Sand grains are lifted by wind and hop downwind, the primary mode of aeolian sand transport that drives dune migration.
When the slope exceeds the angle of repose (~34°), sand avalanches down the lee face, shaping the dune's slip face.
Crescent-shaped barchan dunes emerge naturally from the interplay of saltation transport and avalanche relaxation.
This simulation models how barchan dunes form and migrate using a cellular automaton on a 2-D height grid. Each cell stores an integer grain count. At every step the model applies three physical rules: wind supply deposits fresh grains at the upwind (left) edge; saltation stochastically lifts grains and re-deposits them a hop-length downwind, representing the bouncing transport that dominates aeolian environments; and avalanche relaxation redistributes sand between neighbours whenever the height difference exceeds the angle-of-repose threshold, recreating the steep slip face that characterises real dunes. Crescent barchan shapes emerge spontaneously from these simple rules, demonstrating how complex natural patterns can arise from local interactions.
Use the Wind slider to change hop length and saltation probability, Supply to control how much fresh sand enters from the left, and Avalanche angle to adjust the steepness threshold. A low angle produces smoother mounds; a high angle permits towering columns before collapse. Press Flatten to start from a bare surface and watch dunes nucleate from scratch, or Reset to reseed a few random proto-dunes. The simulation runs in pure Canvas 2-D with no external libraries — colour encodes grain height from dark sienna at the base to bright tan at the crest.
What is a barchan dune?
A barchan is a crescent-shaped sand dune with two horn-like arms pointing downwind. It forms in areas with a consistent wind direction and limited sand supply, such as coastal deserts and the floors of Mars. The curved shape arises because sand moves fastest over the thin horns and slowest over the thicker central crest.
What is saltation?
Saltation (from the Latin saltare, to leap) is the hopping motion of sand grains carried by wind. A grain is lifted, travels a short arc through the air, then strikes the surface, either re-embedding or ejecting further grains. It is the dominant transport mechanism in aeolian dune systems and accounts for most of the sand flux in a dune field.
What is the angle of repose?
The angle of repose is the maximum slope that a granular material can sustain before grains slide. For dry quartz sand it is approximately 30–34 degrees. In the simulation the avalanche-angle slider controls this threshold: when a height difference between adjacent cells exceeds it, sand cascades to the lower cell, recreating the steep slipface avalanche seen on real dunes.
The model divides the domain into a rectangular grid of cells, each storing an integer grain count. Each simulation step applies: (1) left-edge injection of new grains proportional to the supply rate; (2) stochastic saltation that lifts grains with probability proportional to wind speed and re-deposits them a fixed hop-length to the right with a small lateral scatter; (3) avalanche relaxation repeated several times per step to propagate cascades. The combination produces realistic dune morphodynamics from just three local rules.
Sand is continuously eroded from the windward (stoss) face and deposited on the leeward (lee) face. The crest slowly shifts downwind as this one-sided flux persists. Smaller dunes have a shorter distance between stoss and lee faces and therefore migrate faster than large dunes, a property that causes dunes to merge when a fast small dune overtakes a slower large one.
The horns appear because sand flux is proportional to local height: the edges of the dune are thinner, so the saltation hop carries sand all the way to the horn tip before depositing. The thicker central body traps more sand and grows more slowly. The lateral imbalance sculpts the characteristic crescent outline without any external instruction — it is a self-organised emergent shape.
Higher wind speeds increase both the saltation hop length and the probability that a grain is lifted. Faster winds tend to create longer, flatter dunes with more sand in transit. Very high speeds can prevent stable dunes from forming because grains are transported across the domain before they can accumulate. The Wind slider lets you explore this transition from stable barchans to sheet-like transport.
No — dunes form wherever wind, sand, and sufficient fetch co-exist. Coastal dunes stabilise shorelines on every continent; river dunes build up in sandy riverbeds; and aeolian dunes cover large areas of Mars, Titan, Venus, and even Pluto. The same cellular automaton rules capture dune morphology across these environments when parameters are adjusted to reflect local gravity, grain size, and fluid density.
The model is a qualitative cellular automaton inspired by the Werner (1995) framework, which correctly reproduces the emergence of barchan shapes, dune merging, and migration speed scaling. It simplifies three-dimensional geometry, grain-size distribution, turbulent wind profiles, and moisture effects. It is accurate enough for education and visual exploration but not for quantitative field prediction, where continuous-field models are used instead.