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Cellular automata (CA) is an important modelling paradigm for complexsystems. In the design of cellular automata, the most difficult task is to findthe transformation rules that describe the temporal evolution or pattern of amodelled system. A CA with weights(CAW) yields transition rules algorithm isproposed in this paper, which have ample physical meanings and extend thecategory of CA. Firstly, the weights are increased to connect the updated celland its neighbours, and the output of each cell depends on the states of cellsin the neighbourhood and their respective weights. Secondly, the errorcorrection algorithm is adopted to find correct transition rules by adjustingweights. When the error is zero, the required transition rules with correctweights will be found to describe the fixed configuration. The CAW with thecorrect rules will relax to the fixed configuration regardless of the initialstates. Finally, the mathematical analysis and simulation are carried out withone-dimensional CAW, and the results show that the proposed algorithm has theability to find correct transition rules as the error converges exponentially.

An algorithm of finding rules for a class of cellular automata