Since dual-rail siphon gates have a fan out of 2, it’s easy to connect gates together to make larger circuits. If a larger fan out is needed then an AND gate with one input set to True can be used to achieve this.

It turns out that these dual rail siphon logic gates have the interesting and useful property that if, after operating, they are fed the inverse of the inputs, they return back to their original state (and output the inverse of the outputs).

To see why, it is enough to consider a single siphon and reason by induction.

Consider first an empty siphon. During its operation in a circuit a siphon will  receive either A : zero, B : one, or C : two inputs. Only in case C will it produce an output. Only in case B will the siphon not be in the same state as it was at the beginning.

If the siphon now receives the inverse of its inputs, it will produce an output for cases A and B, and for all cases A,B and C it will be back in the same state as it was initially.

So during the second step the siphon returned to its original state, and because the siphon output the inverse of what it output during the first step, alil downstream siphons will also return to their original states.

Similar reasoning applies when the siphon is initially half full.

You can watch this happening in the video linked to in the first log entry.