27: Peer Pressure (Cellular Automata)

The fabric of the natural world is an issue of no small contention: philosophers and truth-seekers universally debate about and study the nature of reality, and exist as long as there are observers in that reality. One topic that has grown from a curiosity to a branch of mathematics within the last century is the topic of cellular automata. Cellular automata are named as such for the simple reason that they involve discrete cells (which hold a (usually finite and countable) range of values) and the cells, over some field we designate as "time", propagate to simple automatic rules. So what can cellular automata do? What have we learned from them? And how could they be involved in the future of the way we view the world?