Another version of the sand pile model, called the “single source” model, starts from a different initial condition: instead of all cells at the same level, all cells are set to 0 except the center ce...Another version of the sand pile model, called the “single source” model, starts from a different initial condition: instead of all cells at the same level, all cells are set to 0 except the center cell, which is set to a large value. Run the CA until it stabilizes again, keeping track of T, the number of time steps it takes, and S, the number of cells affected.
We’ll count the number of cells in a small box at the center of the pile, then see how the number of cells increases as the box gets bigger. The estimate for level 3 is indistinguishable from 2, but g...We’ll count the number of cells in a small box at the center of the pile, then see how the number of cells increases as the box gets bigger. The estimate for level 3 is indistinguishable from 2, but given the results for the other values, the apparent curvature of the line, and the appearance of the pattern, it seems likely that it is also fractal.
