Algorithm for parallel Laplacian growth by iterated conformal maps

2003/05/22 by Anders Levermann, Itamar Procaccia
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #nlin.CD

paper · pdf · doi:10.1103/physreve.69.031401

Sumitted to Phys. Rev. Lett. Further details at http://www.pik-potsdam.de/~anders

arxiv created 2003/05/22 · openalex publication_date 2004/03/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We report an algorithm to generate Laplacian growth patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth patterns are compared to those obtained by the best algorithms of direct numerical solutions. The fractal dimension of the patterns is discussed.

Citations

• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
• Convergent calculation of the asymptotic dimension of diffusion limited aggregates: Scaling and renormalization of small clusters