Summary: The local function of cellular automata is usually applied to all cells in the lattice in just one single time step. Such a synchronous update may lead to limitations, as when models for real-world systems are being created. As a counterbalance, asynchronous forms of update have been more and more explored in the literature, as they can provide an extra degree of freedom. The standard way to define deterministic asynchronism by setting an update priority to each cell depends totally on the cell position in the lattice. In a previous work, we proposed a new way to address deterministic asynchronism, where the update priority would rely on the state transitions underlying the local function, in a way that any cell might be updated multiple times during the same iteration. Here, we consider a restricted version of the latter, by which the cells are necessarily updated just once during any time step. By focussing on the elementary cellular automata space, we provide a complete characterisation of the resulting number of distinct dynamics of the entire space, out of all possible independent updates, and contrast it with the case of multiple updates.
For the entire collection see [Zbl 1491.11006].