Self-organized criticality in asynchronously tuned elementary cellular automata

Self-organized criticality (SOC) reveals a mechanism by which a system is autonomously evolved to be in a critical state without needing parameter tuning. Whereas various biological systems are found to be in critical states and the significance of SOC is being re-estimated, a simple model in a general platform has not been established. Here, we present SOC in asynchronously tuned elementary cellular automata (AT_ECA), based on asynchronously updating and tuning the consistency between local dual modes of transitions. This duality was defined by adjunction, which can be ignored during synchronous updates. Duality coupled with asynchronous updating can demonstrate that SOC coincides with the criticality in a phase transition of AT_ECA with respect to density decay.