
## 2 **Adamatzky Et Al**

by compact patterns traveling in an 'empty' space and performing computation by mutual collisions. The absence or presence, and type, of traveling patterns encode values of logical variables. The trajectories of patterns approaching a collision site represent input variables. Trajectories of the patterns ejected from a collision represent the results of logical operations, i.e. output variables.

Amongst many possible natural systems supporting localizations, reactiondiffusion chemical media seem to be most appropriate candidates for **experimental**
implementation of collision-based computing architectures. The medium does not require expensive or over-sophisticated equipment, can be handled and tuned with relative ease, and allows for visual identification of experimental results. For example, there is a particular type of reaction-diffusion chemical system, the BelousovZhabotinsky reaction in sub-excitable mode **17, that supports the existence of localized wave-fragments (somewhat analogous to dissipative solitons**
11) which can play the role of the 'billiard-balls' 12 **in a collision-based computing system** 3,9.

In our previous works we have designed and studied a range of hexagonal cellular-automaton models of reaction-diffusion excitable chemical systems, particularly those with concentration dependent inhibition of the activator 4,21,**5. We**
have analyzed three-state totalistic cellular automata on a two-dimensional lattice with hexagonal tiling, and discovered a set of specific rules that support a variety of mobile (gliders) and stationary (eaters) localizations, and generators of localizations (glider guns). In 5 **we demonstrated that rich spatio-temporal dynamics**
of interacting localizations and generators of localizations can be used in implementing purposeful computation, including signal routing, multiple-valued logical operations and finite state machines. Despite success of preliminary studies, and some techniques developed 20 **to pinpoint 'best' rules supporting localizations, we**
remained somewhat puzzled and uncertain on whether rules manually **selected are**
good representatives of a set of localization-supporting cell-state transition rules. We therefore applied the full power of evolutionary computation methods to evolve and select all possible rules that support mobile localizations in two-dimensional hexagonal ternary state cellular automata. Results of these studies are discussed in present paper.

The paper is structured as follows. In Sect. 2 we introduce and define ternary state hexagonal cellular automaton. The evolutionary algorithm used to breed glider-supporting rules is outlined in Sect. 3. The evolved set of glider-supporting rules is characterised in Sect. 4. In Sect. 5 we present a set of quasi-chemical reactions derived from the evolved rules. We demonstrate, in Sect. 6, that by integrating the most common glider-supporting rules in one set, we select the rules supporting only stationary localizations. Outcomes of the present studies are discussed in Sect. 7.