bigbang.gif

 

 

This movie is an answer to Exercise 18 on page 249 of Volume I of Harmonic Analysis on Symmetric Spaces and Applications, old edition.

It shows the big bang phenomenon discovered by Harold Stark.  The Mathematica program used to create it is as follows.

            green[x_]:=green[x]=If[(x-Floor[x])<=.5,x-Floor[x],x-Floor[x]-1]

            gre[z_]:=gre[z]=green[Re[z]]+I*Im[z]

            har[t_]:=har[t]=(perm={};For[j=1,j<=51,j++,(z=(j/51)+I/(2^t);Label[begin];z=gre[-1/z];If[Abs[z]<1,Goto[begin],perm=Append[perm,z]])])

           

            pict[n_]:=pict[n]=(har[n];

            pts=Table[{Re[perm[[j]]],10-1/Im[perm[[j]]]},{j,1,51}];

            Graphics[{PointSize[Medium],Red,Point[pts]},Axes->True,PlotRange->{{-2,2},{8.5,10}},AspectRatio->1,AxesOrigin->{0,0}])

           

            ListAnimate[Table[pict[n],{n,0,21,.05}]]

           

            Export["bigbang.avi",%]