Here's a set of results that's fairly well organized specifically for one-time turners, as opposed to splitters. It includes constellations made up of Spartan-ish still lifes that fit inside 8x8 in a "well-separated" way, with no pseudo still lifes. I.e., these are constellations made up of separate [block, boat, beehive, tub, pond, ship, loaf, eater, longboat] still lifes.

The current enumeration code (in the ZIP file) is fairly silly, and among other things holds its output in memory and spits it out to the clipboard, which wouldn't be any good at all for longer and more ambitious enumerations.

Still, 8x8 is a big enough space to allow for thousands of one-time turners, including just about every possible combination of color and output timing in a fairly wide range. Here's a ZIP file with a separate RLE file for each equivalence class:

For example, here are all the entries in the 90degCP0col17 bucket. These are the one-time turners that behave

*exactly* like a Snark, not just same-as-a-Snark-mod-8 which would be all eighteen of the "90degCP0" buckets:

Code: Select all

```
x = 29, y = 506, rule = LifeHistory
18.2A$17.A.A$11.2A4.A$9.A2.A2.2A.4A$9.2A.A.A.A.A2.A$12.A.ABABAB$12.A.
AB2AB$13.AB.2B$16.3B$16.4B6.2A$14.3B2AB6.A$14.3B2AB3.BA.A$12.10B.B2A$
11.13B$10.6B3D5B$9.7BD7B$8.4B2.3BD4B$7.4B5.6B$6.4B4.9B$5.4B5.2A4.4B$
4.4B7.A5.4B$3.4B5.3A7.4B$2.4B6.A10.4B$.D3B19.B3C$BDBD21.C2B$B2D23.CB
13$12.B$9.7B$8.3B2A5B$9.BA2BA6B$9.BABA7B$9.2BA7B$7.12B$7.2A11B$7.2A4B
4.4B$7.4B7.4B$6.4B9.4B$5.4B11.4B$4.4B13.4B$3.4B15.4B$2.4B17.4B$.D3B
19.B3A$.DBD21.A2B$.2D23.A11$11.2B$11.3B$10.BA3B$9.BABA3B$9.B2A4B$10.B
2.4B$9.9B$9.B2A3B2AB$10.2A2BABA2B$9.4B.BA4B$8.4B2.7B$7.4B3.8B$6.4B4.
9B$5.4B6.9B$4.4B7.10B$3.4B9.10B$2.4B13.2B2.4B$.D3B19.B3A$.DBD21.A2B$.
2D23.A10$16.2B$13.8B$12.9B$11.10B$10.11B$10.11B$10.13B$11.14B$11.B2A
12B$10.2B2A11B$9.15B$8.2A13B$7.B2A12B$6.4B.2BA9B$5.4B2.BABAB4.4B$4.4B
5.AB6.4B$3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.A10$19.3B$
18.5B$16.7B$16.2B2A4B$15.2BA2BA3B$14.3BA2BA3B$13.5B2A3BA$12.10BABA$
11.12BA$10.4B.4B2.3B$9.4B2.5B2.B$8.4B5.4B$7.4B7.4B$6.4B9.4B$5.4B11.4B
$4.4B13.4B$3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.A8$18.B$
17.3B$16.4B$16.5B$17.2B2A2B$17.BABA3B$15.2BABA3B$13.2A3BA2B$13.ABA3B$
12.2BA3B$11.7B$10.4B.4B$9.4B3.4B$8.4B5.4B$7.4B7.4B$6.4B9.4B$5.4B11.4B
$4.4B13.4B$3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.A8$21.B$
20.3B$20.3B$16.2A6B$14.2B2A4BAB$14.7BABA$13.9BAB$13.4B2A4B$13.3BABA4B
$12.5BA3B$11.8B$10.9B$9.4B3.4B$8.4B5.4B$7.4B7.4B$6.4B9.4B$5.4B11.4B$
4.4B13.4B$3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.A5$14.2B$
13.4B$12.6B$12.8B$11.9B.2B$11.3B2A7B$11.3B2A8B$11.9BA3B$11.8BABA2B$
11.3B2A4BA2B$12.2BABA5B$12.3B2A5B$12.9B$11.10B$10.11B$9.4B.7B$8.4B3.
6B$7.4B5.B.4B$6.4B9.4B$5.4B11.4B$4.4B13.4B$3.4B15.4B$2.4B17.4B$.D3B
19.B3A$.DBD21.A2B$.2D23.A15$7.2B$6.4B$6.2A3BA2B2.B$6.2A2BABA5B$7.3BA
2BA5B$7.4B2A2B.4B$8.8B.4B$7.8B3.4B$6.6B2A2B3.4B$5.4B.2B2AB5.4B$4.4B3.
4B6.4B$3.4B5.2B8.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.A13$14.2B$
13.4B$8.2A2.2B2AB$8.2AB.2B2A2B$8.9B$10.8B$9.4B2A2B.B$9.3BA2BA4B$8.2A
2BABA6B$7.B2A3BA2B2.4B$6.6B7.4B$5.6B9.4B$4.4B13.4B$3.4B15.4B$2.4B17.
4B$.D3B19.B3A$.DBD21.A2B$.2D23.A9$16.B$10.8B$8.4B2A3BA2B$7.5B2A2BABAB
$8.9BA2B$9.11B$10.2B2A5B$11.A2BA2B2A$11.BABA2B2A2B$11.2BA7B$10.11B$9.
14B$8.4B.11B$7.4B2.12B$6.4B2.14B$5.4B3.13B$4.4B4.13B$3.4B5.14B$2.4B6.
5B5.5B$.D3B8.3B8.B3A$.DBD9.2B10.A2B$.2D23.A5$12.B$11.3B$11.3B$10.5B$
10.5B$10.6B$8.8B$7.2B2A2B2A$7.BABA2BABA$7.B2A4BA$7.9B$8.8B$8.B2A6B$9.
ABA6B$9.B2A2B.4B$9.4B3.4B$8.4B5.4B$7.4B7.4B$6.4B9.4B$5.4B11.4B$4.4B
13.4B$3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.A13$14.2B$13.5B
$13.2B2A2B$12.2BABA2B$11.2BABA3B$11.3BA3B2A$10.8BABA$9.10BAB$8.4B.2A
7B$7.4B2.2A.6B$6.4B7.6B$5.4B11.4B$4.4B13.4B$3.4B15.4B$2.4B17.4B$.D3B
19.B3A$.DBD21.A2B$.2D23.A10$22.B$20.2B2A2B$16.3B.2BABAB$16.2B2A3B2AB$
15.2BA.BA5B$14.3BA2BA6B$13.5B2A3BA3B$12.10BABA3B$11.12B2A4B$10.4B.4B
2.7B$9.4B2.5B2.4B$8.4B5.4B2.B$7.4B7.4B$6.4B9.4B$5.4B11.4B$4.4B13.4B$
3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.A13$12.B$9.7B$8.3B2A
5B$9.BA2BA6B$9.BABA7B$9.2BA7B$7.12B$7.2A11B$6.ABA4B4.4B$7.A3B7.4B$6.
4B9.4B$5.4B11.4B$4.4B13.4B$3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$
.2D23.A13$10.4B$8.6B$7.BA6B$6.BABA6B$6.2B2A7B$6.7B.4B$3.2A.6B3.4B$2.A
BA3B2A2B4.4B$2.BA3BABAB6.4B$2.5B2A2B7.4B$3.2B.4B9.4B$5.4B11.4B$4.4B
13.4B$3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.A6$15.3B$14.5B$
14.6B$13.8B$12.9B$13.10B$10.13B$10.13B$9.15B$8.16B$9.4B2A9B$10.2BABA
8B$9.3B2A9B$8.A13B$7.ABA11B$6.B2A4B2A6B$6.6BABA2B.4B$6.4B.2BAB4.4B$5.
4B3.2B6.4B$4.4B13.4B$3.4B15.4B$2.4B17.4B$.D3B19.B3A$.DBD21.A2B$.2D23.
A!
```

The scripts that do the post-enumeration sorting are also alpha-level code and slightly embarrassing, so I've hidden them in the attached ZIP file as well.

The "buckets" / OTT equivalence classes are designed for 90-degree turners, so they don't really work quite as well for 180-degree or 0-degree turners. Ideally there would be eight different classes for each output lane, but they end up all mixed together. Not going to spend time on fixing that right now -- if anyone wants to do a better job of sorting those out, I'd be most grateful. It should be possible to find anything that's needed in the current buckets, it might just take some searching in the 0-degree and 180-degree cases.

For example, here are 4- and 5-object constellations that pseudo-Heisenburp a glider, producing a new glider on the same lane with the same timing, plus a 90-degree glider:

Code: Select all

```
x = 53, y = 14, rule = LifeHistory
4.2A36.2A$4.A32.2A3.2A$5.3A29.A.A$7.A30.A$13.2A27.2A$12.A2.A25.A.A$2A
2.2A6.A2.A21.2A2.2A$2A2.2A7.2A22.2A3$10.3A17.3A17.3A$10.A19.A19.A$11.
A19.A11.2A6.A$43.2A!
```

This four-object constellation does the same, but produces lots of extra junk that could maybe be tamed with catalysts to get some of the original still lifes back (to make a cheaper pseudo-Heisenburp device):

Code: Select all

```
x = 13, y = 14, rule = LifeHistory
4.2A$4.A$5.3A$7.A3$2A2.2A$2A2.2A3$10.3A$10.A$2.2A7.A$2.2A!
```

Or this four-object constellation produces a Herschel, leaving a block as a target. The block could be rebuilt into the original constellation by an slsparse-generated slow salvo:

Code: Select all

```
x = 14, y = 13, rule = LifeHistory
4.2A$4.A$5.3A4.A$7.A3.A.A$11.2A2$2A2.2A$2A2.2A3$10.3A$10.A$
11.A!
```

Also, once the non-90-degree cases have been redefined, it would be nice to go through the

**bucketmulti2** and

**bucketmulti3** classes, and figure out what the equivalence class is for each of the individual gliders produced by each splitter.

In the meantime, simsim314's splitter tables higher up in this thread are a lot better organized than my

**mult2** and

**multi3** buckets. The only shortcomings of simsim314's old 10x10 search results are that they seem to be divided into only eight equivalence classes sometimes, instead of the full sixteen -- and they sometimes include mangoes and pseudo-still-life arrangements, which are maybe a bit more expensive on average in terms of glider constructions.