Clear["`*"]; ifs[prob_,A_,init_,max_]:=FoldList[#2.{#[[1]],#[[2]],1}&,init,RandomChoice[prob->A,max]]; L={{{0.03,0},{0,0.1}},{{0.85,0},{0,0.85}},{{0.8,0},{0,0.8}},{{0.2,-0.08},{0.15,0.22}},{{-0.2,0.08},{0.15,0.22}},{{0.25,-0.1},{0.12,0.25}},{{-0.2,0.1},{0.12,0.2}}}; B=Map[List,{{0,0},{0,1.5},{0,1.5},{0,0.85},{0,0.85},{0,0.3},{0,0.4}},{2}]; {A,prob,init,max}={N@Join[L,B,3],{2,60,10,7,7,7,7}/100.,{0.,2.},10^5}; pts=ifs[prob,A,init,max];//AbsoluteTiming Graphics[{{Darker@Green,PointSize@Tiny,Point@pts},{Hue@Random[],PointSize@Large,Point@#}&/@RandomChoice[pts,200]},AspectRatio->1.5]
