Sand, Smoke, Fire and Water: The Cellular Automaton Behind the Sandbox

A grid of simple rules, not a physics engine

Sand, smoke, fire and water in this simulation are not modelled with real fluid equations — they are a cellular automaton: a grid of cells, each holding a material type, updated every frame by a small set of local rules that look only at each cell's immediate neighbours. This is the same family of technique as Conway's Game of Life, just with more than two states and rules tuned to look like physical materials. It is the same trick used in classic "falling-sand" games — cheap to compute, easy to make interactive, and visually convincing without solving a single differential equation.

Sand: gravity plus a coin flip

Each sand cell asks, every frame: is the cell directly below empty? If yes, fall into it. If the cell directly below is occupied but one of the two diagonal cells below is empty, move there instead — this is what lets sand form the realistic sloped piles you see when it lands, called the angle of repose, instead of a single unnatural vertical column. When both diagonals are free the automaton typically picks one at random, which is what gives sand piles their slightly irregular, natural-looking edges rather than perfect symmetric triangles.

Smoke and fire: diffusion and buoyancy

Smoke does the opposite of sand — it tends to rise and spread. Each smoke cell has a chance to move upward or sideways into an empty neighbour, and its density or life value slowly decays each frame until it disappears, which is what makes a smoke plume thin out and fade the higher it climbs. Fire cells behave like smoke but also carry a rule for combustion: a fire cell next to a flammable cell (like sand standing in for fuel) has a chance to convert its neighbour into fire too, and burning cells convert themselves into smoke once their fuel value runs out. This local infection-and-decay pattern is enough to produce flame that flickers, spreads across a fuel source and leaves a smoke trail — all from rules that only ever look one cell away.

SAND:  if below empty        → fall down
       elif diag empty (either) → fall diagonally (random pick)
       else                     → stay

FIRE:  each frame: chance to ignite a flammable neighbour
       fuel -= decay_rate; fuel <= 0 → convert to SMOKE

SMOKE: chance to move up/sideways into empty cell
       life -= decay_rate; life <= 0 → cell becomes empty

Water: the slow-flowing case

Water cells add one more rule on top of sand's falling behaviour: if a water cell cannot fall down or diagonally, it tries to move sideways into an empty neighbour, in either direction. That single extra option — spreading horizontally when blocked from below — is what turns a falling-sand rule into something that pools, finds its own level and spreads out into puddles instead of piling into a heap.

None of this is a Navier-Stokes solver; there is no pressure field, no viscosity term, no velocity vector per particle. What it captures is the qualitative behaviour of each material — sand piles, water spreads, smoke rises and thins, fire eats fuel and produces smoke — which is exactly the level of realism a click-and-draw sandbox needs to feel alive and responsive at 60 frames per second on a grid of tens of thousands of cells.

Frequently asked questions

Try it live

Everything above runs in your browser — open Magic Sand & Smoke and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.