Numba-Accelerated 2D Diffusion-Limited Aggregation: Implementation and Fractal Characterization
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| Format: | Preprint |
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2026
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| author | Herho, Sandy H. S. Fajary, Faiz R. Anwar, Iwan P. Khadami, Faruq Trilaksono, Nurjanna J. Suwarman, Rusmawan Irawan, Dasapta E. |
| author_facet | Herho, Sandy H. S. Fajary, Faiz R. Anwar, Iwan P. Khadami, Faruq Trilaksono, Nurjanna J. Suwarman, Rusmawan Irawan, Dasapta E. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_15440 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Numba-Accelerated 2D Diffusion-Limited Aggregation: Implementation and Fractal Characterization Herho, Sandy H. S. Fajary, Faiz R. Anwar, Iwan P. Khadami, Faruq Trilaksono, Nurjanna J. Suwarman, Rusmawan Irawan, Dasapta E. Pattern Formation and Solitons Computational Physics 82C24, 60G50, 28A80, 82C80 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. |
| title | Numba-Accelerated 2D Diffusion-Limited Aggregation: Implementation and Fractal Characterization |
| topic | Pattern Formation and Solitons Computational Physics 82C24, 60G50, 28A80, 82C80 |
| url | https://arxiv.org/abs/2601.15440 |