Intention to explore the role of discretization in the emergence of self-organization in certain approximations of continuous cellular automata and other complex dynamic systems

Abstract

John H. Conway's Game of Life, as well as cellular automata in the larger family of Life-like CA, are discrete: the cells have a binary state space and the birth and survival transition rules are 9-bits apiece. Inspired by Life, several projects have developed continuously-valued cellular automata frameworks in 2 dimensions. These CA systems are necessarily imperfect approximations of ideal continuous systems when they are implemented in a digital computer, and this inevitably leads to discretization errors. As we know since at least the time of Poincair\'e's work on the three-body problem, arbitrarily small errors in a complex dynamic system can lead to substantial behavioral deviation over time. This outline of intent is based on observations in cellular automata that, in certain cases, errors are not only well-tolerated, but are essential for self-organization. This manuscript describes a set of experiments to investigate the importance of discretization in approximating continuously valued dynamic systems, how and when discretization is required for self-organization to occur, and the relevance the results might have with respect to emergent agency and analogies for consciousness.