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Mathematics

The Theory of Cellular Automata and Rule 110

Quick fact

Rule 110 is a one-dimensional cellular automaton that is Turing-complete, meaning it can simulate any computation, yet its local rule is simple enough to fit in a single line of code. This was proven in 2000 by Matthew Cook, a fact that surprised many because such a simple rule can exhibit such computational power.

Why this is interesting

What if a few simple rules applied to a row of cells could create something as powerful as a computer? Rule 110, a seemingly trivial automaton, does exactly that—and its behavior is so complex that it was only proven to be universal decades after its discovery.