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Bidimensional smooth sand piles

This page is about a new sand pile model called Smooth Sand Pile Model, proposed by Stefano Brocchi and Paolo Massazza. The aim is to propose an evolution rule that only allows a grain to fall where the potential is maximal, avoiding unreasonable configurations reachable in the standard SPM model. In this page, the bidimensional model is represented, even if actually the studyied properties refer more to the monodimensional case. It is interesting to notice that even without imposing global constraints on the model, through the simple evolution rule the fixed points result to be physically reasonable. A paper about the monodimensional model has been presented at the 6th International Workshop on Reachability Problems.

On this page, a Javascript program allows to test the evolution of the model. The clickable arrows represent allowed moves, opaque ones the potentials equal to the maximal ones minus 1. Under the configuration of the grains, there is the array of potentials. The program is mainly referred to the model called SmSPM* in the forthcoming paper, even if some functionalities are related to SmSPM.

Initial configuration:
Reset Triangle Height: Step: Add grain in 1 (+10) Remove grain from 1

Moves:
Back (undo move) Random SmSPM* move Random SmSPM move Evolve (2 moves per second) Stop Find fixed point