Deterministic solutions of fractal growth
- 1 November 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 32 (5) , 3156-3159
- https://doi.org/10.1103/physreva.32.3156
Abstract
We study the problem of pattern formation on a lattice. A maximum-likelihood growth algorithm is formulated to supplement the integral solution of Laplace’s equation. This allows us to study diffusion-limited aggregation and viscous flow in porous media. Our deterministic solution for the aggregation process displays the same fractal dimension (D≊1.7) as Monte Carlo diffusion-limited aggregation. We also compare our solution to Laplace’s equation with the experimentally observed pattern in one limit of a Hele-Shaw cell experiment. Lastly, we present a second deterministic algorithm which results in a pattern with tips which appear parabolic.Keywords
This publication has 21 references indexed in Scilit:
- Diffusion-Limited Aggregation and Two-Fluid Displacements in Porous MediaPhysical Review Letters, 1984
- Geometrical models of interface evolutionPhysical Review A, 1984
- Boundary-layer model of pattern formation in solidificationPhysical Review A, 1984
- Dynamics of Interfacial Pattern FormationPhysical Review Letters, 1983
- Geometrical Approach to Moving-Interface DynamicsPhysical Review Letters, 1983
- Diffusion-limited aggregationPhysical Review B, 1983
- Radial fingering in a Hele Shaw cellJournal of Fluid Mechanics, 1981
- Diffusion-Limited Aggregation, a Kinetic Critical PhenomenonPhysical Review Letters, 1981
- Instabilities and pattern formation in crystal growthReviews of Modern Physics, 1980
- The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquidProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1958