Mechanical implementation [of cyclic tag systems]

Cyclic tag systems admit a particularly straightforward mechanical implementation. Black and white balls are kept in a trough as in the picture below. At each step the leftmost ball in the trough is released, and if this ball is black (as determined, for example, by size) a mechanism causes a new block of balls to be added at the right-hand end of the trough. This mechanism can work in several ways; typically it will involve a rotary element that determines which case of the rule to use at each step. Rule (e) from the main text allows a particularly simple supply of new balls. Note that the system will inevitably fail if the trough overflows with balls.