  We consider hexagonal cellular automata with immediate cell neighbourhood and
three cell-states. Every cell calculates its next state depending on the
integral representation of states in its neighbourhood, i.e. how many
neighbours are in each one state. We employ evolutionary algorithms to breed
local transition functions that support mobile localizations (gliders), and
characterize sets of the functions selected in terms of quasi-chemical systems.
Analysis of the set of functions evolved allows to speculate that mobile
localizations are likely to emerge in the quasi-chemical systems with limited
diffusion of one reagent, a small number of molecules is required for
amplification of travelling localizations, and reactions leading to stationary
localizations involve relatively equal amount of quasi-chemical species.
Techniques developed can be applied in cascading signals in nature-inspired
spatially extended computing devices, and phenomenological studies and
classification of non-linear discrete systems.
