Lecture 8A (2025-04-29): Complex Systems Models of Computation – Cellular Automata and Neighbors

This lecture introduces approaches for understanding (and building) computational systems that emerge out of Complex Adaptive Systems (CAS). It first motivates the idea that systems of many, interconnected parts that each are relatively easy to understand in isolation can come together in a system whose network of interactions leads to emergent global phenomena that cannot be predicted from the properties or behaviors of any individual component. We then focus on the role of space in the functions and properties that emerge at a global level. We do this through the example of the Interacting Particle System (IPS) known as the "voter model", which can be viewed as a model for neutral evolution in spatially structured populations. We show that the dual process for the Voter Model is a time-reversed set of coalescing random walkers for which consensus in the model corresponds to whether walkers are sure to coalesce into a single walker in the past of the dual process. This lets us apply Pólya's recurrence theorem and show that consensus is guaranteed (with probability 1) for 1- and 2-dimensional lattices but not guaranteed for lattices of 3 dimensions or higher. This implies that neutral evolution (for example) in a 3D spatial structure may not always lead to fixation on one genotype. We then pivot to introducing Elementary Cellular Automata (ECA) and describe a few rules that demonstrate how they work. We close the regular lecture by connecting CA's back to neural networks (the previous unit) and evolutionary algorithms (the first unit), thus introducing the Cellular Evolutionary Algorithm (cEA). We then extend the lecture a little longer than usual in order to do a demonstration of several ECA's in NetLogo, including a demonstration of how to combine two ECA rules to generate a reliable density classifier.

Whiteboard notes for this lecture can be found at:
https://www.dropbox.com/scl/fi/gfna3a2aj49fq2a4sovst/IEE598-Lecture8A-2025-04-29-Complex_Systems_Models_of_Computation-Cellular_Automata_and_Neighbors-Notes.pdf?rlkey=mo5jag4axljxrbpnq6wkk9egh&dl=0