Clear["`*"];
t0 = AbsoluteTime[];
ifs[prob_, A_, init_, maxIter_] :=
  FoldList[#2.{#[[1]], #[[2]], 1} &, init,
   RandomChoice[prob -> A, maxIter]];

init = {0., 0.};
prob = N@{85, 6, 8, 1};
A = N@{{{0.83, 0.03, 0}, {-0.03, 0.86, 1.5}}, {{0.2, -0.25, 0}, {0.21,
       0.23, 1.5}}, {{-0.15, 0.27, 0}, {0.25, 0.26, 0.45}}, {{0, 0,  0}, {0, 0.17, 0}}};
iter = 10^5;
pts = ifs[prob, A, init, iter];
Graphics[{PointSize[0.002], Green, Point[pts]}]
AbsoluteTime[] - t0