New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps

TL;DR

This paper introduces a novel algorithm that uses iterated conformal maps to generate Laplacian growth patterns, effectively overcoming previous challenges and enabling detailed analysis of fractal properties.

Contribution

The paper presents a new algorithm for Laplacian growth using iterated conformal maps, improving pattern generation and analysis capabilities.

Findings

Growth patterns are comparable to those from numerical solutions.

Fractal dimension of patterns is analyzed.

Algorithm effectively overcomes growth layer challenges.

Abstract

We report a new 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.