Stable patterns formation by totalistic cellular automata

Evolution of totalistic cellular automata (CA) with weighed templates are studied. As a result of simulation various stable patterns are obtained and investigated. Both synchronous and asynchronous modes of CA operation are tested. As a result of simulation by synchronous and asynchronous CA, different stable patterns emerging from one nucleation cell are obtained and classified. The influence of weight matrix entries on stable patterns is studied. The theorem about the stable patterns dependence on the ratio of positive to negative entries of a weight matrix is proved. Stable patterns formed of two nucleation cells are also investigated.