I agree with Nick.
A new age of Game of Life exploration and design!
This marks an important turning point in Life technology, comparable to the discovery of the Gosper Glider Gun and stable Herschel tracks.
What is the range of velocities that can be achieved in this way?
Any velocity less than c/2 (by the L1, or Manhattan metric) can be attained by a Universal constructor. The proof is quite long-winded, so I won't mention it unless you are interested.
For each velocity, what are the smallest spaceships (by various definitions of "smallest")?
A spaceship of period n
, where n
is equal to or greater than a constant, can have diameter of O(sqrt(log(n
))). However, a configuration of diameter x
can have a much larger period than O(exp(x²)); the maximum period of a spaceship in an x
box is an uncomputable function in x
, similar in nature to the Busy Beaver function.
How about rakes, guns, puffers, breeders based on such spaceships, and/or constructing them?
Gemini can be trivially modified into a rake, puffer or breeder. For a rake, it simply needs to release an extra glider (but two are generated, due to its nature); a puffer would leave two copies of a piece of debris each period; a breeder could construct a Herschel-based gun, or even a Gosper gun. Gosper guns can be constructed by four pairs of perpendicular gliders, by re-arranging Dieter's synthesis.
Producing a Gemini gun is more difficult, but not totally intractable. A practical method of synthesis would be to generate the 'shell' of a Gemini, and then synthesise an active Gemini in front of it. That way, the active Gemini would delete the shell, and not the gun. Anyway, it's much easier than Dave Greene's ambition to create a Caterpillar gun!
How readily can changes in velocity be programmed into such a ship?
Gemini can only have a constant velocity, and not a variable velocity. It would be possible if the twin constructors had independent instruction tapes, but the same instruction tape is used for both in the original Gemini.
Can sets of such ships, with varied velocities, be used to simulate isotropic collisions, etc. to an acceptable degree of accuracy?
To an arbitrary degree of accuracy, in fact. A Unit CA Cell could be equipped with constructors to copy itself, thereby simulating that CA in the infinite Life plane, with only a finite initial configuration. Then, it could be programmed to simulate any lattice gas, such as FHP, which is totally isotropic, despite residing on a hexagonal grid. It amazes me how a grid with Di(6) symmetry at the microscopic level can behave with U(2) symmetry at the macroscopic level.
...all the required Herschel-related knowledge was contained in the prototype pattern...
Yes, there is not a single new Herschel track in that construction. That was also true of my Pi calculator -- the entire set of components are contained within my Phi calculator; only the algorithm differs.
... two variants of a 90-desgree reflector which yield an output glider of the same or different colour parity respectively.
The 497-tick Silver reflector is ideal in this respect. It has a 180° output, a 90° colour-preserving output, a 90° colour-changing output, and a 0° colour-changing output. It might be possible to build a universal constructor out of the eight orientations of this reflector.
Another thing I love about this design is the redundancy in the six 12-gang reflector arrays,
It's not redundancy; it allows the same instructions to serve both ends of Gemini. A stroke of genius, in my opinion!
Another thing that impresses me is the fact that it is composed of only three components: the Chapman-Greene construction arm, the fishhook eater, and the Silver reflector. These have also proven useful in many of my constructions, although they are found in combination with other, occasionally customised, components.