This monograph provides an account of the subject of new approaches to computation (such as neural computation and cellular automata) for dealing with complex systems. Computation based on reaction-diffusion processes in chemical, physical and biological systems is one of the new approaches being followed. Nonlinear media exhibit a variety of spatio-temporal phenomena. Circular waves, spiral waves and self-localized excitations are the most familiar examples. How to use these phenomena to perform useful computations is the main theme of the book. The author explains how computation in media such as chemical solutions, molecular layers and swarms of social insects is usually carried out by the use of excitation waves, phase diffusion waves and trigger waves. The algorithms are intuitive. Data is represented in the distribution of reagents, the reagents diffuse on the substrate, diffusive or excitation waves interact one with another and form stationary or dissipative structures as the result of their interactions. These final structures or patterns of reagents can be interpreted as the results of the computation.
The most well-known examples include Voronoi-like subdivision of lattice and plane, approximation of the skeleton of a planar shape and computation of spanning tree. Problems are solved in cellular-automata models, ant-colony systems and real chemical processors. The possible applications of such systems to balance telecommunication networks and control of robot navigation are also examined. Physical systems, which demonstrate computation-universality, fall into two classes. The first physical interpretation has logical gates at the intersection of wire-like channels for information transfer and interaction-based computations. The second physical interpretation is when computation is carried out in entirely homogeneous media (so-called "gateless computation") where the quanta of information are represented by self-localized excitations. The book shows which logical gates and circuits can be realized in such systems. Illustrative examples of collision-based gates in two- and three-dimensional excitable lattices are supplied.
This book closes with estimations on how soon we will be able to develop real-life reaction-diffusion computers and universal computers with collision-based architecture.