Evolving multiplication as emergent behavior in cellular automata using conditionally matching rules

In this paper we present an approach for evolutionary design of computational processes in two-dimensional uniform binary cellular automata. A special representation technique called conditionally matching rules will be utilized to encode the transition functions of the cellular automata. The principle of the computational process in a cellular automaton is to interpret some cells as input bits some (possibly other) cells as output bits (i.e. the result) of the computation. The goal is to find using genetic algorithm a suitable transition function according to which a specific computation could be observed during the development of the cellular atuomation for all the possible binary combinations stored in the input cells. Both the input values and the result is represented by the state values of the cells. The input of the computation will be represented by the initial state of the cellular automaton. After a finite number of development steps the cells representing the output bits are expexted to contain the result of computation. It will be shown that non-trivial computations can be realized in uniform two-dimensional cellular array. In the experiments presented in this paper some different setups of conditionally matching rules and arrangement of the input and output cells will be investigated.