst, pt, cr, ptlst, x, y]; RandomSeed[]; dlst = Table[Random[Integer, {1, 2}], {n, 100000}]; f[{x_, y_}, 1] := N[{2*x*y/(x^2 + y^2), (y^2 - x^2)/(y^2 + x^2)}]; f[{x_, y_}, 2] := N[{(2*((x - y)/Sqrt[2]) - (x + y)/ Sqrt[2])/(2.83), (2*((x - y)/Sqrt[2]) + (x + y)/ Sqrt[2])/(2.83)}]; 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 = {PointSize[.001], Point[Rest[FoldList[f, {.5, .75}, dlst]], VertexColors -> cr /@ dlst]}; Show[Graphics[Join[{PointSize[.001]}, ptlst]], AspectRatio -> Automatic, PlotRange -> All] Sincerely, John Fultz jfultz at wolfram.com User Interface Group Wolfram Research, Inc.
