Re: Iterated Function System
- To: mathgroup at smc.vnet.net
- Subject: [mg67693] Re: Iterated Function System
- From: dh <dh at metrohm.ch>
- Date: Wed, 5 Jul 2006 04:17:07 -0400 (EDT)
- References: <e8d0uo$4dk$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi James, you could e.g. try: M = {{1/2, 0}, {0, 1/2}}; T[1, x_] := {0, 0} + M.x; T[2, x_] := {1/2, 0} + M.x; T[3, x_] := {1/4, Sqrt[3]/4} + M.x; zi = {Random[], Random[]}; res = NestList[T[Random[Integer, {1, 3}], #] &, zi, 20000]; ListPlot[res, PlotJoined -> False] Daniel JAMES ROHAL wrote: > I am looking for a faster way to plot Iterated Function Systems in Mathematica. Currently my method is using Barnsley's algorithm which randomly chooses a transformation and applies it to a previous point to get the next point. I then store the points in a list corresponding to the transformation that was applied to it. Is there a faster way to program this using functional programming in Mathematica? Thanks in advance. > > << Graphics`MultipleListPlot` > << Graphics`Colors` > > steps = 30000; > > M = {{1/2, 0}, {0, 1/2}}; > T1[x_] := {{0}, {0}} + M.x; > T2[x_] := {{1/2}, {0}} + M.x; > T3[x_] := {{1/4}, {Sqrt[3]/4}} + M.x; > > zi = {{Random[]}, {Random[]}}; > T1listPoints = {}; > T2listPoints = {}; > T3listPoints = {}; > > For[i = 1, i < steps, i++; > rand = Random[Integer, {1, 3}]; > Switch[rand, > 1, {zi = T1[zi], T1listPoints = Append[T1listPoints, Flatten[zi]]}, > 2, {zi = T2[zi], T2listPoints = Append[T2listPoints, Flatten[zi]]}, > 3, {zi = T3[zi], T3listPoints = Append[T3listPoints, Flatten[zi]]} > ]; > ]; > > graph1 = ListPlot[T1listPoints, PlotStyle -> {PointSize[0.00001], RGBColor[1, 0, 0]}, DisplayFunction -> Identity]; > graph2 = ListPlot[T2listPoints, PlotStyle -> {PointSize[0.00001], RGBColor[0, 1, 0]}, DisplayFunction -> Identity]; > graph3 = ListPlot[T3listPoints, PlotStyle -> {PointSize[0.00001], RGBColor[0, 0, 1]}, DisplayFunction -> Identity]; > Show[{graph1, graph2, graph3}, DisplayFunction -> $DisplayFunction]; > > James Rohal > College of Wooster 2007 > >