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

2026/01/21 by Sandy H. S. Herho, Faiz R. Fajary, Iwan P. Anwar +4 · 1 voice
Physics and Astronomy · #nlin.PS #physics.comp-ph

paper · pdf

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 ≈ 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 ≈ 1.87) in high-density environments, attributed to the saturation of the screening length. Beyond standard mass-radius scaling, we employ generalized Rényi 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.

Citations

• amangkurat: A Python Library for Symplectic Pseudo-Spectral Solution of the Idealized (1+1)D Nonlinear Klein-Gordon Equation
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Discussions

• Herho, Fajary, Anwar, Khadami, Trilaksono, Suwarman, Irawan: Numba-Accelerated 2D Diffusion-Limited Aggregation: Implementation and Fractal Characterization https://arxiv.org/abs/2601.15440 https://ar [bsky, 0 points, 0 comments]

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