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The science
Angle of repose
A granular pile stays put while the slope is below the angle of repose theta; steeper columns avalanche. The automaton (identical to the 3D page) moves a share 0.5 * settle * (excess) of the height difference above tan(theta) * cell to each lower 4-neighbour, capped at half the column height, three relaxation passes per step. Material poured has a Gaussian footprint (sigma 1.1 cells).
Cone volume
An ideal cone of height h and slope tan(theta) has radius h / tan(theta) and volume pi h^3 / (3 tan^2 theta), so peak height grows only as the cube root of the poured volume.
Honest simplifications
This is a height-field model: no inertia, no dilatancy, no hysteresis between the angle of repose and the avalanche angle, no grains. The 4-neighbour rule makes slopes exactly tan(theta) along the grid axes but about sqrt(2) times steeper along the diagonal, so the pile is diamond-shaped and reaches only 1/sqrt(2) as far diagonally; the diagonal section makes this grid artefact visible. Heights are drawn with a 62 cm tray for scale; the 3D page has no physical unit.
Try this
Pour snow (28 deg) and sand (34 deg) and compare peak heights for the same volume; move the pour point near the edge to see material spill; fire a wind gust and watch the downwind drift.