On oscillators in phyllosilicate excitable automata

Phyllosilicate is a sheet of silicate tetrahedra bound by basal oxygens. A phyllosilicate excitable automaton is a regular network of finite state machines, which mimics structure of a silicate sheet. A node of the silicate sheet is an automaton, which takes resting, excited and refractory states, and updates its state in discrete time depending on a sum of excited states of its three (silicon automata) or six (oxygen automata) closest neighbours. Oscillator is a localised compact configuration of non-quiescent states which undergoes finite growth and modification but returns to its original state in a finite number of steps. We show that phyllosilicate excitable automata exhibit spiral and target waves, and oscillating localisation dynamics. Basic types of oscillators are classified and characterised.