Wireworld
A cellular automaton designed by Brian Silverman in 1987 for simulating electronic logic. Four cell states, four rules, and enough expressive power to build clocks, diodes, and logic gates — a Turing-complete computer from nothing but colored squares.
The rules
Wireworld has four cell states: empty, conductor, electron head, and electron tail. Each generation, four rules apply simultaneously: empty stays empty; an electron head becomes an electron tail; an electron tail becomes a conductor; a conductor becomes an electron head if exactly 1 or 2 of its eight neighbors are electron heads. That is the entire specification.
Why it matters
Despite its simplicity, Wireworld is Turing complete — you can build any digital circuit from these four rules. Signals propagate along conductor wires. A diode allows one-way flow. Logic gates combine signals. From there, you can build adders, memory, and in principle an entire computer. It is a beautiful demonstration that computation requires nothing more than the right local rules applied uniformly.
Building circuits
Draw conductor paths with the conductor tool. Place electron heads at the start of a wire to inject a signal. Use the preset circuits to see how diodes (which use asymmetric geometry to block reverse flow) and logic gates (which use the 1-or-2-neighbor rule to combine signals) work. Then try building your own.