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Billiard-ball computing: Fredkin gate from switch gates

The Fredkin gate swaps two inputs depending on a control input (the top one here). When the control is zero it swaps the other two inputs, when one it outputs them unchanged. The control is always output unchanged.

The Fredkin gate is reversible, as demonstrated here. Note the absence of sinks or extra sources.

This implementation is made from four switch gates. It isn’t immediately obvious where they are among all the rest of the wiring—look for where the interactions happen.

The layout I ended up with here almost has horizontal symmetry—only the crossover in the centre breaks it.