Guam wrote:How to define whether easy glider-constructible stable pattern?
That's a very good and interesting question... interesting to me, anyway! My own short answer is that "easy" glider-constructible patterns are made of common seven-bit-or-smaller still lifes, spaced a few cells from each other. No pseudo-still-life constellations if possible... and no aircraft carriers or snakes, since those appear significantly less often in random ash
than even fishhook eaters do, and anyway it's usually trivial to use one end or another of an eater instead. Paul Chapman and I started using the word "Spartan" around 2004 as shorthand for this seven-bit-no-snakes limit.
In Herschel-circuit construction problems so far, there are generally extra constraints on the construction gliders: they can come in only one at a time from one direction (as in Paul Chapman's 'Glue' search utility, and constructor-memory-tape.rle in Golly's Patterns/Life/Signal-Circuitry) or two at a time 90 degrees apart (as in Andrew Wade's Gemini spaceship). And between the volleys of gliders, the intermediate pattern generally needs to settle down and not throw off any uncaught gliders. Anything that doesn't appear very regularly in random ash is likely to be fairly difficult to glider-construct _in all possible orientations_ with these constraints, especially in close quarters with other still lifes nearby.
Now, this seven-bit limit is definitely a rule of thumb -- an approximation, not an exact science! It will always be perfectly _possible_ to build still lifes with higher cell counts, even in closely packed constellations, as long as there's any known glider construction at all.
The 'Spartan' dividing line was chosen after quite a bit of experimentation. The idea was to try to minimize the total complexity of construction -- the length of the "glider recipe". Yes, larger catalysts like tub-with-tails or dead spark coils could definitely be included in self-constructing Herschel circuits. Having more conduit options would certainly allow an actual self-constructing circuit to be smaller and more efficient: it might contain, say, 10% or 20% fewer catalysts. *But* if each catalyst takes, on average, 30% more gliders to construct, and the constructions maybe have to be hand-optimized instead of being automatically compiled by a program... then maybe minimizing the total number of catalysts isn't really what's important.
For example, part of glider synthesis of bookends, tub with tail and dead spark coil:
x = 42, y = 19, rule = B3/S23
If short Gemini construction recipes are discovered for both orientations of dead spark coil -- and especially if someone can produce Gemini recipes to build Paul Callahan's old G5 Herschel transmitter in all eight possible orientations -- then that would be a very good argument for stretching the "Spartan" definition to include dead spark coils. Long-span Herschel transceivers are mostly just empty space, and you can't get any easier to construct than that!
But I think the odds are low that anyone will come up with those recipes: dead spark coils are very far down Achim's top-100 list of 'natural' still lifes ("JC", #49) -- way below tub_with_tail (#32) or snake (#25). With any luck someone will prove me wrong about this...!
By the way, this is an odd case where a p2 oscillator could be used in "stable" circuitry perfectly well -- a regular 'live' spark coil would work perfectly well in place of a dead one, if it turned out to be easier to construct. The periodic part wouldn't affect the catalysis at all.
Along the same lines as the spark coil: if there's a way to get all eight possible tub-with-tail orientations using Gemini-style gliders from just two directions, and you can use all those recipes to build tub-with-tail-plus-block eaters, then your new almost-Spartan G5 transmitter could be added to the self-constructing-circuitry toolkit, along with Stephen Silver's receiver and a number of other useful devices. It would certainly be handy to have a good compact easy-to-construct Herschel transmitter (along with a Spartan Herschel splitter, while I'm wishing!)... but when I looked at the tub-with-tail construction problem several years ago it didn't seem too likely to work: in practice, the constructions just plain take up too much space, making it hard to construct other nearby catalysts.
... That's enough for tonight, I think! If all this brings up more questions than it answers, please let me know.