10 **Adamatzky et al**

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## 7. Conclusion

We have hybridized the paradigm of reaction-diffusion cellular automata 4,21,5 **with**
evolutionary techniques of breeding glider-supporting rules 13,14,15,16 **to statistically evaluate the set of all possible totalistic cell-state transition functions which**
support mobile and stationary localizations. We calculated exact structures of glider likehood matrices and interpreted them in terms of abstract reactions. We demonstrated that quasi-chemical systems derived from glider-supporting rules exhibit classical dynamics of excitable chemical systems. We obtained computational experiment evidences that by reducing glider likehood matrices to their **strong components we obtain a set of local transition rules that exhibit exclusively stationary**
localizations. Results of the research undertaken provide a priceless tool for designing collision-based computing schemes in spatially extended non-linear **systems.**

## References
