The rule for updating the state of the graph is based on the amount of sand at each point and a value called the threshold.
Any cell which has an amount of sand equal or greater than some threshold value gives 1 grain to each of its neighbors. This transfer of sand is called toppling. In the grid based model the threshold is 4.
Cells with less than 4 neighbors lose sand, decreasing the amount of sand in the system. When no point in the system has enough sand to topple the system is said to be in a stable state.
Interaction of Neighbors
Because the tranformation rule is applied to all cells in the grid simultaneously, adjacent cells which are toppling can interact.
When two adjacent points topple, they exchange a grain of sand. Thus the amount of sand on these two points does not decrease by the threshold value but by threshold - 1, since each gives the other a grain of sand. A cell that is toppling may be simultaneously receiving sand from all of its neighbors for a 0 net change after that time step.
