Occupancy-Probability Scaling in Diffusion-Limited Aggregation
- 26 August 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 55 (9), 1026-1029
- https://doi.org/10.1103/physrevlett.55.1026
Abstract
A continuous-time random-walk theory of diffusion-limited aggregation yields perimeter occupancy probabilities. Scaling relates the fractal dimension to the cluster-tip occupancy probabilities. These agree with the analytic probabilities near cusps of a lattice-symmetric array of traps. On a two-dimensional square lattice , whereas for the Eden model, and for the dielectric breakdown model. is not universal: for the two-dimensional triangular lattice. The square and triangular lattices bracket (±2.5%) Meakin's large off-lattice simulations ().
Keywords
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