Numba-Accelerated 2D Diffusion-Limited Aggregation: Implementation and Fractal Characterization

TL;DR

This paper introduces a high-performance, Numba-accelerated Python framework for simulating 2D Diffusion-Limited Aggregation, analyzing fractal properties and phase transitions with novel quantitative metrics.

Contribution

It provides a reproducible, open-source simulation tool that combines high computational efficiency with detailed fractal and heterogeneity analysis of DLA growth.

Findings

Standard fractal dimension Df ≈ 1.71 in dilute regimes

Crossover to Eden-like growth with Df ≈ 1.87 at high densities

Quantitative characterization of aggregate heterogeneity using Re9nyi dimensions and lacunarity

Abstract

We present dla-ideal-solver, a high-performance framework for simulating two-dimensional Diffusion-Limited Aggregation (DLA) using Numba-accelerated Python. By leveraging just-in-time (JIT) compilation, we achieve computational throughput comparable to legacy static implementations while retaining high-level flexibility. We investigate the Laplacian growth instability across varying injection geometries and walker concentrations. Our analysis confirms the robustness of the standard fractal dimension $D_f \approx 1.71$ for dilute regimes, consistent with the Witten-Sander universality class. However, we report a distinct crossover to Eden-like compact growth ($D_f \approx 1.87$) in high-density environments, attributed to the saturation of the screening length. Beyond standard mass-radius scaling, we employ generalized R\'{e}nyi dimensions and lacunarity metrics to quantify the monofractal character and spatial heterogeneity of the aggregates. This work establishes a reproducible, open-source testbed for exploring phase transitions in non-equilibrium statistical mechanics.