The Effects of Interaction Functions Between Two Cellular Automata

Abstract: Biological systems are notorious for complex behavior within short timescales (e.g. metabolic activity) and longer time scales (e.g. evolutionary selection), along with their complex spatial organization. Because of their complexity and their ability to innovate with respect to their environment, living systems are considered to be open-ended. Historically, it has been difficult to model open-ended evolution and innovation. As a result, our understanding of the exact mechanisms that distinguish open-ended living systems from non-living ones is limited. One of the biggest barriers is understanding how multiple, complex parts within a single system interact and contribute to the complex, emergent behavior of the system as a whole. How do interactions between parts of a system lead to more complex behavior of the system as a whole? This paper presents two interacting cellular automata (CA) as an abstract model to address the effects of complex interactions between two individual entities embedded within a larger system. Unlike elementary CA, each CA changes its update rules as a function of the system's state as a whole. The resulting behavior of the two-CA system suggests that complex interaction functions between the two CA have little to no effect on the complexity of each individual CA behavior and structure. However, having an interaction function that is random results in open-ended evolution regardless of the specific type of state-dependency.