On memory and structural dynamism in excitable cellular automata with defensive inhibition

Commonly studied cellular automata are memoryless and have fixed topology of connections between cells. However by allowing updates of links and short-term memory in cells we may potentially discover novel complex regimes of spatio-temporal dynamics. Moreover, by adding memory and dynamical topology to state update rules we somehow forge elementary but nontraditional models of neurons networks ( aka neuron layers in frontal parts). In the present paper, we demonstrate how this can be done on a self-inhibitory excitable cellular automata. These automata imitate a phenomenon of inhibition caused by hight-strength stimulus: a resting cell excites if there are one or two excited neighbors, the cell remains resting otherwise. We modify the automaton by allowing cells to have few-steps memories, and create links between neighboring cells removed or generated depending on the states of the cells.