Lorentz gas cellular automata on graphs
Lorentz Gas Cellular Automata (LGCA) are models of parallel many-tape Turing machines generated by the motion of localized (point) objects (particles, signals, wave trains, etc.) on a graph. In each vertex v of the graph we store a symbol. A read/write head of the Turing machine is represented as an object that hops from one vertex of the graph to another according to a rule (symbol) stored in the vertex. Thus, the symbols stored in the vertices represent scattering rules (or simply scatterers) of the lattice gas. It is assumed that initially the scatterers are randomly distributed among the vertices of the graph. The random environment formed by the scatterers may either be fixed or evolve due to collisions with the moving object. The collisions simulate storing of a new symbol in the vertex of the graph. We investigate these models with fixed environment in general types of graphs and the models with evolving environments on trees. Remarkably, it occurred that all models with fixed environments and many models with evolving environment behave like a depth-first search on the underlying graph. Observe that such behavior occurs for any initial random distribution of scatterers rather than for some "specially prepared" initial configurations of scatterers. We also give estimates of periods of orbits on finite graphs. (C) 2003 Elsevier B.V. All rights reserved.
cellular automata random environment depth-first search lorentz lattice gases