The Hénon map

A blob of random initial conditions, stroboscopic animation

Clear[map,a,b]
imsize=550;xlim=1.9;ylim=0.5;
frame=12;
points=700;(*points per frame*)

icoord=RandomReal[{-0.4,0.4},{points,2}];(*random blob of points, initial condition*)
a=1.4;b=0.3;
map[ic_,i_]:={1-a ic[[i,1]]^2+ic[[i,2]],b ic[[i,1]]}

sol=NestList[Table[map[#,i],{i,1,points,1}]&,icoord,frame];
ListAnimate[Table[ListPlot[sol[[i]],PlotRange->{{-xlim,xlim},{-ylim,ylim}},Frame-> True,PlotStyle->Black,PlotMarkers->{"•",6},FrameLabel->{x,y},AspectRatio->0.9,LabelStyle->20,ImageSize->imsize],
{i,1,frame}],
AnimationRunning->False,SaveDefinitions->True]

Creation of this notebook was supported by IT Academy program of Information Technology Foundation for Education (HITSA).