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

TL;DR

rd-spiral is an open-source Python library that efficiently simulates 2D reaction-diffusion systems using pseudo-spectral methods, combining high accuracy with educational clarity.

Contribution

It introduces a novel Python framework that integrates FFT-based discretization with adaptive time integration for simulating complex reaction-diffusion dynamics.

Findings

Revealed non-Gaussian statistics in stable states.

Quantified coupling reductions during turbulence.

Handled high stiffness ratios with automated features.

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.