I want to simulate urban growth in the French Riviera with a cellular automaton. The following program works and analyzes the results. Rule 1000 seems appropriate. St. Wolfram has classified the behavior of cellular automata. But can we have a phenomenological classification ? What are the useful rules to simulate a simple diffusion or a diffusion equivalent to a flight Levy ?

ClearAll["Global`*"]

image={}

coteazur = ArrayPad[ImageData[Binarize[ColorNegate[image,30];

etats = Flatten[
   CellularAutomaton[{1000, {2, 1}, {1, 1}}, coteazur, 20], {1}];
imd = Image[etats[[1]]];
imf = Image[etats[[20]]];
GraphicsRow[{ColorNegate[imd], ColorNegate[imf]}, ImageSize -> 300]
ImageMeasurements[imd, {"Mean", "StandardDeviation", 
  "IntensityCentroid", "Entropy"}, "Dataset"]
ImageMeasurements[imf, {"Mean", "StandardDeviation", 
  "IntensityCentroid", "Entropy"}, "Dataset"]
ColorNegate[ImageDifference[imf, imd]]
flist = {EuclideanDistance, ManhattanDistance, CorrelationDistance, 
   "DifferenceNormalizedEntropy"};

Grid[Table[{f, ImageDistance[imd, imf, DistanceFunction -> f]}, {f, 
   flist}], Alignment -> {{Right, Left}, Center}]
croissance = Table[Count[Flatten[etats[[i]]], 1], {i, 1, 20, 1}];

ts = TimeSeries[croissance, {Range[1, 20]}];
ListLinePlot[ts]

model = TimeSeriesModelFit[ts];
Normal[model]