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by wwei23 » September 19th, 2020, 6:20 pm
I had an interesting idea for a true-period geminoid-like spaceship.
Each side consists of a main glider duplicator, a merge circuit, and some reflectors, as well as a faraway pair of Snarks, or a boojum reflector, or a rectifier, or whatever 180-degree reflector you want, for that matter. (Hooray, a 180-degree reflector being a key component to circuitry!) One side is 1hd forwards in the direction of travel with respect to the other side.
The operation works as follows: The front side receives the instruction tape, and it copies it. One copy gets sent to the faraway reflector through the merge circuit, and the other is sent at the back side, shooting it down and rebuilding it (including the reflector), with an offset of (1,1). This causes the positions to swap, the front is now the back, and vice versa.
Now, the other copy of the instruction tape finally arrives from the reflector, and is sent to the back (now the front) side . Before, this shot down the back side. However, the (1,1) move causes it to line up with the now-front side perfectly, allowing it to receive the instruction tape. Everything now repeats, reflected, and after that, the cycle repeats, with the entire spaceship having moved one cell diagonally in the cycle.
I think it's worth building one of these, since it would be possible to show that there were infinitely many spaceships that moved at a true-period c/n. This also operates differently than a usual geminoid, since usually each side constructs its next copy and removes its previous copy, as opposed to being removed and rebuilt by the other side. This allows for lower displacement values because the bounding box of each side is not a worry anymore, there's never more than one copy of each side. This would also allow for different displacements than the (1,1) mentioned, and might make a true geminoid knightship possible, since as far as I know, it never actually got completed.
(I have no idea how to make an explicit example of a self-constructing spaceship though lol)
