Generating textile designs using cellular automata

Abstract

Cellular automata (CA) are discrete dynamical systems of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The rule numbers in one-dimensional automata ranging from 0 to 255 have been tested and found to generate mostly geometric patterns. In two-dimensional automaton, the various rule numbers have been tested in 80×80 matrix with a grid size of five pixels and the matrix size extended to 110×110 with a grid size of three pixels each that resulted in chaotic, stable and high life. The behaviour of the neighbourhood cells has been analyzed by their categories, grouped together and represented graphically, resulting in uniform and non -uniform patterns, which may well be utilized for textile designs. The algorithm is designed with an option to generate the rule number itself randomly and hence the design generated is highly unpredictable and it is observed that different patterns are generated to each iteration of the algorithm.