Generating Multi State Cellular Automata by using Chua ’ s ” Universal Neuron ”

In 1999 Chua demonstrated that it is possible to obtain boolean Cellular Au-tomata (CA) by using Cellular Neural Networks (CNNs), implemented as chips, which definitely reduce the time of simulation for discrete dynamical systems such as CA and allow for a better understanding of complexity. In this work we demonstrate that Chua's Universal Neuron which simulates boolean CA can be generalized for multistate CA. This new approach allows to investigate the nature of the CA rule space, in relationship with the Universal Neuron parameter space, establishing relationships between discrete and continuous dynamical systems and analysing the nature of local and global rules in affecting the behaviour of these systems. The method which we have developed is fruitful since we have found a lot of CA which can be considered complex rules of class IV, in the Wolfram classification. Furthermore we have used the idea of genetical computation in considering the values of the Universal Neuron parameter space as a sort of genotype which determines and produces variations in the CA behaviour. On this basis, we have implemented a genetic algorithm which fits very well with the searching for CA complex rules. WSPC-Proceedings Trim Size: 9in x 6in bilotta˙diblasi˙giambo˙pantano 2 temporal dimension of many biological phenomena and processes.