Imperfect Automata: Effects of “mutation” on the evolution of automaton 01101110 (Rule 110)
Cellular automata are discreet mathematical models. They consist of cells; each cell can exist in a limited number of mutually exclusive states, like 0 or 1. The state of each cell at time t is determined by simple rules, based on the states of its neighboring cells. While exploring their relevance to behavioral sciences (McDowell & Popa, 2009) one aspect caught my attention: it seemed that all emerging structures and patterns could be traced back to the first few generations; patterns were evolving, colliding, changing, and disappearing, but no new patterns or structures were emerging from non-patterns (i.e., "uniformity"). In biological systems, novelty is made possible by mutation (Thomas, 1974) – a concept central to my computational work on learning (Popa & McDowell, 2016) and on the emergence of psychological objects and phenomena from changes in neuronal activation states (Popa, 2019). Unlike biological systems, automata are deterministic systems, governed by precise rules. The question examined here was: what if these rules weren’t precise? What if every time a cell is created, there’s a small probability to make a mistake, to write 0 instead of 1 and vice-versa? I explored this idea in the context of Rule 110 (01101110), an elementary CA notorious for its fascinating properties (Wolfram, 2002). A small amount of mutation – e.g., 0.00005 probability to make mistakes – facilitated the emergence of new patterns and structures, disconnected from the initial conditions. Mutation rates of 0.0001 – 0.0005 produced an abundance of irregular, interacting structures. Mutation rates higher than 1% prevented the emergence of discernible patterns, producing instead an amalgam of ill-defined, organic-looking structures. These results suggested that imperfect automata may provide useful insight on the evolution of non-deterministic systems and on the emergence of novelty – two key topics in machine learning and artificial intelligence.