Angular gaps in radial diffusion-limited aggregation: two fractal dimensions and nontransient deviations from linear self-similarity.
When suitably rescaled, the distribution of the angular gaps between branches of off-lattice radial diffusion-limited aggregation is shown to approach a size-independent limit. The power-law expected from an asymptotic fractal dimension D = 1.71 arises only for very small angular gaps, which occur only for clusters significantly larger than M = 10(6) particles. Intermediate size gaps exhibit an effective dimension around 1.67, even for M--> infinity. They dominate the distribution for clusters with M<10(6). The largest gap approaches a finite limit extremely slowly, with a correction of order M(-0.17).
Mandelbrot
Benoit B
BB
Department of Mathematics, Yale University, New Haven, Connecticut 06520-8283, USA.
Kol
Boaz
B
Aharony
Amnon
A