3.1 Reaction-Diffusion and Excitation

A great variety of natural processes can be described in terms of propagating fronts. Well-known phenomena include: the dynamics of excitation in heart and neural tissue, calcium waves in cell cytoplasm, the spreading of genes in population dynamics, and forest fires. All these systems, and many more, are capable of implementing some basic computational operations. In this chapter, we consider mostly those based on wave dynamics in nonlinear chemical systems.

A nonlinear chemical medium is bistable: Each microvolume of the medium has at least two steady stable states, and the microvolume switches between these states. In the chemical medium, fronts of diffusing reactants propagate with constant velocity and wave form; the reagents of the wave front convert reagents ahead of the front into products left behind (Epstein and Showalter 1996). In an excitable chemical medium, the wave propagation occurs because of coupling between diffusion and autocatalytic reactions. When autocatalytic species are produced in one microvolume of the medium, they diffuse to the neighboring microvolumes and thus trigger an autocatalytic reaction there. That is why an excitable medium responds to perturbations that exceed a excitation threshold by generating excitation waves (Epstein and Showalter 1996; Adamatzky 2001).

Why are excitation waves so good for computing? Unlike mechanical waves, excitation waves do not conserve energy but conserve waveform and amplitude; they do not interfere, and generally do not reflect (Krinsky 1984). Because of these properties, excitation waves can play an essential role of information transmission in active nonlinear media processors.