Diffusion Image

diffuse[point_, t_] :=
  Total[Join[{point},
    RandomReal[NormalDistribution[0, 0.5], {t, 2}]]];
img = ImageCrop[
  Rasterize[
   Graphics[Text[Style["diffusion", FontSize -> 100], {0, 0}]]]];
imgdata = ImageData[img];
time[x_, \[Alpha]_, \[Beta]_] :=
 Module[{g = x/Length[imgdata[[1]]]},
  Floor[\[Alpha] Abs[g]^\[Beta] + 1]];
coords = Flatten[
   Table[{{i, -j}, imgdata[[j]][[i]]}, {j, Length[imgdata]}, {i,
     Length[imgdata[[1]]]}], 1];
frame[\[Alpha]_, \[Beta]_] :=
 Module[{points, diffused},
  points = Map[#[[1]] &, Select[coords, Norm[#[[2]] ] < 0.01 &]];
  diffused =
   Map[{ColorData["TemperatureMap"][#[[1]]/Length[imgdata[[1]]]],
      Point[diffuse[#, time[#[[1]], \[Alpha], \[Beta]]]]} &, points];
  Graphics[diffused, Background -> Black, ImageSize -> {1000}]];

frame[200, 2.5]