Établissement
ISISS M. Casagrande (Pieve di Soligo)
Année
2016-2017
Résumé
Lets consider a n x n grid with an integer number of snow flakes. If in a moment a cell contains at least 4 flakes, it is unstable: it avalanches giving all its flakes to the 4 neighbouring cells. If the avalanching cell is on the border, the flakes that would fall outside the grid are considered lost.
We analyzed the evolution of the system according to the imposed rules with reference to the proposed problem, starting from some restrictive hypothesis. We put all N flakes in the central cell of an unlimited grid nxn, without counting any lost flake. Flakes propagate until reaching stability after a number of steps, occupying a certain number of cells that let determinate a maximum radius r that is the maximum number of cells neighbouring to the central one. In this work we will analyze the relation between the number N of flakes in the starting cell and the radius r of the stability's con guration.
We analyzed the evolution of the system according to the imposed rules with reference to the proposed problem, starting from some restrictive hypothesis. We put all N flakes in the central cell of an unlimited grid nxn, without counting any lost flake. Flakes propagate until reaching stability after a number of steps, occupying a certain number of cells that let determinate a maximum radius r that is the maximum number of cells neighbouring to the central one. In this work we will analyze the relation between the number N of flakes in the starting cell and the radius r of the stability's con guration.
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