16-in-16: Oscillator Edition

[muzik]

Since all still lifes with 4 to 16 cells are now synthesizable with 16 or less gliders each as of 2019, I figured it might be interesting to extend this to all (minimum-)16-bit periodic objects (i.e. still lifes, oscillators and spaceships), rather than just still lifes. I've spent a couple of days creating list pages on the wiki, including one with all oscillators up to and including 16 cells, which also contains Catagolue links and synthesis costs for each, which can be used to keep track of values for each oscillator and highlight what needs reduction.

Since there aren't any spaceships with less than 17 cells bar the standard four, we only have oscillators to deal with.

Synthesising all of these at a cost of one-glider-per-cell or cheaper also has the added bonus that since the current reverse-caber-tosser upper limit is 17, this would result in all periodic objects (still lifes, oscillators, spaceships - we need a better umbrella term for (x,y)c/p non-unboundedly-growing patterns...) being constructible with one glider per cell at worst.

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Unsynthesized 16-Cell Objects
Currently (extrapolating from Mark Niemiec's lists and Catagolue), there are two 16-cell oscillators with no known syntheses. Unsurprisingly, all of these are of the sparse-and-made-of-interacting-sparks breed (or, as I like to call them, sparkling springs):

- xp2_g1l141lpz11, which is a sort of barberpole-extended version of what we currently call "15P2.1" (my personal name for which is "grief"): (7 natural occurrences: https://catagolue.hatsya.com/object/xp2 ... z11/b3s23/) EDIT by dvgrn: 8 natural occurrences now, and someone has completed it in 11 gliders)

Code: Select all

x = 8, y = 6, rule = B3/S23
b3ob3o2$2bobobo$7bo$obo3b2o$2o!

- xp2_bh284gljz01 (0 natural occurrences: https://catagolue.hatsya.com/object/xp2 ... z01/b3s23/) EDIT by dvgrn: this one now has a 30G synthesis)

Code: Select all

x = 8, y = 6, rule = B3/S23
2o4b2o$obo4bo$4bobo$o2bo$bo3b3o$bo!

In addition, there's also https://catagolue.hatsya.com/object/xp2 ... z32/b3s23/, which has no explicit synthesis so far, but Mark Niemiec has laid out some steps for a brute-force synthesis from soup, which could be refined into a 24G synthesis: EDIT by dvgrn: this one now has an 18G synthesis)
https://www.conwaylife.com/forums/viewt ... 676#p39676

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Room for Improvement
These are the oscillators which do have known syntheses (most are on Catagolue, and I'm in the process of porting over what's missing to Catagolue from Mark's old database), but that fail the one-glider-per-bit test. Improvements for these where possible are much preferred.

Melting clock (one of what are currently the two 14-bit stragglers which we still haven't seen naturally) requires 30 gliders, which is 16 above the limit:
https://catagolue.hatsya.com/object/xp2 ... 302/b3s23/

Blinkers bit pole currently costs 35 (+20):
https://catagolue.hatsya.com/object/xp2 ... z11/b3s23/

Nonapole currently costs 16 (+1):
https://catagolue.hatsya.com/object/xp2 ... 321/b3s23/

This 16p2 (muttering moat 1 with a symmetric barberpole extension) costs 17 (+1):
https://catagolue.hatsya.com/object/xp2 ... 201/b3s23/

This 16p2 (wishing fox with two barberpole extensions) costs 18 (+2):
https://catagolue.hatsya.com/object/xp2 ... 642/b3s23/

This 16p2 (wishing fox with one double-barberpole extension) also costs 18 (+2):
https://catagolue.hatsya.com/object/xp2 ... 642/b3s23/

And finally, this phoenix-with-cavity-esque 16p2 which Mark's site labels as "16pxbe" (I have no idea what "be" stands for, since object names aren't listed for 16-cell oscillators and up; phoenix with cavity was explicitly named and the file was also titled "15pxcav" so I can only assume "be" stands for something) costs a comical 58 gliders, over three and a half times its population:
https://catagolue.hatsya.com/object/xp2 ... 602/b3s23/

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Not sure I really have anything more to contribute here other than compiling these, updating the wiki page and barking orders, since oscillator component syntheses tend to be a tad more confusing than still life component syntheses, something I still have less than an introductory grasp on. So, anyone who knows what they're doing with this, fire away, and get the upper limit down to 17 once and for all!

[dvgrn]

Looks like a good wish-list for synthesis improvements. The most expensive item ((EDIT: sorry, second most expensive) on the list, blinkers bit pole, can clearly be done in less than 17G -- there's a second soup for it now that implies this:

Code: Select all

x = 29, y = 12, rule = LifeHistory
19.3A3.A.A$18.A5.A2.A$19.A.A2.A3.A$20.A3.A2.A$25.3A3$4.D.2D$.D2.D3.D
6.D$3D.D2.D6.3D4.2A$.D2.D.D7.D5.A2.A$4.D.3D12.2A!

That should count pretty much as a beginner-level synthesis (since even I could do it). So if anyone new to the field wants some experience, try running synthesise-patt.py against an R-pentomino and hunt down some three-glider recipes that fit in these two contexts, along with (hopefully) the sparky 2G blinker synthesis.

[Hdjensofjfnen]

Looks like a good wish-list for synthesis improvements. The most expensive item on the list, blinkers bit pole, can clearly be done in less than 17G -- there's a second soup for it now that implies this:

Code: Select all

x = 29, y = 12, rule = LifeHistory
19.3A3.A.A$18.A5.A2.A$19.A.A2.A3.A$20.A3.A2.A$25.3A3$4.D.2D$.D2.D3.D
6.D$3D.D2.D6.3D4.2A$.D2.D.D7.D5.A2.A$4.D.3D12.2A!

That should count pretty much as a beginner-level synthesis (since even I could do it). So if anyone new to the field wants some experience, try running synthesise-patt.py against an R-pentomino and hunt down some three-glider recipes that fit in these two contexts, along with (hopefully) the sparky 2G blinker synthesis.

Here's the main step:

Code: Select all

x = 50, y = 34, rule = B3/S23
bo$2bo$3o4$43bo$43bobo$24bo18b2o$25bo$23b3o11$13bo18bo$14bo16bobo$12b
3o16bo2bo7b2o$32b2o7bo2bo$42b2o2$48b2o$47b2o$49bo$23b2o$22bo2bo8b2o$
23b2o8bo2bo$34b2o!

[dvgrn]

Here's the main step...

Great! Looks like that will be well under the 16G limit, since a couple of the hivenloaf constellations have 3G recipes. I've gone ahead and non-magic-boxed the following -- gameoflifeboy's script wasn't finding a 1G cleanup (not counting the traffic light suppression already included above) for some reason or other, but I stumbled on one with Seeds of Destruction:

Code: Select all

x = 344, y = 39, rule = B3/S23
283bo$284bo$282b3o$343bo$341b2o$342b2o$325bo$325bobo$306bo18b2o$307bo$
305b3o7$221bo$219bobo$220b2o$227bo$114bo99bo12bobo65bo18bo$113bobo97bo
bo11b2o67bo16bobo$113bo2bo96bo2bo77b3o16bo2bo7b2o$6b2o106b2o98b2o98b2o
7bo2bo$5b2o5b2o310b2o$b2o4bo4bobo$obo9bo317b2o$2bo326b2o$331bo$205b2o
98b2o$116b2o86bo2bo8b2o86bo2bo8b2o$115bo2bo86b2o8bo2bo86b2o8bo2bo$108b
2o6b2o98b2o98b2o$108bobo$108bo$101b2o$100bobo$102bo!