⛱️ Granular Materials — Sand Pile
Drop grains of sand onto a pile and watch complex collective behaviour emerge: heap formation, the characteristic angle of repose, and sudden avalanches triggered when local slope exceeds the critical angle. A cellular automaton (BTW model) governs redistribution.
Mode
Parameters
Statistics
If z[i] - z[i±1] > zc:
z[i] -= 1, z[i±1] += 1
(toppling cascade → avalanche)
θ = arctan(zc/grain_d)
Granular Physics
Granular materials (sand, grain, gravel) behave like solids, liquids, or gases depending on conditions — they are a distinct state of matter. The angle of repose θ is the maximum stable angle a pile can sustain before grains slide: θ depends on grain shape, surface roughness, and moisture. The Bak-Tang-Wiesenfeld (BTW) cellular automaton models how local slope relaxation cascades into large avalanches following a power-law size distribution — a signature of self-organised criticality. When the pile reaches the critical slope globally, it hovers at the edge of stability; any added grain may or may not trigger an avalanche.