The study presents a reaction-diffusion–inspired activator-inhibitor cellular automaton constructed as a tunable nonlinear medium. The automaton implements two distinct families of local nonlinear interactions: a continuous sigmoid activator and a logistic-step relaxer. Each family has a single family-specific parameter that alters the nonlinear response or relaxation dynamics while the neighbourhood wiring—how cells influence one another—remains fixed.
This design intentionally separates topology (neighbourhood coupling) from local dynamics (nonlinear response), providing a controlled system for exploring how changes in local nonlinear behaviour affect global dynamical regimes and information-processing capabilities.
By varying the family-specific parameter within each activation family, the automaton can be moved between several qualitatively distinct dynamical regimes. The authors identify four named regimes: collapsed, structured, saturated, and overshooting. These regimes describe recurring macroscopic behaviours that arise from the same underlying neighbourhood wiring but different local nonlinear settings.
The source frames these regimes as a controlled means to link nonlinear parameter settings to observable patterning outcomes without altering connectivity.
The work links each dynamical regime to measurable properties of the system’s state space, specifically state-level diversity and pattern compressibility. Regimes that promote spatial structure tend to show larger state diversity and different compressibility profiles compared with collapsed or saturated regimes. Pattern compressibility provides a way to quantify how structured or redundant spatial configurations are under each regime.
These relationships permit an interpretable mapping from local nonlinear settings (for example, effective gain, threshold, or relaxation dynamics) to macroscopic descriptors of pattern complexity and information content.
Rather than treating reservoir computing as an architecture to be optimised, the authors adopt it as a diagnostic tool to probe the untrained medium’s computational characteristics. The automaton is evaluated for three canonical reservoir properties:
This framing positions the automaton itself as the reservoir substrate and uses standard reservoir metrics to characterize how well different nonlinear regimes support computation.
Across systematic sweeps of the family-specific parameter for each nonlinear activation type, the study finds that stronger memory and better input separability are not distributed uniformly across parameter space. Instead, these computationally favourable properties concentrate near transition regions between dynamical regimes. In other words, the boundaries where the system shifts from one regime to another tend to deliver improved fading memory and separability compared with deep within a single regime.
This concentration near transitions suggests a trade-off: regimes optimized for stable pattern formation may not simultaneously maximize transient information processing, while transition zones can provide a balance that supports reservoir-style computation.
The findings highlight that interpretable parameters—effective gain, threshold, and relaxation—can be used to tune the balance between pattern formation and computational properties such as memory and separability. Because the neighbourhood wiring is held fixed, these parameters provide direct control levers over whether the medium behaves primarily as a pattern-forming substrate or as an information-processing reservoir.
The cellular automaton therefore functions as an unconventional but interpretable reservoir substrate: by adjusting simple local nonlinear parameters, one can steer the medium between regimes that favour long-lived spatial structure and regimes or transition zones that favour temporal information processing.
More broadly, the study supports the conceptual view that tissue-like or physical pattern-forming media may, in principle, shift between patterning and information-processing modes by modulating local nonlinear dynamics. This suggests a pathway for understanding or engineering materials and biological media that can flexibly alternate between producing spatial organization and performing temporal computation by tuning local response properties.
Additional notes from the source: the authors declared no competing interests, and funding from the Medical Research Council (MRC) is reported. Data and code availability are referenced in the original source. Specific implementation details, quantitative metrics, and numerical results were not reproduced here and should be consulted directly in the source document for experimental parameters and results.