Elementary cellular automata realized by stateful three-memristor logic operations

Abstract Cellular automata (CA) are computational systems that exhibit complex global behavior arising from simple local rules, making them a fascinating candidate for various research areas. However, challenges such as limited flexibility and efficiency on conventional hardware platforms still exist. In this study, we propose a memristor-based circuit for implementing elementary cellular automata (ECA) by extending the stateful three-memristor logic operations derived from material implication (IMP) logic gates. By leveraging the inherent physical properties of memristors, this approach offers simplicity, minimal operational steps, and high flexibility in implementing ECA rules by adjusting the circuit parameters. The mathematical principles governing circuit parameters are analyzed, and the evolution of multiple ECA rules is successfully demonstrated, showcasing the robustness in handling the stochastic nature of memristors. This approach provides a hardware solution for ECA implementation and opens up new research opportunities in the hardware implementation of CA.