Diffusion limited aggregation

size = 200;
Clear[sticky];
Tmax = 1000;
n = 10000;
sticky[x_, y_] := False;
sticky[Floor[size]/2, Floor[size]/2] = True;
free = RandomReal[{0, size}, {n, 2}];
f[{x_, y_}] := {Clip[Round[x], {1, size}],
   Clip[Round[y], {1, size}]};
frames = {};
stuck = {};
Do[
  newfree = {};
  Do[
   {x, y} = f[free[[i]]];
   If[sticky[x, y],
    Table[
     sticky[x + xshift, y + yshift] = True;, {xshift, -1,
      1}, {yshift, -1, 1}];
    AppendTo[stuck, {x, y}];
    ,
    AppendTo[newfree, free[[i]]];
    ];
   , {i, Length@free}];
  newfree += RandomReal[{-1, 1}, {Length@newfree, 2}];
  free = newfree;
  AppendTo[frames, {newfree, stuck}];
  , {t, Tmax}];
Manipulate[
 With[{free = frames[[i, 1]], stuck = frames[[i, 2]]},
  Graphics[{PointSize[Small], Opacity[0.3], Point[free], Opacity[1],
    Table[{ColorData["FallColors"][1 - i/Length@stuck],
      Disk[stuck[[i]], 1]}, {i, Length@stuck}]
    },
   PlotRange -> {{0, size}, {0, size}}, ImageSize -> 250
   ]
  ],
 {i, 1, Tmax, 1}]