Falling SandBeta

About Falling Sand

A falling-sand game is a cellular automaton in which every grid cell holds exactly one element. On each step this tool updates the cells row by row from the bottom up, choosing at random for each row whether to sweep left-to-right or right-to-left, and it never touches a particle twice in the same step. All motion comes down to one operation — swap places with a neighbouring cell — and whether a swap is allowed is decided by density.

So the physics here is rules, not Newton's laws. The angle a sand pile settles at, how fast water spreads, and why oil floats all fall out of a few lines of code and a handful of numbers. What follows spells out those rules and where they part ways with real physics.

One grain's rule, and the 45° pile

Sand, gravel and gunpowder try to move straight down each step. If that cell is blocked, they try down-left or down-right, picking which to try first at random. If both are blocked, they stay put. There is no sideways slide.

That rule alone fixes the slope. A grain only comes to rest when the cell below and both diagonals below are full, so sand poured on one spot forms a triangle that widens by one cell on each side per row — a 45° pile. A triangle h rows high holds 1 + 3 + 5 + … + (2h − 1) = h² cells, so 400 cells of sand poured in one place stand about 20 rows tall. Real dry sand collapses at a gentler slope that depends on friction and grain shape. The fixed 45° here is a property of a grid whose neighbours stop at the diagonals.

Falling speed comes from the rules too. A particle moves at most one cell per step, so it never accelerates no matter how far it falls. In real free fall, speed grows in proportion to time.

Layers from a density ranking

A moving particle can only enter a cell holding something less dense. The ranking in this tool is gravel 10 > sand 9 > gunpowder and seeds 8 > lava 7 > snow 6 > water and acid 5 > oil 4 > smoke, steam, fire and gas 1 > empty 0. Pour sand into water and it swaps its way to the bottom; put oil beneath water and it climbs one cell at a time until it floats on top.

That works well for liquids but not for mixtures of grains. Mix gravel and sand here and the gravel sinks through the sand to the floor. Real granular mixtures that are shaken often do the opposite, with large particles rising to the top — the “Brazil nut effect”, whose mechanism Rosato and colleagues analysed with simulations in 1987. Separation driven by size and shaking cannot come from a simple density comparison.

Water here has no pressure

When water cannot move down, it flows up to four cells sideways in a single step; oil flows up to two. That difference is why oil spreads more slowly than water — a stand-in for viscosity.

What water cannot do is move up. Build a U-tube and fill only one arm, and the levels never even out, unlike real water. In reality the pressure at the bottom pushes water up the other side, but each water particle here only looks at its immediate neighbours. Fountains and siphons fail for the same reason. Commercial games work around this by layering separate pressure calculations or rigid-body physics on top of the particle rules; Petri Purho's GDC 2019 talk on Noita, a game built entirely on falling-sand simulation, describes how those layers were combined.

A few reaction rules

Fire checks the four cells above, below, left and right each step. Per-step ignition odds are 0.6 for gas, 0.15 for oil and 0.05 for wood, plants and seeds. Fire on wood lasts 90 to 150 steps, which is why gas flashes and vanishes while a wood pile smoulders for a long time.

Fire touching water turns the water to steam and goes out. Lava touching water becomes stone (gravel) and turns the water to steam. Steam rises, and when its lifetime runs out it has a 30% chance of becoming a water droplet that falls again — the whole rain cycle comes from that one line. Gunpowder touched by fire or lava blows out a radius of six cells.

• Open floor: moving particles in the bottom row drain away, handy for waterfalls that keep flowing.
• Cloner: it keeps producing the first element that touched it, so a water cloner next to a lava cloner makes stone endlessly.
• “Extreme” resolution: smaller cells push the particle count into the millions. The rules do not change, so piles still stand at 45°.

Worked examples

How to use it

1. Pick an element from the palette and drag on the canvas to pour it (right button erases).
2. Use Line and Box to build walls or containers first.
3. Add fire, lava or gunpowder to watch reactions, or shake things up with the Bomb or Lightning.

Frequently asked questions