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arXiv · 2506.20633

rd-spiral: An open-source Python library for learning 2D reaction-diffusion dynamics through pseudo-spectral method

Sandy H. S. Herho·Iwan P. Anwar·Rusmawan Suwarman
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Abstract

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis $>96$) in stable states. Information-theoretic metrics show $10.7\%$ reduction in activator-inhibitor coupling during turbulence versus $6.5\%$ in stable regimes. The solver handles stiffness ratios $>6:1$ with features including automated equilibrium classification and checkpointing. Effect sizes ($\delta=0.37$--$0.78$) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

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Sandy H. S. Herho, Iwan P. Anwar, Rusmawan Suwarman. 2025-06-25. rd-spiral: An open-source Python library for learning 2D reaction-diffusion dynamics through pseudo-spectral method. https://arxiv.org/abs/2506.20633

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