On generative morphological diversity of elementary cellular automata

Purpose - Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space-time configurations. No one has tried to analyze a generative power of cellular-automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large-scale spatially extended systems. Design/methodology/approach - Let all but one cell be in alike state in initial configuration of a one-dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three-by-three cell blocks occurred in the automaton's space-time configuration. Findings - The paper builds a hierarchy of generative diversity of one-dimensional cellular automata with binary cell-states and ternary neighborhoods, discusses necessary conditions for a cell-state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions. Research limitations/implications - The method developed will be used in conjunction with other complexity measures to built a complete complexity maps of one- and two-dimensional cellular automata, and to select and breed local transition functions with highest degree of generative morphological complexity. Originality/value - The hierarchy built presents the first ever approach to formally characterize generative potential of cellular automata.