PATTERN GROWTH IN ELEMENTARY CELLULAR-AUTOMATA

A classification of elementary cellular automata (CA) based on their pattern growth is introduced. It is shown that this classification is effective, that is, there exists an algorithm to determine to which class a given CA belongs. This algorithm is based on the properties of the local rule of CAs, not requiring the observation of their evolution. Furthermore, necessary and sufficient conditions to detect all the elementary CAs exhibiting a shift-like behavior are given; these CAs have interesting dynamical properties and chaotic characteristics.