phenomenomological classification of automaton cellular

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 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] `
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