"Defective" Logic: Using spatiotemporal patterns in coupled relaxation oscillator arrays for computation

An intriguing interpretation of the time-evolution of dynamical systems is to view it as a computation that transforms an initial state to a final one. This paradigm has been explored in discrete systems such as cellular automata models, where the relation between dynamics and computation has been examined in detail. Here, motivated by microfluidic experiments on arrays of chemical oscillators, we show that computation can be achieved in continuous-state, continuous-time systems by using complex spatiotemporal patterns generated through a reaction-diffusion mechanism in coupled relaxation oscillators. We present two paradigms that illustrate this computational capability, namely, using perturbations to (i) generate propagating configurations in a system of initially exactly synchronized oscillators, and (ii) transform one time-invariant pattern to another. In particular, we have demonstrated a possible implementation of NAND logic. This raises the possibility of universal computation in such systems as all logic gates can be constructed from NAND gates. Our work suggests that more complex schemes can potentially implement arbitrarily complicated computation using reaction-diffusion processes, bridging pattern formation with universal computability.