The Universality Class of Diffusion Limited Aggregation and Viscous Fingering

TL;DR

This paper investigates whether viscous fingering and diffusion limited aggregation share the same universality class, using large datasets and a novel conformal mapping technique, revealing strong evidence of their universality despite visual differences.

Contribution

It introduces a new conformal mapping method and provides empirical evidence that viscous fingering and DLA belong to the same universality class.

Findings

Viscous fingering and DLA are in the same universality class.

Large datasets support the universality hypothesis.

A novel conformal mapping technique was developed.

Abstract

We investigate whether fractal viscous fingering and diffusion limited aggregates are in the same scaling universality class. We bring together the largest available viscous fingering patterns and a novel technique for obtaining the conformal map from the unit circle to an arbitrary singly connected domain in two dimensions. These two Laplacian fractals appear different to the eye; in addition, viscous fingering is grown in parallel and the aggregates by a serial algorithm. Nevertheless, the data strongly indicate that these two fractal growth patterns are in the same universality class.