Chapter 3: Computing in Reaction-Diffusion and Excitable Media - Case Studies of Unconventional Processors

Andrew Adamatzky

Overview

Recently, we have seen an explosive growth of interest in nonstandard computing architectures, materials, and algorithms: molecular electronics, quantum computation, genetic algorithms, membrane computing, DNA computing, and many others. Computation based on wave dynamics and reaction-diffusion processes in physical, chemical, and biological systems (generally classified as nonlinear media) is one of the new approaches being followed (Adamatzky 2001). In this chapter, we will provide a brief account of the subject.

Target waves, spiral waves, and self-localized mobile excitations, to mention a few, are typical space-time patterns in active nonlinear media. Is it possible to employ these phenomena to carry out something useful, to process images, to compute logical functions, to control robots? The answer is yes; we shall prove it in this chapter. Consider, for example, an active chemical medium and a change in the concentration of reagents at a few sites: Diffusive or phase waves are generated and spread, they interact with each other and form dynamic or stationary patterns as a result of their interactions. The medium's microvolumes update their states simultaneously. Aside from a small degree of asynchronous acting that can be neglected, molecules also diffuse and react in parallel. Thus the medium can be thought of as a massive parallel processor. In this wet processor, data and the results of a computation are encoded as concentration profiles of reagents, while the computation is achieved by the spreading and interaction of the waves. In this chapter, we show how these wet processors work and how they employ space-time dynamics in the form of activity patterns to perform useful computations. We demonstrate how various problems are solved in active nonlinear media, where data and results are given by spatial defects, and information processing is implemented by the spreading and interaction of phase or diffusive waves.

The field of reaction-diffusion and excitable computing is rapidly expanding. It has already affected domains as diverse as smart materials, computational complexity, theory of computation, robotics, logic, and mathematical physics. Lack of space prevents us from exposing the full spectrum of results obtained in the field; we would rather refer the reader to present textbooks (Adamatzky 2001, 2002), where every element of this unconventional computing has been scrutinized. This chapter is restricted to discussing classical examples of wet processors, exemplifying critical issues of the research, and outlining our perspective for further studies.