Collision-based implementation of a two-bit adder in excitable cellular automaton

In a collision-based computer [Adamatzky A, editor. Collision based computing, Springer; 2003] the information is represented by localizations (gliders, solitons, breathers, kinks) traveling in a spatially-extended nonlinear medium, and the computation is implemented when localizations interact with each other, parameters of the localizations after interaction represent results of the computation. Using cellular automaton model of two-dimensional excitable lattice we construct fully functional two-bit adder and thus demonstrate viability of collision-based computing schemes in excitable media. Every resting cell of the automaton lattice takes excited state if there is exactly two excited neighbors, transitions from excited state to refractory state, and from refractory state to resting state are unconditional. We envisage that designs presented in the paper will be used in future developments of arithmetical circuits in excitable media and collision-based chips.