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 $D=1.71\mathrm{}$ arises only for very small angular gaps, which occur only for clusters significantly larger than ${M=10\mathrm{}}^6$ particles. Intermediate size gaps exhibit an effective dimension around 1.67, even for $M\to \infty$. They dominate the distribution for clusters with $M<\mathrm{}{10}^6$. The largest gap approaches a finite limit extremely slowly, with a correction of order $M^{-0.17\mathrm{}}$.