Re: tetrahedral Siegel Disk Julia map
- To: mathgroup at smc.vnet.net
- Subject: [mg52413] Re: tetrahedral Siegel Disk Julia map
- From: Roger Bagula <tftn at earthlink.net>
- Date: Fri, 26 Nov 2004 01:04:49 -0500 (EST)
- References: <co4ebr$lbo$1@smc.vnet.net>
- Reply-to: tftn at earthlink.net
- Sender: owner-wri-mathgroup at wolfram.com
http://www.math.harvard.edu/~ctm/gallery/menu.html A gallery of tetrahedral / K3 Siegel disk dynamics by Dr McMullen Dynamics on K3 surfaces K3 movie <http://www.math.harvard.edu/%7Ectm/gallery/movies/k3.movie.gif> K3 surface <http://www.math.harvard.edu/%7Ectm/gallery/k3/k3.surf.gif> Tame <http://www.math.harvard.edu/%7Ectm/gallery/k3/k3.tame.gif> Wilder <http://www.math.harvard.edu/%7Ectm/gallery/k3/k3.wild.gif> Ergodic <http://www.math.harvard.edu/%7Ectm/gallery/k3/k3.ergo.gif> Stable manifold <http://www.math.harvard.edu/%7Ectm/gallery/k3/stableman.gif> Tame blowup <http://www.math.harvard.edu/%7Ectm/gallery/k3/k3.tameblowup.gif> Poncelet's theorem <http://www.math.harvard.edu/%7Ectm/gallery/k3/conics.gif> Poncelet Java <http://www.math.harvard.edu/%7Ectm/gallery/poncelet/index.html> (Schwartz) <http://www.math.umd.edu/%7Eres> Dynamics on a (2,2) curve <http://www.math.harvard.edu/%7Ectm/gallery/k3/curve22.gif> Roger Bagula wrote: >Siegel disks don't just happen in complex dynamics of quadratics. >You can set this type of "motion" going on other Riemannian surfaces >as Dr. McMullen suggested in his paper on K3 surfaces >using an tetraheral implicit surface and a Salem based irrational number. >In this simulation an Siegel disk is located on a Riemannian >tetraheral surface. > >Clear[x,y,a,b,s,f,g,a0,t] >(*tetrahedral Siegel Disk Julia map*) >(* idea based on McMullen K3 ( tetrahedral) surface Siegel disk dynamics*) >z=x[n-1,t]+I*y[n-1,t] >z4=ComplexExpand[z^4-2*Sqrt[3]*I*z^2+1] >(* Riemannian Tetrahedron polynomial from Elliptic Curves, McKean and Moll, > p22, Ellipical invariants of Platonic solids*) >(* j[z]=(z^4-2*Sqrt[3]*I*z^2+1)^3/(z^4+2*Sqrt[3]*I*z^2+1) *) >f[n_,t_]=Re[z4] >g[n_,t_]=Im[z4] >gm=N[(1+Sqrt[5])/2]; >a=Cos[2*Pi*gm]; >b=Sin[2*Pi*gm]; >digits=1500; >x[n_,t_]:=x[n,t]=x[n-1,t]*a-y[n-1,t]*b+f[n,t]/4 >y[n_,t_]:=y[n,t]=x[n-1,t]*b+y[n-1,t]*a+g[n,t]/4 >x[0,t_]:=0.27/(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] >Respectfully, Roger L. Bagula > >tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : >alternative email: rlbtftn at netscape.net >URL : http://home.earthlink.net/~tftn > > > -- Respectfully, Roger L. Bagula tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : alternative email: rlbtftn at netscape.net URL : http://home.earthlink.net/~tftn