# a bettter Siegel disk program in Mathematica

From: Roger Bagula (tftn_at_earthlink.net)
Date: 11/23/04

```Date: Tue, 23 Nov 2004 22:35:18 GMT

```

I tried to make it work better.
You really have to watch getting the starting point too large!

Clear[x,y,a,b,s,g,a0,t]
(*Siegel Disk Julia map*)
gm=N[(1+Sqrt[5])/2];
a=Cos[2*Pi*gm];
b=Sin[2*Pi*gm];
digits=400;
x[n_,t_]:=x[n,t]=(x[n-1,t]*a-y[n-1,t]*b+x[n-1,t]^2-y[n-1,t]^2)
y[n_,t_]:=y[n,t]=(x[n-1,t]*b+y[n-1,t]*a+2*x[n-1,t]*y[n-1,t])
x[0,t_]:=0.50/(1+t/2);y[0,t_]=0.01/(1+t/2);
a=Flatten[Table[Table[{x[n,t],y[n,t]},{n,0, digits}],{t,1,10}],1];
ListPlot[a, PlotRange->All]
b=Table[a[[n]][[2]],{n,1,digits+1}];
ListPlot[b,PlotJoined->True, PlotRange->All]

Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net

```
```

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