Computing in nonlinear media and automata collectives (Q2719318)

The first chapter -- Reaction-diffusion, excitation and computation -- starts with a discussion of unconventional computing. Some methods for modeling reaction-diffusion and excitable media, the cellular automata automata architecture and different examples of computing in nonlinear media are presented.NEWLINENEWLINENEWLINEIn the second chapter -- Subdivision of space -- the construction of Voronoi diagrams and skeletons are presented using distance-to-time transformations implemented in the spread of diffusion or phase waves and some original algorithms for the computation of discrete convex hulls. This chapter familiarizes readers with the essential steps of reaction-diffusion processors design.NEWLINENEWLINENEWLINEThe third chapter -- Computation on and with graphs -- contains some problems of construction and optimization on graphs, particularly the shortest-path problem. It is shown how to find the shortest path in cellular-automata models and in Belousov-Zhabotinsky reactors. The construction of proximity graphs in nonlinear media and the computation of spanning trees are discussed in detail. Also chemical processors for computing shortest paths are presented.NEWLINENEWLINENEWLINEThe fourth chapter -- Computational universality of nonlinear media -- begins with an overview of various types of computation universality. Three examples of architecture-based universality -- sand-piles, mass transfer gates and wave gates -- are presented. An important part of this chapter is devoted to cellular-automata of excitable media. Also, a remarkable spectrum of logic gates implemented in self-localization is constructed. The behavior of solitons, light bullets, breathers, gaussons, and excitons in monomolecular arrays and defects in tubulin microtubes are analyzed. NEWLINENEWLINENEWLINEIn the fifth chapter -- Emergence of computation in excitable lattices -- it is shown which parameters of behavior of medium's local elements can be taken into account for the scrutiny of the computational properties of the medium. Different classifications of excitable lattices are provided together with applications of emerging properties to image processing and the control of robot navigation. Finally, it is shown how to classify the potential ability of excitable lattices using a combination of morphological, dynamic and parametric classifications.