An algorithm of finding rules for a class of cellular automata

TL;DR

This paper introduces a weighted cellular automata algorithm that uses an error correction method to find accurate transition rules, enabling the automaton to reliably reach fixed configurations from various initial states.

Contribution

The paper proposes a novel weighted CA algorithm with an error correction approach to identify transition rules, extending traditional CA models with physical interpretability.

Findings

The algorithm can find correct transition rules with exponential error convergence.

The weighted CA model has physical meaning and extends traditional CA.

Simulation results confirm the effectiveness of the proposed method.

Abstract

Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled system. A CA with weights(CAW) yields transition rules algorithm is proposed in this paper, which have ample physical meanings and extend the category of CA. Firstly, the weights are increased to connect the updated cell and its neighbours, and the output of each cell depends on the states of cells in the neighbourhood and their respective weights. Secondly, the error correction algorithm is adopted to find correct transition rules by adjusting weights. When the error is zero, the required transition rules with correct weights will be found to describe the fixed configuration. The CAW with the correct rules will relax to the fixed configuration regardless of the initial states. Finally, the mathematical analysis and simulation are carried out with one-dimensional CAW, and the results show that the proposed algorithm has the ability to find correct transition rules as the error converges exponentially.