Numba-Accelerated 2D Diffusion-Limited Aggregation: Implementation and Fractal Characterization
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 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.
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Sandy H. S. Herho
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2026-01-23T09:38:14.736Z
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Sandy Hardian Susanto Herho
sandyherho
user
sandyherho
69731ad1fb12c92b735b7579
Faiz R. Fajary
69731ad1fb12c92b735b757a
Iwan P. Anwar
69731ad1fb12c92b735b757b
Faruq Khadami
69731ad1fb12c92b735b757c
Nurjanna J. Trilaksono
69731ad1fb12c92b735b757d
Rusmawan Suwarman
69731ad1fb12c92b735b757e
Dasapta E. Irawan
Numba-Accelerated 2D Diffusion-Limited Aggregation: Implementation and Fractal Characterization
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 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.