Nonlinear regime transitions enable reservoir computation in activator-inhibitor cellular automata

Abstract

Activator-inhibitor systems are usually studied as pattern-forming media, but the same local nonlinear interactions can also shape how information is stored and separated over time. Here we first introduce a reaction-diffusion-inspired cellular automaton as a tunable nonlinear medium with two activation families, a continuous sigmoid and a logistic-step relaxer. In each case, a single family-specific parameter changes the nonlinear response or relaxation dynamics while leaving the neighbourhood wiring fixed. This provides a controlled way to move the activator-inhibitor system between collapsed, structured, saturated, and overshooting regimes, and to relate these regimes to state-level diversity and pattern compressibility. We then use reservoir computing to test whether these tuned pattern-forming regimes support fading memory, input separability, and downstream readout learning. In this role, reservoir computing is not treated as an architecture to be optimised, but as a diagnostic of the computational properties of the untrained medium. Across parameter sweeps, stronger memory and separability are concentrated near transition regions rather than distributed uniformly across parameter space. These results identify activator-inhibitor cellular automata as interpretable unconventional reservoir substrates in which effective gain, threshold, and relaxation parameters tune the balance between pattern formation, memory, and separability. More broadly, they support the view that tissue-like or physical pattern-forming media may, in principle, shift between patterning and information-processing regimes by modulating local nonlinear dynamics.