Re: Iterated Function System
- To: mathgroup at smc.vnet.net
- Subject: [mg67702] Re: Iterated Function System
- From: "JAMES ROHAL" <jrohal at wooster.edu>
- Date: Wed, 5 Jul 2006 04:17:51 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Daniel,
Thanks for the quick response, your algorithm runs much faster. Is there also a way to keep the colors as well? For the NestList function there is no way to differentiate between which function is applied, is there?
James Rohal
College of Wooster 2007
>>> dh <dh at metrohm.ch> 07/04/06 5:01 AM >>>
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
>
>