Universal dynamical computation in multidimensional excitable lattices

We study two- and three-dimensional lattices nodes of which take three states: rest, excited. and refractory, and deterministically update their states in discrete time depending on the number of excited closest neighbors. Every resting node is excited if exactly 2 of its 8 (in two-dimensional lattice) or exactly 4 of its 26 (in three-dimensional lattice) closest neighbors are excited. A node changes its excited state into the refractory state and its refractory state into the rest state unconditionally. We prove that such lattices are the minimal models of lattice excitation that exhibit bounded movable patterns of self-localized excitation (particle-like waves). The minimal, compact. stable, indivisible, and capable of nonstop movement particle-like waves represent quanta of information. Exploring all possible binary collisions between particle-like waves, we construct the catalogue of the logical gates that are realized in the excitable lattices. The space and 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 models and their high affinity to real-life analogues affirm that excitable lattices may be the minimal models of real-like dynamical universal computation.