CNN genes for one-dimensional cellular automata: A multi-nested piecewise-linear approach

This paper introduces a novel CNN cell which guarantees the implementation of any local rule on three variables defined by a Boolean truth table. More over, since the output of the cell is completely specified by a simple math ematical formula, it is possible to develop a systematic theory for locatin g those regions in the CNN genes parameter space where complex behaviors ma y occur. The output cell formula is a simple piecewise-linear function, and for the case of a one-dimensional CNN the entire set of 256 CNN genes asso ciated with the corresponding local Boolean functions are listed in this pa per.