Re: AMERICAN MATHEMATICAL MONTHLY -April 2009:Transformations Between
- To: mathgroup at smc.vnet.net
- Subject: [mg98471] Re: AMERICAN MATHEMATICAL MONTHLY -April 2009:Transformations Between
- From: Roger Bagula <rlbagula at sbcglobal.net>
- Date: Fri, 10 Apr 2009 04:56:24 -0400 (EDT)
- References: <grcgfr$pil$1@smc.vnet.net> <grhp5r$mg6$1@smc.vnet.net>
David Bailey wrote: > >> >> >> >> >Roger, > >Which parameter do you vary to go between the two types of fractal - >your calculation takes a bit too long to figure this out by guesswork! > >David Bailey >http://www.dbaileyconsultancy.co.uk > > > David Bailey You can speed it up by changing: dlst = Table[ Random[Integer, {1, n0}], {n, 100000}]; to dlst = Table[ Random[Integer, {1, n0}], {n, 25000}]; The article uses alpha, beta, gamma: I use a and b and c instead. Besides the Sierpinski gasket a=b=c=1/2 special symmetrical form there is this one a=b=c=1/3 and the a=b=c=2/3 with is the same one rotated. http://www.geocities.com/rlbagulatftn/triangle3rdsaffine.jpg The code here is very slow for the better graphics: remove one zero for a fast result. Clear[f, dlst, pt, cr, ptlst, M, p, a, b, c, x0, x, y] n0 = 3; dlst = Table[ Random[Integer, {1, n0}], {n, 250000}]; rotate[theta_] := {{Cos[theta], -Sin[theta]}, {Sin[theta], Cos[theta]}}; a = b = c = N[1/3] M = {{{-1 + b, -1/2 + b/2 + a/2}, {0, a}}, {{b + c/2 - 1/2, b/2 - c/4 + 1/4}, {1 - c, c/2 - 1/2}}, {{c/2, -1/2 + a/ 2 - c/4}, {-c, -1 + a + c/2}}} a0 = Table[Det[M[[i]]], {i, 1, 3}] Apply[Plus, a0] in = {{1 - b, 0}, {1 - b, 0}, {1/2, 1}}; Length[in] f[j_, {x_, y_}] := M[[j]]. {x, y} + in[[j]] pt = {0.5, 0.5}; cr[n_] := Flatten[Table[If[i == j == k == 1, {}, RGBColor[i, j, k]], { i, 0, 1}, {j, 0, 1}, {k, 0, 1}]][[1 + Mod[n, 7]]]; ptlst[n_] := Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]}, {j, Length[dlst]}]; Show[Graphics[Join[{PointSize[.001]}, ptlst[n]]], AspectRatio -> Automatic, PlotRange -> All]
