## 16 in 16: Efficient 16-bit Synthesis Project

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### Re: 16 in 16: Efficient 16-bit Synthesis Project

chris_c wrote:...It brings 16.745 down to 16G. Are there any constellations that can reduce this further?

`16G synth`

Using a TL-block constellation brings it down to 15G:

`x = 135, y = 427, rule = B3/S23116b3o2\$114bo5bo\$114bo5bo\$114bo5bo2\$12b3o5bo95b3o\$14bo3bobo\$13bo5b2o2\$22bo\$20b2o99b2o\$21b2o98b2o59\$55bo\$54bo\$54b3o\$10bo\$8bobo\$9b2o23\$134bo\$16b3o97b3o15bo\$134bo\$14bo5bo93bo5bo\$14bo5bo93bo5bo\$14bo5bo93bo5bo2\$16b3o97b3o5\$21b2o98b2o\$21b2o98b2o56\$64bo\$64bobo\$64b2o15\$8bobo\$9b2o\$9bo12\$17bo96b2o\$17bo15b3o78b2o\$17bo\$118b2obo\$13b3o3b3o96bob2o2\$17bo101b5o\$17bo99bo2bo2bo\$17bo99b2o4\$21b2o\$21b2o15\$54b2o\$54bobo\$54bo5\$5b2o\$4bobo\$6bo58\$10bo\$11bo\$9b3o3\$14b2o\$14b2o2\$18b2obo96b2obo\$18bob2o96bob2o2\$19b5o95b5o\$17bo2bo2bo93bo2bo2bo\$17b2o98b2o87\$2bo\$obo\$b2o6\$18b2obo96b2obo\$18bob2o96bob2o2\$19b5o95b5o\$17bo2bo2bo96bo2bo\$17b2o99bo\$118b2o13\$9bo\$2b2o5b2o24bo\$bobo4bobo23b2o\$3bo9b2o19bobo\$12bobo\$14bo!`

Goldtiger997

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

Goldtiger997 wrote:Using a TL-block constellation brings it down to 15G:

Thanks. I guess this should give 16.713 in 11G but I'm not going to complete it until tomorrow:

`x = 52, y = 49, rule = B3/S23o\$b2o\$2o16\$27b2o\$26bo2bo\$27b2o2\$30b2o\$30b2o2\$22bo\$21bobo\$20bo3bo\$20bo3bo\$20b2ob2o5\$30b3o4\$50b2o\$49b2o\$51bo6\$22b3o\$24bo\$23bo!`
chris_c

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

chris_c wrote:Thanks. I guess this should give 16.713 in 11G but I'm not going to complete it until tomorrow:

`rle`

Yes, 16.713 in 11 gliders:

`x = 64, y = 61, rule = B3/S23o\$b2o\$2o3\$58bobo\$58b2o\$59bo14\$42bobo\$42b2o\$43bo3\$35bo\$33bobo\$34b2o2\$36b3o\$38bo\$37bo6\$24bo\$24b2o\$23bobo11bobo\$37b2o\$31bo6bo\$30b2o\$30bobo4b2o\$36b2o\$38bo4\$62b2o\$61b2o\$63bo6\$22b3o\$24bo\$23bo!`

Here are some predecessors for 16.1323 that have a hope of taking only 10 gliders, which would give 16.1398 in 15 gliders:

`x = 47, y = 17, rule = B3/S236bo34bo\$6bo34bo\$6bo34bo3\$8bo34bo\$6b2obo31b2obo\$7bobo32bobo\$8bo34bo2\$9b2o33b2o\$9b3o32bobo\$45bo\$2bo34bo\$bobo32bobo\$o2bo31bo2bo\$b2o33b2o!`

Goldtiger997

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

Goldtiger997 wrote:
chris_c wrote:...It brings 16.745 down to 16G. Are there any constellations that can reduce this further?

`16G synth`

Using a TL-block constellation brings it down to 15G:

`x = 135, y = 427, rule = B3/S23116b3o2\$114bo5bo\$114bo5bo\$114bo5bo2\$12b3o5bo95b3o\$14bo3bobo\$13bo5b2o2\$22bo\$20b2o99b2o\$21b2o98b2o59\$55bo\$54bo\$54b3o\$10bo\$8bobo\$9b2o23\$134bo\$16b3o97b3o15bo\$134bo\$14bo5bo93bo5bo\$14bo5bo93bo5bo\$14bo5bo93bo5bo2\$16b3o97b3o5\$21b2o98b2o\$21b2o98b2o56\$64bo\$64bobo\$64b2o15\$8bobo\$9b2o\$9bo12\$17bo96b2o\$17bo15b3o78b2o\$17bo\$118b2obo\$13b3o3b3o96bob2o2\$17bo101b5o\$17bo99bo2bo2bo\$17bo99b2o4\$21b2o\$21b2o15\$54b2o\$54bobo\$54bo5\$5b2o\$4bobo\$6bo58\$10bo\$11bo\$9b3o3\$14b2o\$14b2o2\$18b2obo96b2obo\$18bob2o96bob2o2\$19b5o95b5o\$17bo2bo2bo93bo2bo2bo\$17b2o98b2o87\$2bo\$obo\$b2o6\$18b2obo96b2obo\$18bob2o96bob2o2\$19b5o95b5o\$17bo2bo2bo96bo2bo\$17b2o99bo\$118b2o13\$9bo\$2b2o5b2o24bo\$bobo4bobo23b2o\$3bo9b2o19bobo\$12bobo\$14bo!`

Reduced to 13G:
`x = 65, y = 170, rule = B3/S2358bo\$58bo\$58bo2\$54b3o3b3o2\$4bo53bo\$4b2o4bo47bo\$3bobo5b2o45bo\$10b2o2\$12bo\$11bo50b2o\$11b3o48b2o33\$28bo\$28bobo\$28b2o2\$8bo46b2o\$8bo46b2o\$8bo\$59b2obo\$4b3o3b3o46bob2o2\$8bo11bo39b5o\$8bo12b2o35bo2bo2bo\$8bo11b2o2b3o31b2o\$24bo\$25bo2\$12b2o\$12b2o2\$16b3o\$18bo\$17bo30\$3bo\$bobo\$2b2o\$5b2o\$5b2o2\$9b2obo46b2obo\$9bob2o46bob2o2\$10b5o45b5o\$8bo2bo2bo43bo2bo2bo\$8b2o48b2o45\$bo7b2obo46b2obo\$2bo6bob2o46bob2o\$3o\$10b5o45b5o\$8bo2bo2bo46bo2bo\$8b2o49bo\$59b2o5\$8b2o\$b3o5b2o6b2o\$3bo4bo7b2o\$2bo9b3o3bo\$14bo\$13bo!`
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
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### Re: 16 in 16: Efficient 16-bit Synthesis Project

Goldtiger997 wrote:Yes, 16.713 in 11 gliders

Thanks!

Godltiger997 wrote:Here are some predecessors for 16.1323 that have a hope of taking only 10 gliders, which would give 16.1398 in 15 gliders:

In 12G...
`x = 73, y = 95, rule = B3/S233bo\$4b2o\$3b2o18\$o\$b2o\$2o25\$40bo\$28bo11bobo\$29b2o9b2o\$28b2o4\$38bo\$34bob2o\$32bobo2b2o\$33b2o6\$41bo\$40bobo\$23b3o8b2o4bo2bo\$25bo7b2o6b2o\$24bo10bo3\$35b2o\$34b2o\$36bo20\$71bo\$70b2o\$70bobo!`

Here's a quick peek at the SLs at 20G and above:

`16.1139    xs16_kq23z124871         2516.353     xs16_321fgc453           2316.621     xs16_g5r8jdz11           2316.829     xs16_0md1e8z1226         2316.1702    xs16_4a5p68ozx121        2316.1740    xs16_69acga6zx32         2316.1846    xs16_25a8c93zw33         2216.2313    xs16_08u16853z32         2216.159     xs16_2egmd1e8            2116.218     xs16_3pajc48c            2116.774     xs16_69raa4z32           2116.1084    xs16_31ke12kozw11        2116.1682    xs16_8k9bkk8zw23         2116.1693    xs16_8k8aliczw23         2116.1753    xs16_695q4gozw23         2116.1954    xs16_8kk31e8z065         2116.2096    xs16_wck5b8oz311         2116.2309    xs16_8kk31e8z641         2116.217     xs16_3146pajo            2016.228     xs16_178bp2sg            2016.712     xs16_3pc0qmzw23          2016.723     xs16_i5p64koz11          2016.833     xs16_0mp2sgz1243         2016.872     xs16_2lla8oz065          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        20`
chris_c

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

16.1139 in 15G:
`x = 339, y = 34, rule = B3/S23238bo\$236bobo29b2o28b2o\$225bo11b2o29b2o28b2o\$226bo\$224b3o10bo57b3o\$237b2o58bo\$236bobo57bo7\$2bobo31bo29bo29bo29bo29bo29bo29bo15bo13bo29bo29bo29bo\$3b2o29b3o27b3o27b3o27b3o27b3o27b3o27b3o16bo10b3o27b3o27b3o27b3o\$3bo29bo29bo29bo29bo29bo29bo29bo17b3o9bo29bo29bo29bo\$33b2o24bo3b2o27bobo27bobo27bobo27bobo27bobo27bobo29bo29bo29bo\$3o57bo32b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o\$2bo55b3o96b2o28b2o28b2o28b2o24bo3b2o24bo3b2o24bo3b2o\$bo155bo20bo8bo29bo29bo26bo2bo26bo2bo26bo2bo\$60b3o64b2o26bobo21bo5bobo26b2obo26b2obo27bobo27bobo27bobo\$60bo65b2o27b2o20b3o5b2o27bobo27bobo29bo29bo29bo\$61bo61b2o3bo\$122bobo55b3o\$124bo57bo\$181bo\$188bo\$187b2o\$187bobo3\$247b3o\$247bo\$248bo!`
-Matthias Merzenich
Sokwe
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### Re: 16 in 16: Efficient 16-bit Synthesis Project

16.353 takes 12 (left) but might be as few as 10 (right):
`x = 47, y = 18, rule = B3/S2311b2o\$11b2o3\$41bo2b2o\$41bo2bo\$4b3o7b2o19b2o4bo3bo\$14bo19bo2bo7b2o\$b2o11bobo18b2o\$o2bo11b2o\$b2o2\$40bo\$39bobo\$6bo32bo2bo\$5bobo32b2o\$5bo2bo\$6b2o!`

Reaction for 16.621:
`x = 111, y = 98, rule = B3/S2396bo\$95bo\$95b3o35\$42b2o\$41bo2bo\$42b2o3\$42b2o\$41bobo\$42bo4bo\$47b2o\$46bobo\$46b2o\$46bo6bobo\$53b2o\$34b2o18bo\$33bo2bo10bo\$34bobo9bobo\$35bo9bo3bo\$46bobo\$47bo35\$3o\$2bo\$bo3\$109bo\$108b2o\$108bobo!`
Last edited by BlinkerSpawn on April 27th, 2017, 7:22 am, edited 1 time in total.
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### Re: 16 in 16: Efficient 16-bit Synthesis Project

BlinkerSpawn wrote:16.353 takes 12 (left) but might be as few as 10 (right):
`RLE`

Definitely ten:
`x = 18, y = 21, rule = B3/S2315bo\$14bo\$11bo2b3o\$12bo\$10b3o3\$13bo\$13bobo\$13b2o\$6b3o\$b2o\$o2bo11bobo\$b2o12b2o\$16bo3\$6bo4b3o\$5bobo3bo\$5bo2bo3bo\$6b2o!`

However, I have a strong suspicion that it can be made with even less, at least partly because of this:
`x = 6, y = 8, rule = B3/S232bo\$obo\$b2o2\$3b2o\$2bo2bo\$2bobo\$3bo!`
I Like My Heisenburps! (and others)

Extrementhusiast

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

16.697 can be done in 12G by trivially modifying the synthesis of 16.698:
`x = 75, y = 24, rule = B3/S2310bo\$9bo\$9b3o\$70bobo\$2bo34bobo30b2o\$3b2o32b2o32bo\$2b2o2bo26bo4bo30bo\$6bobo20b2obobo24b2ob2o4b2o\$6b2o22bobobo2b2o21bobo5bobo\$29bo2b2o2b2o21bo2bobo\$29b2o7bo20b2o2b2o8bo\$72b2o\$72bobo\$2o\$obo\$o58b2o\$58bobo\$60bo\$66b2o\$66bobo\$66bo\$60b2o\$59bobo\$61bo!`
-Matthias Merzenich
Sokwe
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### Re: 16 in 16: Efficient 16-bit Synthesis Project

Extrementhusiast wrote:
BlinkerSpawn wrote:16.353 takes 12 (left) but might be as few as 10 (right):
`RLE`

Definitely ten:
`rle`

My estimate of ten was based upon making the sparked-R octomino in 3 gliders like the G+loaf collision does and everything else in 2, and the G+loaf collision doesn't seem to fit with 2G blinker syntheses.
Unless you can make the three-object constellation in 4G total your synthesis would still take 11 or 12 (5G + 5-6 for three objects + 1 cleanup).
Another reaction for 16.621, this time neater:
`x = 13, y = 9, rule = B3/S234bobo2\$5bo\$5b2ob3o\$5b2o2\$bo8b3o\$b2o\$obo!`
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

Sokwe wrote:16.1139 in 15G:...

Nicely done!

chris_c wrote:
Godltiger997 wrote:Here are some predecessors for 16.1323 that have a hope of taking only 10 gliders, which would give 16.1398 in 15 gliders:

In 12G...

I'll see if I can reduce it (I highly doubt I'll get it to ten though).

BlinkerSpawn wrote:16.353 takes 12 (left) but might be as few as 10 (right):
`x = 47, y = 18, rule = B3/S2311b2o\$11b2o3\$41bo2b2o\$41bo2bo\$4b3o7b2o19b2o4bo3bo\$14bo19bo2bo7b2o\$b2o11bobo18b2o\$o2bo11b2o\$b2o2\$40bo\$39bobo\$6bo32bo2bo\$5bobo32b2o\$5bo2bo\$6b2o!`

16.353 in 9 gliders:

`x = 30, y = 28, rule = B3/S23bo\$2bo\$3o6\$27bobo\$27b2o\$28bo\$17bo\$15bobo\$11bo4b2o\$9bobo\$10b2o6b3o\$20bo6bo\$19bo6bo\$26b3o2\$12bobo5b2o\$13b2o4bobo\$13bo7bo3\$20b2o\$19b2o\$21bo!`

Goldtiger997

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

Sokwe wrote:16.697 can be done in 12G by trivially modifying the synthesis of 16.698:

The same component also reduces 16.1105 and 16.1464

Goldtiger997 wrote:16.353 in 9 gliders:

This reduces 16.358 to 14G.

Here is 16.2313 in 15G:

`x = 128, y = 411, rule = B3/S2327bo\$26bo\$26b3o\$21bo\$22bo\$20b3o\$123b2o\$123b2o3\$125b3o2\$22b2o\$23b2o\$22bo69\$13bobo4bo13bo\$14b2o2bobo12bo\$14bo4b2o12b3o4\$120b2o2b2o\$120b2o2b2o16\$23b2o98b2o\$23b2o98b2o3\$25b3o97b3o74\$4bo\$5b2o\$4b2o2\$122bo\$20b2o2b2o95bobo\$20b2o2b2o95bob3o\$120b2o4bo\$121bo3b2o\$119bo\$119b2o12\$23b2o\$23b2o3\$25b3o5\$6b2o\$7b2o\$6bo2\$2o\$b2o\$o20\$63b3o\$63bo\$64bo45\$22bo99bo\$21bobo97bobo\$21bob3o95bob3o\$20b2o4bo93b2o4bo\$21bo3b2o94bo3b2o\$19bo99bo\$19b2o98b2o4b2o\$124bobo\$125bo7\$15b2o\$14bobo\$16bo67\$42bo\$41bo\$16bo24b3o\$14bobo\$15b2o12\$22bo99bo2b2o\$21bobo97bobo2bo\$21bob3o95bobobo\$20b2o4bo93b2o2bo\$21bo3b2o94bo\$19bo99bo\$19b2o4b2o92b2o\$24bobo\$25bo9\$41bo\$40b2o\$40bobo\$10bo\$10b2o\$9bobo!`

SLs at 20G or above:

`16.621     xs16_g5r8jdz11           2316.829     xs16_0md1e8z1226         2316.1702    xs16_4a5p68ozx121        2316.1740    xs16_69acga6zx32         2316.1846    xs16_25a8c93zw33         2216.159     xs16_2egmd1e8            2116.218     xs16_3pajc48c            2116.774     xs16_69raa4z32           2116.1084    xs16_31ke12kozw11        2116.1682    xs16_8k9bkk8zw23         2116.1693    xs16_8k8aliczw23         2116.1753    xs16_695q4gozw23         2116.1954    xs16_8kk31e8z065         2116.2096    xs16_wck5b8oz311         2116.2309    xs16_8kk31e8z641         2116.217     xs16_3146pajo            2016.228     xs16_178bp2sg            2016.712     xs16_3pc0qmzw23          2016.723     xs16_i5p64koz11          2016.833     xs16_0mp2sgz1243         2016.872     xs16_2lla8oz065          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        20`

EDIT

16.621 in 14G:

`x = 120, y = 80, rule = B3/S2347bo\$46bo\$46b3o\$19bo\$20bo\$18b3o3\$43bo\$42bo\$42b3o4\$12bo19bo\$13bo19b2o\$11b3o18b2o4\$51bo\$35bobo12bo\$36b2o12b3o\$36bo5\$32b2o81b2ob2o\$31bobo82bobo\$33bo81bo3bo\$116b2obo\$114bobobo\$114b2o\$20bo\$20b2o\$19bobo2\$31bo\$31b2o75b2o\$30bobo74bo2bo\$45b2o61b2o\$45bobo\$38b2o5bo57b3o\$38bobo64bo\$38bo65bo32\$2o\$b2o\$o!`

EDIT2: 16.829 in 8G:

`x = 23, y = 26, rule = B3/S237bo\$8bo\$6b3o10bo\$18bo\$18b3o\$11bo\$12b2o\$11b2o\$6b3o\$8bo\$7bo\$2o\$b2o\$o4\$12bo\$12b2o7bo\$11bobo6b2o\$20bobo3\$13b3o\$15bo\$14bo!`
Last edited by chris_c on April 27th, 2017, 7:21 pm, edited 2 times in total.
chris_c

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

Tough reaction for 16.829:
`x = 23, y = 10, rule = B3/S2313b3o\$13b3o2\$7b2ob3o\$b2o4b2o\$o2bo\$b2ob2o\$b2ob2o14b2o\$3bo16bobo\$20bo!`
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### Re: 16 in 16: Efficient 16-bit Synthesis Project

chris_c wrote:SLs at 20G or above:
...
16.2309 xs16_8kk31e8z641 21

This one is an easy 14G from the first soup I tried, and can no doubt be done in less -- possibly starting from T=175 in this pattern:

`#C 16.2309 in 14Gx = 153, y = 151, rule = B3/S23bo\$2bo\$3o6\$129bo\$127b2o\$128b2o51\$103bo\$103bobo\$103b2o14\$70b2o\$69bobo\$71bo\$78b2o\$77b2o\$79bo2\$64b2o\$63bobo\$65bo2\$103b3o\$60b2o19b2o20bo\$59bobo19bobo20bo\$61bo19bo3\$56bo\$56b2o\$55bobo2\$61bo26b2o\$61b2o24b2o\$60bobo26bo29\$150b2o\$150bobo\$150bo17\$b2o\$obo\$2bo!`

Minor apologies for the arbitrary continuous synthesis -- it's really ten separate stages.

EDIT: Ooh, the next soup builds the still life in stages, starting from the eater:

`x = 26, y = 18, rule = B3/S2314bo\$13bobo\$12bo3bo\$12bo3bo\$12bo3bo\$13bobo\$14bo2\$11b2o11bo\$11b2o4b3o3bobo\$17b3o3bobo\$bo14bo3bo3bo\$b2o14b3o\$obo14b3o2\$21bo\$21bo\$21bo!`

dvgrn
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### Re: 16 in 16: Efficient 16-bit Synthesis Project

From 13G w/ that second reaction:
`x = 48, y = 60, rule = B3/S2345bo\$45bobo\$45b2o13\$14bobo\$15b2o9bo\$15bo10bobo\$26b2o3\$12bo\$13b2o\$12b2o5bo\$17bobo13bo\$18b2o11b2o\$32b2o4\$35b2o\$34b2o\$9b2o25bo\$10b2o\$9bo\$bo17b2o\$b2o17b2o\$obo16bo10b2o\$30bobo\$30bo\$26b3o\$28bo\$27bo15\$6b2o\$5bobo\$7bo!`
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### Re: 16 in 16: Efficient 16-bit Synthesis Project

`x = 23, y = 10, rule = B3/S2313b3o\$13b3o2\$7b2ob3o\$b2o4b2o\$o2bo\$b2ob2o\$b2ob2o14b2o\$3bo16bobo\$20bo!`

16.829 in 9 gliders:

`x = 37, y = 31, rule = B3/S238\$26bo\$24b2o\$25b2o2\$4bo\$4bobo\$4b2o15bo\$2bo17bo\$obo12bo4b3o\$b2o4bobo5bobo\$7b2o6b2o\$8bo\$28b2o\$27b2o\$10b2o17bo\$9bobo\$11bo2\$32bo\$31b2o\$31bobo!`

I spent far too long on that synthesis.
Last edited by Goldtiger997 on April 28th, 2017, 8:39 am, edited 1 time in total.

Goldtiger997

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### Re: 16 in 16: Efficient 16-bit Synthesis Project

chris_c wrote:...
Thanks. That synthesis didn't make it into the database because there was a trivial error in the construction of the blinker. It brings 16.1073 down to 17G but doesn't appear to improve 16.1791.
...

Oh, sorry...

16.1702 in 11G or less:
`x = 39, y = 27, rule = B3/S2336bo\$36bobo\$36b2o5\$12bo\$13bo\$11b3o\$bo\$2bo\$3o\$25b2o\$17b2o6b2o\$8b3o5bo2bo\$10bo6b2o\$9bo4\$3b3o\$5bo\$4bo12b2o\$16bobo13b2o\$18bo12b2o\$33bo!`

yootaa

Posts: 35
Joined: May 26th, 2016, 1:08 am
Location: Japan

### Re: 16 in 16: Efficient 16-bit Synthesis Project

yootaa wrote:16.1702 in 11G or less:
`x = 39, y = 27, rule = B3/S2336bo\$36bobo\$36b2o5\$12bo\$13bo\$11b3o\$bo\$2bo\$3o\$25b2o\$17b2o6b2o\$8b3o5bo2bo\$10bo6b2o\$9bo4\$3b3o\$5bo\$4bo12b2o\$16bobo13b2o\$18bo12b2o\$33bo!`

16.1702 in 8 gliders:

`x = 46, y = 32, rule = B3/S2343bo\$43bobo\$43b2o3\$o\$b2o\$2o2\$23bo\$24b2o\$23b2o3\$18bo\$19bo2b2o\$17b3obobo\$23bo9\$3b2o\$4b2o\$3bo13bo\$17b2o23b2o\$16bobo23bobo\$42bo!`

(EDIT: I replaced a 9-glider synthesis with the above synthesis)

Goldtiger997

Posts: 524
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 16 in 16: Efficient 16-bit Synthesis Project

dvgrn wrote:Ooh, the next soup builds the still life in stages, starting from the eater

I did a 4G search for the necessary spark giving 16.2309 in 6G:

`x = 29, y = 31, rule = B3/S235\$13bo\$14bo\$12b3o\$4bo16bobo\$5bo15b2o\$3b3o16bo5\$16bo\$17bo\$15b3o3\$16b2o\$17b2o\$16bo\$5bo\$5b2o\$4bobo!`

Quite often the reaction works as a simple 4G component:

`x = 18, y = 18, rule = B3/S23bo\$2bo\$3o\$14b2obo\$14bob2o3\$13bo\$14bo\$12b3o3\$13b2o\$14b2o\$13bo\$2bo\$2b2o\$bobo!`

I also found this alternative version with more clearance at the bottom in 6G:

`x = 22, y = 26, rule = B3/S2312b2obo\$12bob2o2\$6bo\$obo4bo\$b2o2b3o\$bo4\$9b2o\$10b2obobo\$9bo3b2o\$14bo2\$19b3o\$19bo\$20bo6\$b2o\$obo\$2bo!`

SLs taking 19G and above:

`16.1740    xs16_69acga6zx32         2316.1846    xs16_25a8c93zw33         2216.159     xs16_2egmd1e8            2116.218     xs16_3pajc48c            2116.774     xs16_69raa4z32           2116.1084    xs16_31ke12kozw11        2116.1682    xs16_8k9bkk8zw23         2116.1693    xs16_8k8aliczw23         2116.1753    xs16_695q4gozw23         2116.2096    xs16_wck5b8oz311         2116.217     xs16_3146pajo            2016.228     xs16_178bp2sg            2016.712     xs16_3pc0qmzw23          2016.723     xs16_i5p64koz11          2016.833     xs16_0mp2sgz1243         2016.872     xs16_2lla8oz065          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        2016.18      xs16_caarzbd             1916.131     xs16_660uhar             1916.230     xs16_178jd2ko            1916.801     xs16_08eharz321          1916.1684    xs16_4aab9k8zx32         1916.1694    xs16_4a5p6o8zx121        1916.1912    xs16_at16426z32          1916.1979    xs16_4ap30ga6zw121       1916.2050    xs16_6ik8a52z065         1916.2162    xs16_0at16426z32         1916.2200    xs16_06agc93z2521        1916.2307    xs16_6ik8a52z641         1916.2316    xs16_0at16413z32         19`
chris_c

Posts: 894
Joined: June 28th, 2014, 7:15 am

### Re: 16 in 16: Efficient 16-bit Synthesis Project

chris_c wrote:I did a 4G search for the necessary spark giving 16.2309 in 6G...

Nice! I was hoping there'd be something like that -- the spark looked like it would be small enough to show up in a 3G or 4G search.

Your 4G search was just a quick one-off with gencols, with gliders coming from those two directions? How did you set up the filter to find the spark, exactly?

-- I'm interested in the way these kinds of searches are currently done, because of my ongoing plot to come up with an actual total count for three-glider collisions, along with the various lists of useful constellations that might come out of an exhaustive enumeration. Haven't figured out how to usefully catalogue this kind of edgy spark yet...!

dvgrn
Moderator

Posts: 5711
Joined: May 17th, 2009, 11:00 pm

### Re: 16 in 16: Efficient 16-bit Synthesis Project

dvgrn wrote:
chris_c wrote:I did a 4G search for the necessary spark giving 16.2309 in 6G...

Nice! I was hoping there'd be something like that -- the spark looked like it would be small enough to show up in a 3G or 4G search.

Your 4G search was just a quick one-off with gencols, with gliders coming from those two directions? How did you set up the filter to find the spark, exactly?

-- I'm interested in the way these kinds of searches are currently done, because of my ongoing plot to come up with an actual total count for three-glider collisions, along with the various lists of useful constellations that might come out of an exhaustive enumeration. Haven't figured out how to usefully catalogue this kind of edgy spark yet...!

The spark eventually settles into a beehive, therefore the first task was a 4G search for beehives using some old LifeAPI code. This took the longest time. I intended to post-process this with Golly but it was taking too long. Instead I wrote a LifeAPI program to analyse a series of reactions and output the RLE of the generation that is N generations before the final pattern appears. N was equal to 12 in my case. I post-processed this file in Golly looking for the desired spark. That was still quite slow.

I could post the actual code before too long if there is any interest. It would need a little tidying up first though.

EDIT: I should mention that a possible stepping-stone along the way to the 3G-collision enumeration project would be a more modern version of gencols that is both faster and has better options for detecting particular sparks or final constellations. It won't be top of my to-do list for a while though.
chris_c

Posts: 894
Joined: June 28th, 2014, 7:15 am

### Re: 16 in 16: Efficient 16-bit Synthesis Project

chris_c wrote:...
I did a 4G search for the necessary spark giving 16.2309 in 6G:

`x = 29, y = 31, rule = B3/S235\$13bo\$14bo\$12b3o\$4bo16bobo\$5bo15b2o\$3b3o16bo5\$16bo\$17bo\$15b3o3\$16b2o\$17b2o\$16bo\$5bo\$5b2o\$4bobo!`

Quite often the reaction works as a simple 4G component:

`x = 18, y = 18, rule = B3/S23bo\$2bo\$3o\$14b2obo\$14bob2o3\$13bo\$14bo\$12b3o3\$13b2o\$14b2o\$13bo\$2bo\$2b2o\$bobo!`
...

16.2801 in 8G with this reaction:
`x = 69, y = 20, rule = B3/S2336bobo\$37b2o\$37bo\$48bo\$49b2o\$5bo42b2o\$6bo\$4b3o54b2o\$47b3o11bo\$9bo39bo13bo\$9bobo36bo13b2o\$9b2o50bo\$27b2o23b2o8b2o3b2o\$24bobobo20bobobo10bobobo\$24b2o23b2o13b2o\$35b3o\$3o34bo\$2bo8b2o23bo\$bo9bobo\$11bo!`

Bob Shemyakin
BobShemyakin

Posts: 214
Joined: June 15th, 2014, 6:24 am

### Re: 16 in 16: Efficient 16-bit Synthesis Project

16.723 and 16.833 in at most eleven gliders each:
`x = 84, y = 28, rule = B3/S232o\$2o\$9bo63bo\$7b2o56bo5b2o\$8b2o56bo5b2o\$60bo3b3o\$18b2o41bo\$bo15bo2bo38b3o\$obo15b2o2b2o\$obo19bobo\$bo20bo2\$51b3o2\$6bo\$6bo\$6bo49b3o4b2o\$63bobo\$63bo3\$60b3o\$62bo\$61bo2b3o\$64bo16b3o\$27b3o35bo15bo\$27bo54bo\$28bo!`

The first soup for the latter even suggests a component:
`x = 19, y = 17, rule = B3/S232b2o\$bobo\$bo12bo\$2o11bobo\$2b2o8bo2bo\$2bobo8b2o\$3bo3\$15b3o\$18bo\$18bo\$15b3o2\$12b3o2\$12bo!`

Also, I think it's probably about time to reveal the whole list of 16-bit SLs.

EDIT: 16.18 in nine gliders:
`x = 47, y = 49, rule = B3/S23o\$b2o\$2o13\$22bo\$20b2o\$16bobo2b2o\$17b2o\$17bo3\$25bo\$20bo4bo\$18bobo4bo\$19b2o4\$15b2o\$14bobo\$16bo4\$28b2o\$27b2o\$29bo9\$45b2o\$44b2o\$46bo!`
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1768
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 16 in 16: Efficient 16-bit Synthesis Project

Extrementhusiast wrote:16.723 and 16.833 in at most eleven gliders each:
`rle`

16.723 in 10 gliders (may be further reducible by using 2 constellations):

`x = 116, y = 38, rule = B3/S23bo\$2bo\$3o8\$49b2o28b2o30b2o\$49b2o28b2o30bobo\$39bo48bo24bo\$39bobo44b2o25b2o\$39b2o46b2o22b2o2bo\$37bo72bo2bobo\$17bo17bobo29b2o28b2o11b2o2bo\$15bobo18b2o12bo15bo2bo10bo15bo2bo\$16b2o2bo28bobo15b2o10bobo15b2o2b2o\$20bobo26bobo27bobo19bobo\$20b2o28bo29bo20bo2\$18bo\$19b2o\$18b2o35bo29bo\$55bo29bo\$55bo29bo8\$3b3o\$5bo100b3o\$4bo101bo\$107bo!`

16.833 in 11 gliders (could not find a 3G synthesis of the blinker constellation):

`x = 34, y = 25, rule = B3/S2323bo\$15bo5b2o\$16bo5b2o\$10bo3b3o\$obo8bo\$b2o6b3o\$bo3\$2o\$b2o\$o2\$5bo\$6b2o5b2o\$5b2o6bobo\$13bo2\$6bo\$6b2o2b3o\$5bobo4bo\$11bo2b3o\$14bo16b3o\$15bo15bo\$32bo!`

Extrementhusiast wrote:The first soup for the latter even suggests a component:
`x = 19, y = 17, rule = B3/S232b2o\$bobo\$bo12bo\$2o11bobo\$2b2o8bo2bo\$2bobo8b2o\$3bo3\$15b3o\$18bo\$18bo\$15b3o2\$12b3o2\$12bo!`

It reduces to this:

`x = 33, y = 27, rule = B3/S232b2o18b2o\$bobo2b2o13bobo2b2o\$bo3b2o14bo4bo3bo\$2o18b2o4bo3bobo\$2b2o3bobo12b2o6b2o\$2bobo2b2o13bobo2b2o\$3bo3b2o14bo3b2o14\$2b2o18b2o\$bobo2b2o13bobo2b2o\$bo3b2o14bo3b2o\$2o18b2o\$2b2o3bo14b2o3bobo\$2bobo2b2o13bobo2b3o\$3bo3b3o13bo3b2o!`

EDIT:

Extrementhusiast wrote:EDIT: 16.18 in nine gliders:
`x = 47, y = 49, rule = B3/S23o\$b2o\$2o13\$22bo\$20b2o\$16bobo2b2o\$17b2o\$17bo3\$25bo\$20bo4bo\$18bobo4bo\$19b2o4\$15b2o\$14bobo\$16bo4\$28b2o\$27b2o\$29bo9\$45b2o\$44b2o\$46bo!`

Reduced to 8 gliders:

`x = 47, y = 49, rule = B3/S23o\$b2o\$2o13\$22bo\$20b2o\$16bobo2b2o\$17b2o12bo\$17bo11b2o\$30b2o3\$20bo\$18bobo\$19b2o6b2o\$27bobo\$27bo8\$28b2o\$27b2o\$29bo9\$45b2o\$44b2o\$46bo!`

EDIT2:

16.1740 in 9 gliders:

`x = 38, y = 51, rule = B3/S2313bo\$11bobo\$12b2o5\$18bo\$16bobo\$17b2o2\$28bo\$26bobo\$27b2o2\$23bo5bo\$13b2o6bobo5bobo\$12bobo7b2o5b2o\$14bo6\$17b2o\$16bobo\$18bo16b3o\$35bo\$36bo20\$2o\$b2o\$o!`

Can anyone make a converter out of this?:

`x = 12, y = 17, rule = B3/S238b2o\$10b2o\$5bob2o\$3bobobo\$4b2obobo\$8bobo\$9bo2\$2bo\$obo\$b2o\$4bo\$3bobob2o\$3bobobo\$4b2obobo\$8bobo\$9bo!`

EDIT3:

Here's a synthesis of 16.1846 that is probably cheaper than whatever the above possible converter might give.

16.1846 in 11 gliders:

`x = 24, y = 24, rule = B3/S2323bo\$8bo12b2o\$6bobo13b2o\$7b2o2\$19bobo\$8bo10b2o\$6bobo11bo\$7b2o2bo\$10bo\$10b3o4bobo\$17b2o\$11bo6bo\$10b2o\$10bobo\$2bo\$obo\$b2o2\$3b3o\$5bo3b2o\$4bo5b2o6bo\$9bo7b2o\$17bobo!`

It uses this new converter:

`x = 24, y = 24, rule = B3/S2323bo\$8bo12b2o\$6bobo13b2o\$7b2o2\$19bobo\$3b2o14b2o\$3bobo14bo\$4bobo\$5bobo\$6bobo8bobo\$7bobo7b2o\$8bobo7bo\$9bo2\$2bo\$obo\$b2o2\$3b3o\$5bo3b2o\$4bo5b2o6bo\$9bo7b2o\$17bobo!`

Goldtiger997

Posts: 524
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 16 in 16: Efficient 16-bit Synthesis Project

16.218 in 10G gives 16.217 in 15G:

`x = 127, y = 140, rule = B3/S2344bo\$43bo\$43b3o9\$30bobo\$10bo20b2o\$11bo19bo\$9b3o14bo\$27b2o\$26b2o\$8bo114bobo\$6bobo110b2obob2o\$7b2o110bob2o\$123b2obo\$31b2o90bob2o\$30bobo\$32bo4\$12b2o4b3o\$13b2o5bo\$12bo6bo2\$19bo\$19b2o\$18bobo16b2o\$37bobo\$37bo64\$30bobo\$o29b2o\$b2o28bo\$2o5\$bo\$2b2o\$b2o3\$bo\$2bo\$3o3\$23bobo93b2o2bobo\$19b2obob2o93bo2bob2o\$19bob2o98b2o\$23b2obo96b2obo\$23bob2o96bob2o16\$2bo\$2b2o\$bobo!`

Here are all 16-bit SLs costing at least 16G. There are currently 143:

`16.159     xs16_2egmd1e8            2116.774     xs16_69raa4z32           2116.1084    xs16_31ke12kozw11        2116.1682    xs16_8k9bkk8zw23         2116.1693    xs16_8k8aliczw23         2116.1753    xs16_695q4gozw23         2116.2096    xs16_wck5b8oz311         2116.228     xs16_178bp2sg            2016.712     xs16_3pc0qmzw23          2016.872     xs16_2lla8oz065          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        2016.131     xs16_660uhar             1916.230     xs16_178jd2ko            1916.801     xs16_08eharz321          1916.1684    xs16_4aab9k8zx32         1916.1694    xs16_4a5p6o8zx121        1916.1912    xs16_at16426z32          1916.1979    xs16_4ap30ga6zw121       1916.2050    xs16_6ik8a52z065         1916.2162    xs16_0at16426z32         1916.2200    xs16_06agc93z2521        1916.2307    xs16_6ik8a52z641         1916.2316    xs16_0at16413z32         1916.155     xs16_3pabp46             1816.600     xs16_6421344og84c        1816.665     xs16_699mkiczx1          1816.848     xs16_ca9b8oz0252         1816.914     xs16_8kkja952zx1         1816.926     xs16_3iajc4gozw1         1816.1107    xs16_02egdbz2521         1816.1130    xs16_oe12koz01ac         1816.1558    xs16_3loz1226io          1816.1711    xs16_c8idik8z023         1816.1757    xs16_g8idik8z123         1816.1790    xs16_178cia4z0321        1816.1911    xs16_69q3213z32          1816.1990    xs16_8e1tazx1252         1816.1995    xs16_cik8a52z065         1816.2201    xs16_0ggml96z641         1816.2447    xs16_0g8it248cz23        1816.2480    xs16_3iaczw1139c         1816.15      xs16_178c1f84c           1716.227     xs16_5b8r5426            1716.265     xs16_259m861ac           1716.380     xs16_4a40vh248c          1716.616     xs16_i5pajoz11           1716.640     xs16_c9bkkozw32          1716.668     xs16_gbq1daz121          1716.716     xs16_3pmk46zx23          1716.748     xs16_39ege2z321          1716.799     xs16_c8al56z311          1716.803     xs16_c9bk46z311          1716.843     xs16_4a9liczx56          1716.875     xs16_4a5pa4z2521         1716.1064    xs16_39m88cz6221         1716.1073    xs16_3lkaa4z641          1716.1097    xs16_ck0ol3z643          1716.1276    xs16_3iakgozw1ac         1716.1373    xs16_32q4goz4a43         1716.1398    xs16_g88c93zc952         1716.1685    xs16_c48n98czx23         1716.1715    xs16_64p784czw23         1716.1722    xs16_4aq32acz032         1716.1758    xs16_4a4o796zw121        1716.1847    xs16_39c8a52z033         1716.1867    xs16_069q453z311         1716.1871    xs16_5bo8ge2z32          1716.1882    xs16_259m453zx23         1716.1905    xs16_8u16853z32          1716.1991    xs16_8e1qbzx1252         1716.2014    xs16_25a8kk8z0253        1716.2045    xs16_25ao8ge2z032        1716.2132    xs16_0g8it2sgz23         1716.2356    xs16_25icggozx1ac        1716.2467    xs16_0kc3213z34a4        1716.2555    xs16_4a9jzxpia4          1716.3163    xs16_wo443123zbd         1716.3164    xs16_wo443146zbd         1716.104     xs16_0j5ozj4pz11         1616.115     xs16_0ol3z0mdz32         1616.243     xs16_2egu16426           1616.300     xs16_9fg4czbd            1616.302     xs16_5b8o642ac           1616.350     xs16_312461tic           1616.360     xs16_2egu16413           1616.593     xs16_3123c48gka4         1616.724     xs16_j5o64koz11          1616.762     xs16_jhke1e8z1           1616.771     xs16_69qb8oz32           1616.772     xs16_3h4e1daz011         1616.810     xs16_ca9la4z311          1616.822     xs16_8ehikozw56          1616.836     xs16_4aajkczx56          1616.838     xs16_ci9b8ozw56          1616.840     xs16_c8idiczw56          1616.856     xs16_kc32acz1252         1616.953     xs16_0cil56z6221         1616.995     xs16_0raik8z643          1616.1068    xs16_3lo0kcz6421         1616.1080    xs16_3lo0kcz3421         1616.1085    xs16_3h4e12koz011        1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1581    xs16_8o6413zrm           1616.1583    xs16_4a9jzxha6zx11       1616.1675    xs16_xj96z0mdz32         1616.1710    xs16_4a9bk46zx32         1616.1717    xs16_4aajk46zx121        1616.1720    xs16_4a4o79ozx121        1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1796    xs16_0bt06ioz32          1616.1856    xs16_39u06a4z32          1616.1857    xs16_39u0652z32          1616.1864    xs16_31ke1e8z032         1616.1929    xs16_0g5r8b5z121         1616.1959    xs16_4ai31e8zx56         1616.1994    xs16_0g9fgka4z121        1616.2018    xs16_25a8c826zw33        1616.2025    xs16_069q48cz2521        1616.2028    xs16_25ao48cz2521        1616.2029    xs16_25ao4a4z2521        1616.2030    xs16_0i5q8a52z121        1616.2060    xs16_69akg4czx56         1616.2124    xs16_0g8jd2koz23         1616.2129    xs16_0g8jt246z23         1616.2190    xs16_032q4goz6413        1616.2204    xs16_0gilla4z641         1616.2214    xs16_0mq0c93z641         1616.2219    xs16_0oe12koz643         1616.2305    xs16_6413ia4z6421        1616.2317    xs16_cik8a52z641         1616.2322    xs16_raak8zx1252         1616.2323    xs16_ra248goz056         1616.2445    xs16_ciligzx254c         1616.2549    xs16_g4c3213zdb          1616.2630    xs16_31e8gzxo9a6         1616.2781    xs16_wj9c826z6221        1616.3032    xs16_1784ozx342sg        16`
chris_c

Posts: 894
Joined: June 28th, 2014, 7:15 am

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