A better Implicit Mandelbrot
- To: mathgroup at smc.vnet.net
- Subject: [mg51045] A better Implicit Mandelbrot
- From: Roger Bagula <tftn at earthlink.net>
- Date: Sat, 2 Oct 2004 03:18:59 -0400 (EDT)
- Reply-to: tftn at earthlink.net
- Sender: owner-wri-mathgroup at wolfram.com
Suppose we use both sets of polynomials at once in a rational like function: Rn(c)=Sum[Pcn(0),{n,1,Infinity}]/Sum[D[Pcn(0),c]),{n,1,Infinity}] At n=7 I'm no where near Infinity, but I'm gretting pretty good results. Doing this in any language but Mathematica would be much harder I think, so developing software from it might take some effort and the polynomials still have to be found for each case. After n=7 they become really big. It has been several years since a new visualization approach that is entirely different has been found. There is a scaling problem when doing close ups in the ContourPlot which can almost be handled by making the plot point level the same but not quite ( Don Taylor has been helping me on this as ContourPlot has been crashing on my machine). Mandelbrot Mathematica rational implicit: << Graphics`ImplicitPlot`; g[z_]=z2+c; nl=NestList[g,c,7]; nr=D[nl,c]; c=z; q[z_]=Apply[Times,nl]; p[z_]=Apply[Times,nr]; z=x+I*y; f[x_,y_]=Re[q[z]/(p[z])]; ImplicitPlot[f[x,y]==0,{x, -2.5, 1}, {y, -1.75,1.75},, PlotPoints -> {300, 300}] Plot3D[f[x,y], {x, -2.5, 1}, {y, -1.75,1.75}, PlotPoints -> {145, 145},Mesh->False,Boxed->False,Axes->False] ContourPlot[ f[x,y],{x, -2.5, 1}, {y, -1.75,1.75},PlotPoints -> {300, 300},ImageSize -> 600,ColorFunction->(Hue[2#]&)] DensityPlot[f[x,y], {x, -2.5, 1}, {y, -1.75,1.75}, PlotPoints -> {145, 145},Mesh->False,Axes->False] Respectfully, Roger L. Bagula tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : URL : http://home.earthlink.net/~tftn URL : http://victorian.fortunecity.com/carmelita/435/