Title: On generative morphological diversity of elementary cellular automata
Abstract: 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.