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Sand Dunes

Rules of the board:

Each square represents a pile of sand. Each pile may initially have 0, 1, 2, 3 or 4 grains of sand in it.

A pile is critical if it has 4 or more grains of sand in it. When a pile is critical it will disperse 4 grains of sand to its four immediate neighbours (diagonals do not count as neighbours). Sand that falls off the edges of the board is not recovered.

A step of the board is taken by concurrently checking each pile and distributing sand from critical piles. A step can only be taken if at least one pile is critical. No sand may be added once the first step is taken.

What initial configuration gives rise to the longest number of steps? How can this be proven?

The initial board configuration, including for the previous game, is displayed to the right of the board. You may want to copy the initial configurations for promising rounds for later experimentation.

Left click to add sand to the board. Middle click or Shift+Left clic to remove sand from the board. Note that adding sand to the board once a step has been taken will start a new game and save your old initial configuration.