Diffusion-limited aggregation

The diffusion- limited growth ( diffusion- limited aggregation, DLA) comes about by random addition of particles. This is based on the Brownian molecular motion, according to their laws particles in gases or liquids move thermally. They form one of the simplest mechanisms for generating fractals.

The particles are deposited more likely to already existing at the tips. The resulting highly branched structures ( " Brownian trees " ) are in the limit of infinitely small particles fractals.

The diffusion- limited growth was described in 1981 by Leonard M. Sander and Thomas Witten. They had become aware of the observation of such reminiscent of Mandelbrot's fractal structures in deposits of iron colloids and tried to simulate their formation in a simple computer model. In the Witten- Sander model, a particle moves mainly under the influence of diffusion ( Brownian motion ) until it already deposited particle comes close to a " cluster ". It falls below a minimum distance, it anneals to the cluster. To the surprise of Sander and Witten showed in the simulation ramified, fractal structures.


  • Deposition of soot particles: particles are deposited on the walls of a fireplace and cause clogging of the tube
  • Precipitates in electrolytic solutions, such as Copper sulphate solution, which can be precipitated by suitable cathode to pure copper (see picture, copper refining ).
  • Tree-like structures in biology, such as the formation of the fur patterns in zebra, tiger, leopard, tapir
  • Lichtenberg figures
  • Snowflakes, see also Koch curve