The Effects of Complex Interaction Rules Between Two Interacting Cellular Automata

Biological systems are notorious for their 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. In biology, this is essential for understanding systems such as the human gut, which contain multiple microbial communities that contribute to the overall health of a person. How do interactions between parts of a system lead to more complex behavior of the system as a whole? What types of interactions contribute to open-ended behavior? In this talk, two interacting cellular automata (CA) are used as an abstract model to address the effects of complex interactions between two individual entities embedded within a larger system. Unlike elementary CA, these CA are state-dependent because they change their 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 rules between the two CA have little to no effect on the complexity of each component CA. However, having an interaction rule that is random results in open-ended evolution regardless of the specific type of state-dependency. This suggests that randomness does indeed contribute to open-ended evolution, but not by random perturbations of the states as previously speculated.