Existences of two solutions of one-dimensional computational verb cellular networks

Computational verb cellular networks (CVCNs) represent a new platform of cellular computation. In a CVCN, local rules are computational verb rules. In this paper, the theoretical study of conditions, under which two kinds of pattern solutions form in 1D CVCN, is performed. The mechanisms of forming grid and multicolor flip-flop patterns in one-dimensional CVCN are studied mathematically. Based on the theorems of previous works, the constraints of parameters of 1D CVCNs for generating both pattern solutions are constructed. Numerical experimental results verify the usefulness of the theoretical predictions.