dvgrn wrote:Seems as if the odds are good that there's a spark out there somewhere that keeps moving right as it metamorphoses into an HWSS.

You know, I think I'd better retract that. It's not absolutely impossible, maybe, but I'm now betting that it's very very unlikely -- just a one-in-a-quadrillion or one-in-a-quintillion chance of coming across a working reaction in a slow-salvo search.

Here for example is what looks like a pretty good HWSS edge shooter -- and look how far it is from working. The spark collides with three different *WSSes in the pre-existing stream:

Code: Select all

```
x = 117, y = 199, rule = LifeHistory
.A79.A$2.A79.A$3A77.3A4$22.2A78.2A$21.A2.A76.A2.A$22.2A78.2A7$21.2D
78.2D$10.A10.2D67.A10.2D$10.A79.A$10.A13.3A63.A13.3A3$16.2A78.2A$16.
2A78.2A5$2.A79.A$2.A79.A$2.A79.A32$114.A$113.3A$112.2A.A$112.3A$112.
3A$113.2A5$112.A$111.3A$110.2A.A$110.3A$110.3A$110.3A$111.2A17$114.A$
113.3A$113.A.2A$114.3A$114.3A$114.2A5$112.A$111.3A$111.A.2A$112.3A$
112.3A$112.3A$112.2A17$114.A$113.3A$112.2A.A$112.3A$112.3A$113.2A5$
112.D$111.3D$110.2D.D$110.3D$110.3D$110.3D$111.2D17$114.A$113.3A$113.
A.2A$114.3A$114.3A$114.2A28$114.A$113.3A$112.2A.A$112.3A$112.3A$113.
2A!
```

The key highly-unlikely item has to do with the MWSS spark. It looks like the HWSS-making reaction has to travel at lightspeed for at least five generations to get the long right edge of the HWSS to the correct lane in time after the MWSS has passed by. That translates to a straight line of length 16 at time T-5 -- no other possible options -- and we actually need length 17 to suppress the interaction with the MWSS's spark.

-- And on top of that, the region behind the line has to be adjusted so that when the line shrinks to length 6, a good HWSS (or near predecessor) has magically appeared to the left of it. That takes a lot more optimism than I can come up with:

Code: Select all

```
x = 33, y = 19, rule = LifeHistory
4.A26.A$3.3A24.3A$2.2A.A19.C3.2A.A$2.3A20.C3.3A$2.3A20.C3.3A$3.2A20.C
4.2A$25.C$25.C$3.D21.C4.D$3.D21.C4.D$2.AD21.C4.D$.2AC21.C4.D$2A.C21.C
4.D$3AD21.C4.D$3A22.C$3A22.C$.2A22.C$25.C$25.C!
```

Can anyone point out a flaw in this analysis? If not, we're looking at something like a (wild guess) one-in-10^20 reaction, and the odds are basically zero that any slow-salvo search will ever find it. Even a slow-pairs search won't really help -- to travel fast enough, the reaction still has to produce a length-17 straight line.

What about the idea of upgrading an LWSS or MWSS to an HWSS, though -- or delaying the leading MWSS, or upgrading it from an LWSS? Are those options equally susceptible to this kind of reality-check analysis? Seems as if five ticks of lightspeed would still be needed even to build an LWSS that close to the MWSS, and therefore a length-15 straight line:

Code: Select all

```
x = 33, y = 17, rule = LifeHistory
4.A26.A$3.3A24.3A$2.2A.A19.C3.2A.A$2.3A20.C3.3A$2.3A20.C3.3A$3.2A20.C
4.2A$25.C$25.C$3.D21.C4.D$3.D21.C4.D$2.AD21.C4.D$.2AC21.C4.D$2A.A21.C
$3A22.C$.2A22.C$25.C$25.C!
```

Maybe with the extra distance available between LWSSes, it might be easier to build the MWSS after the LWSS? But that's still pretty close to light speed for several ticks, I think -- haven't tried that analysis yet.

The most likely construction might turn out to be a simultaneous construction, as Hartmut suggested. There's no room to build the seeds separately, so it would have to be a combined seed that happens to produce that exact MWSS+HWSS combination.

That's certainly not impossible. There could easily be a seed like that out there somewhere -- but it seems as if it would be a one-in-10^20 lucky coincidence again, and therefore unfindable without a big breakthrough in the search algorithm.