NestList Examples

NL=NestList[{Sin[2#1[[2]]]-Cos[3#1[[1]]],
Sin[2#1[[1]]]+Cos[#1[[2]]]}&,{-.5,.5},10^5];
ListPlot[NL,Axes->False,PlotStyle->Opacity[.1],
ColorFunction->Function[{x,y},Hue[x*y]],
ImageSize->500,AspectRatio->1,
Background->Lighter[Gray,.7]]