In the Waterbear thread, Codeholic wrote:Could you maybe elaborate a little bit how you do the arithmetic of periods and offsets, maybe illustrating it with some components labeled with extended LifeHistory states?
Back then I didn't use LifeHistory ever and likely left some people in the dust trying to use my own nomenclature without ever giving a satisfying description of what it meant. Here I will try to be better.
I've decided to go with a C26xC8 name scheme rather than a C2xC104, because while I find the latter a more appealing group it doesn't map as intuitively to the degrees of freedom in the problem.
The names apply to the separation between neighboring tracks, so a cluster of 5 tracks has 4 elements in its name. The degrees of freedom I am using here are the lane separation mod 26 and the phase offset mod 8. Tracks with the same values for these degrees of freedom are capable of the same reactions between forerakes and climbers.
Lane separation is just a a number between 0 and 25, and phase is indicated by a letter A-H. Because I have it ingrained in me that A is 1, we have A-G mapped to 1-7 and H for 0. As such, the 5-cluster can be called an 18E-11H-23G-20G track.
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x = 125, y = 42, rule = LifeHistory
20.4B14.4B7.4B45.4B16.4B$19.4B14.4B7.4B45.4B16.4B$18.4B14.4B7.4B45.4B
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$58.A3B19.A$58.3A!
That said, for direct interactions between climbers, the lane separation and timing are strict rather than mod-8/mod-26, so this naming scheme is really only helpful when considering the 23G separation between 3 and 4. I would thus rather call this a 23G track than the whole clunky name, where it is understood that the left of the 23G track is the forerake made from 3 climbers and the right is the rephasing reaction whose spark can absorb, transmit or reflect the glider.
The rephasing reaction is of type 16H, meaning a 23G separation is turned into a 23G + 16H = (23 + 16 - 26 = 13, G + H - H = G) 13G separation. As many rephasings as we try, we will be stuck with an odd number and a G, which is onlyl 1/16 of the space. It is at least fortunate that we have natural forerakes instead of being limited to backrakes though, because if we named things in terms of the backrake degrees of freedom we would be stuck in 1/40 of the space (see my many rants earlier).
The frozen track technology means that a new track can be burned on whatever letter is needed rather than being tied to the timing of its constructor. The lane, however, is fixed. So we will probably need two different recipes for the seed constellation, one of each parity.
Now, this has all so far focused on making sure the UC portion of this ship is as unlimited as it can be, without thinking yet about what it constructs. We ultimately need to synthesize a tightly-packed helix of period-tripled *WSS, many of which are HWSS. The caterpillar synthesis can't be coaxed to work, we can't proceed through intermediate slow salvo because of the angle, and the Waterbear avoided HWSS in its helix. So we still need recipes.
..And fanouts. And a viable tripler, but I'll look into just making that from natural reactions rather than a filter.
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Okay, here's an absurd idea. What if we built the spaceship on the "wrong" side of the helix?
Discussion with codeholic in the 13131 thread (which went unresolved) made me realize that there are multiple viable layouts for an oblique ship relative to its helix. The way I built the Waterbear made the most sense for top-down construction, because the tracks, stills and helix were all mutually drifting apart. A similar design would be made possible in this case by finding a really sneaky HWSS recipe that could insert into a partially-completed helix, but that is still elusive.
We could instead have the HWSS-laden helix release a stream of x3 NE gliders which were caught by a second HWSS-free fanout helix at the opposite end of the front, which converted them to the first construction track. The HWSS-free helix could be constructed in Waterbear fashion, and the HWSS-laden helix would have approach angles permitting many more synthesis options. It would look like the caterpillar in that it is surrounded on both sides by helix, and like the Waterbear in that parts are steadily drifting apart/together in large triangles.
But how do large triangles play nicely with a finite width?
Instead of doing resets out of size consideration we would be forced into them to avoid crashing into the HWSS-laden helix. We end up with a very large unknown regarding how much space to give ourselves, which is a degree of freedom in the two-helix approach (good thing) but also leaves us unable to make this a top-down construction (will slow me in particular down).
If the Waterbear were to be constructed this way, for example, it would look something like the following (really really janky) mockup:
- G68PQwE.png (42.06 KiB) Viewed 214 times
If there is
1) a way to release a NE glider stream from the x3 HWSS-laden helix and
2) a HWSS-free helix that turns such a stream into some frozen form of the construction cluster
then we have a front end. I'll get to making some sample frozen clusters so anyone (codeholic??) can have a definite target.
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Well, the track trio supporting the NE forerake is absolutely impermeable by a NW forerake. This means we will only get NW forerakes for left syntheses when performing a reset, probably meaning one left synthesis per big triangle. These are done in parallel with the syntheses to the right though, so it might be a good thing, and resets
might be needed quite often anyway.
I don't know enough HWSS syntheses off the top of my head to determine the number of coordinated signals required. If we only use W LWSS, NW G, SW G and still lives, can we get a low-signal-count, repeatable and clean HWSS shooter that can insert the HWSS in yellow here?
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x = 334, y = 248, rule = LifeHistory
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Physics: sophistication from simplicity.