“A Fast Fractal Growth Algorithm”

The term ‘fractal’ was coined by Mandelbrot [Mandelbrot 1982] to characterize ‘fractional’ values for physical dimension. While some fractal techniques have since become standard visual effects tools, stochastic fractal growth algorithms, also known as Laplacian growth algorithms, have been largely neglected because they have prohibitive space and time requirements. This is unfortunate because Laplacian growth algorithms have been used in other com- munities to model many phenomena such as snowflakes, lightning, fracture, lichen, coral, riverbeds, vasculature, and urban sprawl pat- terns. From a pure texture synthesis standpoint, they can capture a wide range of visual phenomena that other procedural techniques such as reaction-diffusion and Perlin noise cannot.

MANDELBROT, B. 1982. The Fractal Geometry of Nature. W H Freeman. NIEMEYER, L., PIETRONERO, L., AND WIESMANN, H. J. 1984. Fractal dimension of dielectric breakdown. Physical Review Letters 52, 1033–1036.
WITTEN, T., AND SANDER, L. 1981. Diffusion-limited aggregation, a kinetic critical phenomenon. Physical Review Letters 47, 19, pp. 1400–1403.