Universal dynamical computation in multidimensional excitable lattices

We study two- and three-dimensional lattices nodes of which take three stat es: rest, excited. and refractory, and deterministically update their state s in discrete time depending on the number of excited closest neighbors. Ev ery resting node is excited if exactly 2 of its 8 (in two-dimensional latti ce) or exactly 4 of its 26 (in three-dimensional lattice) closest neighbors are excited. A node changes its excited state into the refractory state an d its refractory state into the rest state unconditionally. We prove that s uch lattices are the minimal models of lattice excitation that exhibit boun ded movable patterns of self-localized excitation (particle-like waves). Th e minimal, compact. stable, indivisible, and capable of nonstop movement pa rticle-like waves represent quanta of information. Exploring all possible b inary collisions between particle-like waves, we construct the catalogue of the logical gates that are realized in the excitable lattices. The space a nd time complexity of the logical operations is evaluated and the possible realizations of the registers, counters, and reflectors are discussed. The place of the excitable lattices in the hierarchy of computation universal m odels and their high affinity to real-life analogues affirm that excitable lattices may be the minimal models of real-like dynamical universal computa tion.