Technique · Geometry
Diffusion-limited aggregation
Random walkers stick where they touch and grow a branching fractal: coral, frost, lichen and lightning.
Diffusion-limited aggregation is drawn geometry, rebuilt as it changes. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- Electrodeposition, growing metal from a salt solution with a small current, makes branching copper trees that are real diffusion-limited aggregates.
- Mineral dendrites, manganese oxide ferns in limestone, were once mistaken for fossil plants.
- A snowflake grows its arms because water vapour reaches the tips first, an instability described by Mullins and Sekerka.
- Diffusion-limited aggregation was described by Thomas Witten and Leonard Sander in 1981; in the plane its fractal dimension is about 1.71.
- The same shapes appear in lightning, electrodeposited metal, dendrites of manganese in stone, and frost on a window.
The mathematics
- The cluster's mass grows as its radius to the power of about 1.71, so doubling its radius multiplies the number of particles by about 3.3, not 4 as for a solid disc.
- A stickiness of 0.60: lower values let walkers slip deeper into the fjords and make a denser, bushier cluster.
In art
- Frost on a window pane is a drawing nobody made: each crystal repeats, at small scale, the branching of the whole.
- Lichtenberg figures, the branching scars that a high-voltage discharge burns into wood or acrylic, belong to the same family of forms, and woodworkers now make them on purpose.
More ways to use it
Related techniques
L-system · Space colonisation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes · Stipple and Delaunay portrait