  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.
