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

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 $10.7\mathrm{\%}$ reduction in activator-inhibitor coupling during turbulence versus $6.5\mathrm{\%}$ 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.