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

16.349 in 15G:

`x = 162, y = 134, rule = B3/S2347bo\$48bo\$46b3o9\$71bo85b2o\$69b2o86bo2b2o\$70b2o86b2obo\$159bo\$159bo\$157b2o\$157bo\$47b2o110bo\$48b2o108b2o\$47bo\$139b2o\$42b3o94b2o16b2ob2o\$44bo112b2ob2o\$43bo3\$30bo\$30b2o26b2o\$29bobo19b3o4bobo\$51bo6bo\$23b2o27bo\$24b2o\$23bo5\$64b3o\$64bo\$65bo2\$37b3o\$39bo30b3o\$38bo31bo\$65b3o3bo\$65bo\$66bo30\$2o\$b2o\$o32\$57b2o98b2o\$57bo2b2o95bo2b2o\$58b2obo96b2obo\$59bo99bo\$59bo99bo\$57b2o98b2o\$57bo99bo\$59bo99bo\$58b2o98b2o2\$39b2o\$39b2o16b2ob2o\$57b2ob2o5\$33b2o\$32bobo\$34bo\$64b2o\$64bobo\$64bo!`
chris_c

Posts: 868
Joined: June 28th, 2014, 7:15 am

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

chris_c wrote:16.349 in 15G:

`RLE`

I used the other soup for ten gliders:
`x = 28, y = 32, rule = B3/S2319bobo\$14bo5b2o\$7bo7b2o3bo\$8bo5b2o10bo\$6b3o16bo\$25b3o3\$21bo\$20b2o\$7b2o11bobo\$6bobo\$8bo4b2o\$14b2o\$13bo2\$17b2o\$16b2o\$b2o15bo\$obo\$2bo9\$26b2o\$25b2o\$27bo!`
I Like My Heisenburps! (and others)

Extrementhusiast

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Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 28G)

Extrementhusiast wrote:I used the other soup for ten gliders:...

Nicely done. I had tried that soup, but the only syntheses for the pattern in the top-right that I found interfered with the formation of the pi.

16.731 in 12 gliders (perhaps improvable through constellations, although I could not find any):

`x = 119, y = 53, rule = B3/S2348bo\$46bobo\$47b2o12\$117bo\$116bo\$116b3o11\$11bo3bo\$9bobo2bo\$2bo7b2o2b3o22b3o37b3o\$obo\$b2o\$4bo111b2o\$4bobo26b2o38b2o41bo\$4b2o26bo2bo36bo2bo37b2obo\$33b2o38b2o37bo2bo\$112b2o\$114b4o\$45b3o37b3o26bo2bo\$17bo\$16bo26bo5bo33bo5bo\$16b3o24bo5bo13b2o18bo5bo\$43bo5bo12bobo18bo5bo\$20bo43bo\$19b2o24b3o37b3o\$19bobo54b2o\$76bobo\$71b2o3bo\$70bobo\$72bo\$74b2o\$74bobo\$74bo!`

16.786 in 9 gliders:

`x = 50, y = 42, rule = B3/S2349bo\$47b2o\$48b2o10\$bo\$2b2o17bo\$b2o16b2o\$20b2o\$16bo\$14b2o\$15b2o3\$27bo\$26bo\$26b3o\$20bo\$19bo\$19b3o3\$19b3o\$19bo\$20bo5\$3b3o\$3bo\$4bo\$3o\$2bo\$bo!`

Now all 16-bit still-lifes can be synthesised in under 28 gliders.
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

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Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 30G)

Goldtiger997 wrote:...

16.778 in 10 gliders:

`x = 44, y = 58, rule = B3/S2315bo\$16b2o\$15b2o22\$35bobo\$36b2o\$36bo2\$42b2o\$32bo8b2o\$22b2o7b2o10bo\$23b2o6bobo\$22bo4\$37bobo\$37b2o\$38bo\$31b2o\$30bobo6b2o\$32bo5bobo\$40bo2\$3o\$2bo\$bo9\$6b2o\$7b2o\$6bo!`

...

This is a mistake. 2 glider (marked on the diagram you will see) interact before:
`x = 44, y = 58, rule = LifeHistory15.A\$16.2A\$15.2A22\$35.A.A\$36.2A\$36.A2\$42.2E\$32.A8.2E\$22.2A7.2A10.E\$23.2A6.A.A\$22.A4\$37.E.E\$37.2E\$38.E\$31.2A\$30.A.A6.2A\$32.A5.A.A\$40.A2\$3A\$2.A\$.A9\$6.2A\$7.2A\$6.A!`

To fix it replace the right glider for two (16.778 in 11G):
`x = 62, y = 62, rule = B3/S2315bo\$16b2o\$15b2o22\$35bobo\$36b2o\$36bo\$42bo\$43b2o\$42b2o2\$45bo\$44bo\$36bo7b3o\$22b2o11b2o\$23b2o10bobo\$22bo18bobo\$41b2o\$42bo5\$31b2o\$30bobo6b2o\$32bo5bobo\$40bo\$57b2o\$3o55bo\$2bo55bobo\$bo54b2obobo\$55bo2bo2bo\$55b2o2b2o7\$6b2o\$7b2o\$6bo!`

Bob Shemyakin
BobShemyakin

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Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 28G)

Goldtiger997 wrote:16.731 in 12 gliders (perhaps improvable through constellations, although I could not find any):

`x = 119, y = 53, rule = B3/S2348bo\$46bobo\$47b2o12\$117bo\$116bo\$116b3o11\$11bo3bo\$9bobo2bo\$2bo7b2o2b3o22b3o37b3o\$obo\$b2o\$4bo111b2o\$4bobo26b2o38b2o41bo\$4b2o26bo2bo36bo2bo37b2obo\$33b2o38b2o37bo2bo\$112b2o\$114b4o\$45b3o37b3o26bo2bo\$17bo\$16bo26bo5bo33bo5bo\$16b3o24bo5bo13b2o18bo5bo\$43bo5bo12bobo18bo5bo\$20bo43bo\$19b2o24b3o37b3o\$19bobo54b2o\$76bobo\$71b2o3bo\$70bobo\$72bo\$74b2o\$74bobo\$74bo!`

Beehive + blinker = 3 gliders : ( 16.731 in 11 )
`x = 118, y = 53, rule = B3/S2347bo\$45bobo\$46b2o12\$116bo\$115bo\$16bo98b3o\$15bo\$15b3o10\$5bo\$5bobo30b3o37b3o\$obo2b2o\$b2o\$bo113b2o\$32b2o38b2o41bo\$31bo2bo36bo2bo37b2obo\$32b2o38b2o37bo2bo\$111b2o\$113b4o\$44b3o37b3o26bo2bo\$16bo\$15bo26bo5bo33bo5bo\$15b3o24bo5bo13b2o18bo5bo\$42bo5bo12bobo18bo5bo\$19bo43bo\$18b2o24b3o37b3o\$18bobo54b2o\$75bobo\$70b2o3bo\$69bobo\$71bo\$73b2o\$73bobo\$73bo!`

Goldtiger997 wrote:16.786 in 9 gliders:

`x = 50, y = 42, rule = B3/S2349bo\$47b2o\$48b2o10\$bo\$2b2o17bo\$b2o16b2o\$20b2o\$16bo\$14b2o\$15b2o3\$27bo\$26bo\$26b3o\$20bo\$19bo\$19b3o3\$19b3o\$19bo\$20bo5\$3b3o\$3bo\$4bo\$3o\$2bo\$bo!`

Block -> glider : ( 16.786 in 8 )
`x = 62, y = 52, rule = B3/S2361bo\$59b2o\$60b2o10\$13bo\$14b2o17bo\$13b2o16b2o\$32b2o\$28bo\$26b2o\$27b2o3\$39bo\$38bo\$38b3o\$32bo\$31bo\$31b3o3\$31b3o\$31bo\$32bo18\$b2o\$obo\$2bo!`

BobShemyakin wrote:
Goldtiger997 wrote:...

16.778 in 10 gliders:

`x = 44, y = 58, rule = B3/S2315bo\$16b2o\$15b2o22\$35bobo\$36b2o\$36bo2\$42b2o\$32bo8b2o\$22b2o7b2o10bo\$23b2o6bobo\$22bo4\$37bobo\$37b2o\$38bo\$31b2o\$30bobo6b2o\$32bo5bobo\$40bo2\$3o\$2bo\$bo9\$6b2o\$7b2o\$6bo!`

...

This is a mistake. 2 glider (marked on the diagram you will see) interact before:
`x = 44, y = 58, rule = LifeHistory15.A\$16.2A\$15.2A22\$35.A.A\$36.2A\$36.A2\$42.2E\$32.A8.2E\$22.2A7.2A10.E\$23.2A6.A.A\$22.A4\$37.E.E\$37.2E\$38.E\$31.2A\$30.A.A6.2A\$32.A5.A.A\$40.A2\$3A\$2.A\$.A9\$6.2A\$7.2A\$6.A!`

To fix it replace the right glider for two (16.778 in 11G):
`x = 62, y = 62, rule = B3/S2315bo\$16b2o\$15b2o22\$35bobo\$36b2o\$36bo\$42bo\$43b2o\$42b2o2\$45bo\$44bo\$36bo7b3o\$22b2o11b2o\$23b2o10bobo\$22bo18bobo\$41b2o\$42bo5\$31b2o\$30bobo6b2o\$32bo5bobo\$40bo\$57b2o\$3o55bo\$2bo55bobo\$bo54b2obobo\$55bo2bo2bo\$55b2o2b2o7\$6b2o\$7b2o\$6bo!`

Bob Shemyakin

Only 2G-loaf timing : ( 16.778 in 10 )
`x = 45, y = 58, rule = B3/S2315bo\$16b2o\$15b2o21\$36bo\$37bo\$35b3o3\$42b2o\$32bo9bobo\$22b2o7b2o9bo\$23b2o6bobo\$22bo4\$37bobo\$37b2o\$38bo\$31b2o\$30bobo6b2o\$32bo5bobo\$40bo2\$3o\$2bo\$bo9\$6b2o\$7b2o\$6bo!`
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).
AbhpzTa

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

16.3227 in 9 gliders:

`x = 51, y = 29, rule = B3/S2319bo\$20bo\$18b3o7bo\$9bobo16bobo\$10b2o16b2o\$10bo2\$15bo\$16bo\$14b3o\$18b2o\$18bobo\$18bo\$28bo\$26b2o\$27b2o3\$49bo\$48b2o\$48bobo5\$26bo\$bo23b2o\$b2o22bobo\$obo!`

16.1979 looks hard. What hook flipping components are known?

AbhpzTa wrote:
Goldtiger997 wrote:16.731 in 12 gliders (perhaps improvable through constellations, although I could not find any):...

Beehive + blinker = 3 gliders : ( 16.731 in 11 )
`x = 118, y = 53, rule = B3/S2347bo\$45bobo\$46b2o12\$116bo\$115bo\$16bo98b3o\$15bo\$15b3o10\$5bo\$5bobo30b3o37b3o\$obo2b2o\$b2o\$bo113b2o\$32b2o38b2o41bo\$31bo2bo36bo2bo37b2obo\$32b2o38b2o37bo2bo\$111b2o\$113b4o\$44b3o37b3o26bo2bo\$16bo\$15bo26bo5bo33bo5bo\$15b3o24bo5bo13b2o18bo5bo\$42bo5bo12bobo18bo5bo\$19bo43bo\$18b2o24b3o37b3o\$18bobo54b2o\$75bobo\$70b2o3bo\$69bobo\$71bo\$73b2o\$73bobo\$73bo!`

Nice! I am wondering what method you use to find 3-glider collisions that make constellations? I use a really slow method of running gencols and a script of chris_c's to find most of the 3-glider collisions that have a certain final population, and then run dvgrn's find.py script to find the appropriate constellation.

Also, happy birthday (for yesterday)!
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

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

Good 16.834 components:
`x = 56, y = 13, rule = B3/S2311bobo19b2o\$10bo22b2o\$10bo3bo\$13b2o\$10b2o\$9bo\$9bobo\$9b2o24b2o10bo\$bo34bo10bo\$b2o31b3o10bo\$ob2o50b2o\$obo50bobo\$2o52bo!`

yootaa

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Location: Japan

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

yootaa wrote:Good 16.834 components:
`rle`

10G:
`x = 60, y = 39, rule = B3/S23o\$b2o\$2o2\$21bo\$22bo\$20b3o5\$22bo\$23bo\$21b3o10\$35bo\$26bo7bo\$27bo6b3o11bo8bobo\$25b3o19bo9b2o\$47b3o8bo\$28b3o\$30bo\$29bo16b2o\$45bobo\$47bo4\$43b2o\$42bobo\$44bo!`
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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

I wrote:Now all 16-bit still-lifes can be synthesised in under 28 gliders.

`x = 51, y = 30, rule = B3/S2321bo28bo\$19b2o27b2o\$9bo10b2o27b2o\$10b2o\$9b2o2\$39bo\$39bobo\$18bobo18b2o\$17bo\$17bo3bo\$5b2o11b4o\$6b2o13bo\$5bo3\$45bo\$29bo13b2o\$29b4o11b2o\$29bo3bo\$33bo\$10b2o18bobo\$9bobo\$11bo2\$40b2o\$39b2o\$2o27b2o10bo\$b2o27b2o\$o28bo!`

16.628 in 8 gliders:

`x = 35, y = 23, rule = B3/S2321bobo\$21b2o\$22bo2\$23bo\$24bo\$22b3o4\$24b3o\$24bo\$20b2o3bo\$21b2o\$20bo11bo\$32bobo\$32b2o\$29b2o\$29bobo\$29bo\$2o18bo\$b2o16b2o\$o18bobo!`

Now all 16-bit still-lifes can be synthesised in under 28 gliders.

Only one 16-bit still-life left taking 27 gliders (16.1979):

`x = 8, y = 7, rule = B3/S232b2o\$bobo2b2o\$o6bo\$b2o3bo\$2bo2bo\$2bobo\$3bo!`
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

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Location: 11.329903°N 142.199305°E

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

Goldtiger997 wrote:Only one 16-bit still-life left taking 27 gliders (16.1979)

It can be done in 19, but I doubt that this method could give a sub-16 synthesis:
`x = 283, y = 32, rule = B3/S23250bo\$251bo\$249b3o\$9bo\$7b2o\$8b2o\$256bobo\$2bo253b2o\$obo246bobo5bo\$b2o6bobo238b2o\$9b2o239bo\$10bo2\$37b2o28b2o28b2o28b2o28b2o28b2o6bo21b2o28b2o28b2o\$36bobo27bobo27bobo27bobo5bo21bobo27bobo5bo21bobo27bobo27bobo2b2o\$35bo29bo7bo21bo29bo7bo21bo29bo8b3o18bo6bo22bo6bo22bo6bo\$17b3o16b2o28b2o4bo23b2o28b2o5b3o20b2o3bo24b2o3bo24b2o3bobo22b2o3bobo22b2o3bo\$13bo3bo19bo29bo4b3o22bo2bo26bo2bo26bo2bobo24bo2bobo4b2o18bo2bobo24bo2bobo24bo2bo\$3bo10b2o2bo18bobo27bobo27bobobo25bobobo4b2o19bobobo25bobobo5bobo17bobobo25bobobo25bobo\$3b2o8b2o23bobo27bobo4b2o21bobo27bobo5bobo19bobo27bobo6bo20bobo27bobo27bo\$2bobo3b2o29bo29bo5bobo21bo29bo6bo22bo29bo29bo29bo6bobo\$9b2o64bo180b2o\$8bo248bo2\$255b2o\$254b2o\$256bo3\$261b2o\$260b2o\$262bo!`
-Matthias Merzenich
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Re: 16 in 16: Efficient 16-bit Synthesis Project

I added all of those so now we are below 27G for all 16-bit still lifes. Looking ahead at a few of the expensive but rare still life shows that this 16G snake -> hook-with-tail sequence is used in quite a few (16.930, 16.1064, 16.1077, 16.1139 for example):

`x = 50, y = 91, rule = Life19bobo\$19b2o\$15bo4bo\$13b2o\$10b2o2b2o3bo\$9bobo6b2o26bo\$11bo6bobo23b3o\$14b2o27bo\$14bo29bo\$15bo29bo\$14b2o28b2o13\$19bo3bo\$17b2o3bo\$18b2o2b3o2\$2bo\$obo\$b2o4\$30bo\$29bo\$16bo12b3o13bo2b2o\$14b3o27bobo2bo\$13bo18b2o10bob3o\$14bo17bobo10bo\$15bo16bo13bo\$14b2o29b2o3\$28b2o\$27b2o\$29bo7\$6bobo\$7b2o\$7bo\$19bo5bo\$18bo6bobo\$18b3o4b2o3\$6bo\$7bo\$5b3o40b2o\$48b2o\$3b2o\$2bobo9bo2b2o\$4bo8bobo2bo28bo\$13bob3o27b3o\$14bo29bo\$15bo29bo\$14b2o28b2o5\$23bo\$23bobo\$23b2o5\$18b2o\$18b2o3\$17bo29bo\$15b3o27b3o\$14bo29bo\$15bo29bo\$14b2o28b2o!`

I wonder if there is a cheaper way? Anyway, here is the list from 20-26G:

`16.1077    xs16_69m88cz6221         2616.1691    xs16_4a9l6o8zx121        2616.1703    xs16_4a9la8ozx121        2616.623     xs16_o5r8jdz01           2516.828     xs16_4alhe8z0641         2516.930     xs16_3iaj21e8zw1         2516.1139    xs16_kq23z124871         2516.1398    xs16_g88c93zc952         2516.706     xs16_39s0qmz023          2416.713     xs16_o8bap3z23           2416.1034    xs16_3lkaa4z065          2416.1064    xs16_39m88cz6221         2416.1323    xs16_031e8gzc9311        2416.1880    xs16_259q453z032         2416.2295    xs16_0g8go8brz23         2416.353     xs16_321fgc453           2316.621     xs16_g5r8jdz11           2316.829     xs16_0md1e8z1226         2316.1702    xs16_4a5p68ozx121        2316.1740    xs16_69acga6zx32         2316.825     xs16_4alhe8zw65          2216.1846    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          2016.1073    xs16_3lkaa4z641          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        20`

EDIT: 16.1323 has soups and has a reasonable conversion to 16.1398. I might look through them later:

`x = 25, y = 18, rule = B3/S2322bo\$7bo14bobo\$5bobo14b2o\$6b2o2\$bo\$2bo\$3o\$6bo\$7bo4b2o\$5b3o4bobo\$14bo5b3o\$5bo8b2o4bo\$5b2o9bo4bo\$4bobo5b4o\$13bo\$11bo\$11b2o!`
chris_c

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

16.1703 in 10 gliders:
`x = 65, y = 80, rule = B3/S2362bo\$62bobo\$2bo59b2o\$obo\$b2o16\$30bo\$28bobo\$29b2o2\$51bo\$50bo\$50b3o10\$36bo\$34bobo\$35b2o7bo\$42b2o\$29b2o12b2o\$30b2o\$29bo3\$53b3o\$53bo\$54bo5\$51bo\$50b2o\$50bobo23\$16b2o\$15bobo\$17bo!`

yootaa

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

chris_c wrote:EDIT: 16.1323 has soups and has a reasonable conversion to 16.1398. I might look through them later:

`RLE`

Reduced that converter by one:
`x = 16, y = 15, rule = B3/S2315bo\$4bo8b2o\$5bo8b2o\$3b3o\$13bo\$12b2o\$4b2ob2o3bobo\$3bobobobo\$4bo4bo\$9b2o\$3o8bo\$2bo4b4o\$bo6bo\$6bo\$6b2o!`
I Like My Heisenburps! (and others)

Extrementhusiast

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

chris_c wrote:Looking ahead at a few of the expensive but rare still life shows that this 16G snake -> hook-with-tail sequence is used in quite a few (16.930, 16.1064, 16.1077, 16.1139 for example):

How, exactly, are these components used in relation to the still lifes?
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Re: 16 in 16: Efficient 16-bit Synthesis Project

16.1077 in fourteen gliders:
`x = 80, y = 20, rule = B3/S2349bo\$47b2o\$44bo3b2o\$45b2o\$44b2o2\$18bo6b2o26b2o17b2o3b2o\$18bobo3bo2bo18bo5bo2bo17bo2bo2bo\$18b2o3bob2o18bobo3bob2o18bobob2o\$22bobo21b2o2bobo21bobo\$obobo10b3o4bobo25bobo23bo\$23bo22b2o3bo3bo20b2o\$18b2o19b2o4bobo7bobo\$18bobo19b2o4bo8b2o\$18bo20bo\$44b2o\$43bobo\$45bo9b2o\$56b2o\$55bo!`
I Like My Heisenburps! (and others)

Extrementhusiast

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

Despite its large number of soups, 16.1691 does not have many good predecessors. Here are some:

`x = 45, y = 31, rule = B3/S232o\$2o7\$2b3o\$b2ob2o\$b2ob2o31bobo\$3bo33bobo\$38bob2o\$3o37b2o\$3o\$obo\$2bo\$2bo\$37b3o\$39bo\$13b2o21b3o4b2o\$13b2o16b2o3bo6b2o\$31b2o5\$2bo3b2o24bo3b2o\$bobobo2bo22bobobo2bo\$2b2obobo24b2obobo\$6bo29bo!`
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 467
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.2295 in 13 griders:
`x = 86, y = 27, rule = B3/S2344bo8bo\$45b2o7bo\$44b2o6b3o3\$9bo\$8bo\$8b3o2\$34b2o15bobo14b2o14b2o\$11bo22b2o16b2o2bobo9b2o14b2o\$11bobo38bo3b2o\$11b2o19b4o21bo5b2ob4o10bob4o\$28b2o2bo2bo27b2obo2bo9bob2o2bo\$bo25bobo49bo\$b2o26bo48b2o\$obo\$30b2o\$6bo23bobo\$5b2o23bo\$5bobo50b3o\$60bo\$59bo3b2o\$63bobo\$63bo9b2o\$72b2o\$74bo!`

EDIT: 16.1880 in 8 griders:
`x = 33, y = 24, rule = B3/S2322bo\$23bo\$21b3o\$25bo\$25bobo\$8bo9bo6b2o\$6bobo10b2o\$7b2o9b2o3\$31bo\$30bo\$30b3o\$18b2o\$17bobo\$19bo\$26b3o\$26bo\$27bo3\$b2o\$obo\$2bo!`

yootaa

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

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

Extrementhusiast wrote:
chris_c wrote:EDIT: 16.1323 has soups and has a reasonable conversion to 16.1398. I might look through them later:

Reduced that converter by one:

Thanks. Immediately that improves 16.213 from 15G to 14G and gives one more glider of leeway for 16.1398 if anyone can make 16.1323 well enough (I couldn't).

Goldtiger997 wrote:Despite its large number of soups, 16.1691 does not have many good predecessors. Here are some.

16.1691 in 15G:

`x = 37, y = 41, rule = Life6bo\$7b2o\$6b2o3\$12bo\$bo11bo\$2bo8b3o\$3o18bo\$20bo\$20b3o\$6bo\$7bo\$5b3o2bo\$11b2o3bo\$10b2o5b2o10bo\$16b2o10bo\$28b3o3\$26b2o\$26bobo\$14bo11bo\$3b2o9b2o\$2bobo8bobo\$4bo4\$12b3o\$14bo\$13bo\$2bo18b3o\$2b2o17bo\$bobo18bo4\$35bo\$34b2o\$34bobo!`

chris_c wrote:Looking ahead at a few of the expensive but rare still life shows that this 16G snake -> hook-with-tail sequence is used in quite a few (16.930, 16.1064, 16.1077, 16.1139 for example):

How, exactly, are these components used in relation to the still lifes?

It would be the following sequences, going downwards through time:

`x = 36, y = 68, rule = Lifeb2o12b2o14b2o\$bo13bo15bo\$2bo13bo15bo\$b2o2bo9b2o12b3obo\$2bobobo8bo3b2o8bo2bo\$2bo2bo10bo2bo12bobo\$b2o14bobo13b2o\$18bo11\$3bo13bo15bo\$b3o11b3o13b3o\$o13bo15bo\$bo13bo15bo\$2bo13bo15bo\$b2o2bo9b2o12b3obo\$2bobobo8bo3b2o8bo2bo\$2bo2bo10bo2bo12bobo\$b2o14bobo13b2o\$18bo11\$bo2b2o9bo2b2o11bo2b2o\$obo2bo8bobo2bo10bobo2bo\$ob3o9bob3o11bob3o\$bo13bo15bo\$2bo13bo15bo\$b2o2bo9b2o12b3obo\$2bobobo8bo3b2o8bo2bo\$2bo2bo10bo2bo12bobo\$b2o14bobo13b2o\$18bo12\$4bo13bo15bo\$2b3o11b3o13b3o\$bo13bo15bo\$2bo13bo15bo\$b2o2bo9b2o12b3obo\$2bobobo8bo3b2o8bo2bo\$2bo2bo10bo2bo12bobo\$b2o14bobo13b2o\$18bo!`

yootaa wrote:16.2295 in 13 griders:

The converter you use here also improves 4 other still lifes. Most notably it improves 16.558 from 17G to 15G:

`x = 148, y = 339, rule = Life51bobo\$41bo9b2o\$41bobo8bo\$41b2o\$55bobo\$55b2o87b2o\$56bo84bobo2bo\$141b2o2bobo\$39b2o105bo\$39bobo\$39bo2\$54b2o\$54bobo\$46b2o6bo\$46bobo\$46bo84\$34bo\$35bo\$33b3o3\$44b2o92bo5b2o\$41bobo2bo90bobobobo2bo\$41b2o2bobo90b2ob2o2bobo\$46bo99bo92\$28bo\$29bo\$27b3o3\$38bo5b2o98b2o\$37bobobobo2bo91b2obobo2bo\$38b2ob2o2bobo90b2ob2o2bobo\$46bo99bo66\$67bo\$66bo\$58bo7b3o\$56b2o\$57b2o\$14bobo\$15b2o\$15bo23\$137b2o\$44b2o92bo5b2o\$38b2obobo2bo91bob2obo2bo\$38b2ob2o2bobo91bob2o2bobo\$46bo99bo18\$50b2o\$8b2o40bobo\$7bobo40bo\$9bo6\$9bo\$3o6b2o\$2bo5bobo\$bo!`

Now the maximum cost is 25G:

`16.623     xs16_o5r8jdz01           2516.828     xs16_4alhe8z0641         2516.930     xs16_3iaj21e8zw1         2516.1139    xs16_kq23z124871         2516.1398    xs16_g88c93zc952         2516.706     xs16_39s0qmz023          2416.713     xs16_o8bap3z23           2416.1034    xs16_3lkaa4z065          2416.1323    xs16_031e8gzc9311        2416.353     xs16_321fgc453           2316.621     xs16_g5r8jdz11           2316.829     xs16_0md1e8z1226         2316.1702    xs16_4a5p68ozx121        2316.1740    xs16_69acga6zx32         2316.825     xs16_4alhe8zw65          2216.1846    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          2016.1073    xs16_3lkaa4z641          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        20`

EDIT: We would need a 5G synthesis of 12.103 to solve 16.1064 in 15G using Extrementhusiast's method for 16.1077. I wonder how much brute forcing has been done on 5G syntheses?

`x = 16, y = 6, rule = B3/S234b2o\$2bo2bo\$bob2o\$obo8bobobo\$obo\$bo!`
chris_c

Posts: 868
Joined: June 28th, 2014, 7:15 am

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

chris_c wrote:EDIT: We would need a 5G synthesis of 12.103 to solve 16.1064 in 15G using Extrementhusiast's method for 16.1077. I wonder how much brute forcing has been done on 5G syntheses?

As far as I know, Bob Shemyakin's recent survey has been the most ambitious effort along these lines, and it could only be declared "complete" for 4-glider collisions (and it wasn't really). Running his SpaceBattle search utility with a wide enough variety of targets and angles of attack might turn up something, but that's always going to be just random sampling, luck of the draw.

It's probably about time to attempt a more systematic brute-force approach, exhaustive through 3 gliders, then choosing promising branches to explore from there.

dvgrn
Moderator

Posts: 5080
Joined: May 17th, 2009, 11:00 pm

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

dvgrn wrote:It's probably about time to attempt a more systematic brute-force approach, exhaustive through 3 gliders, then choosing promising branches to explore from there.

Yeah I have thought about that. I would love to see a recursive glider synthesis search program that works as follows:

-Keep track of the active reaction and then copy a new glider into the pattern at the latest moment that is consistent with that glider having come from infinity.

-Prune the search tree if the active reaction gets bigger than a certain bounding box.

-Bonus points if the program is clever enough to realise that the active reaction has settled down to an oscillator or still life so that trying arbitrarily distant gliders is futile.

-Bonus points if the program is clever enough to recognise interesting objects that appear in the soup for a limited number of ticks before being destroyed.

EDIT:Oh there's something I forgot that occurred to me recently. The above method only catches cases where every new glider added interacts with the main part of the pattern. It would not catch reactions like below where both gliders would miss the block on their own:

`x = 12, y = 6, rule = B3/S235bo4b2o\$6bo3b2o\$4b3o\$3o\$2bo\$bo!`

Since 2-glider interactions are relatively easy to enumerate it should be technically possible to recursively add a 2-glider interaction to an already active pattern. This should do a fairly good job up to 5 gliders in total but would start missing stuff at 6G when 3G-with-3G interactions start to appear. /EDIT

Just so this post is not entirely fantasy here are a few interesting "Top 10" lists:

Top 10 most common SLs with 16 bits or less and having no synthesis in 3 gliders:
`12.3       xs12_g8o653z11                           4   3120615505106.4        xs6_39c                                  4   149209024398.3        xs8_35ac                                 4   58965270539.4        xs9_31ego                                4   54274917558.1        xs8_3pm                                  4   468109419910.24      xs10_g8o652z01                           4   45856394726.1        xs6_bd                                   4   410039695614.36      xs14_g88b96z123                          4   40969753569.5        xs9_178ko                                4   196057368611.30      xs11_g8o652z11                           4   1621211575`

Top 10 most common SLs with 16 bits or less and having no synthesis in 4 gliders:
`13.154     xs13_g88m96z121                          5   5082180310.19      xs10_3542ac                              5   4098949113.27      xs13_4a960ui                             5   3205801116.10      xs16_259e0e952                           5   2791139015.472     xs15_3lk453z121                          5   1930854313.10      xs13_0g8o653z121                         5   1889751312.73      xs12_0ggm96z32                           5   1538243210.1       xs10_g8ka52z01                           5   1491521715.8       xs15_259e0e96                            5   1345406111.12      xs11_g0s256z11                           5   12333761`

Top 10 most common SLs with 16 bits or less and having no synthesis in 5 gliders:
`11.45      xs11_3586246                             6   693280310.3       xs10_4al96                               6   654299716.617     xs16_j1u0uiz11                           6   390708212.8       xs12_0g8o652z23                          6   357776516.728     xs16_j1u06acz11                          6   339463311.41      xs11_32132ac                             6   306668414.9       xs14_g88q552z121                         6   282970911.21      xs11_69jzx56                             6   269188414.280     xs14_0g8o653z321                         6   259211314.12      xs14_g88m552z121                         7   2324684`

Top 10 most common SLs with 16 bits or less and having no synthesis in 6 gliders:
`14.12      xs14_g88m552z121                         7   232468415.969     xs15_0ggca96z3421                        7   155469911.20      xs11_3542156                             7   150908715.1051    xs15_69ak8zx1256                         8   138197115.625     xs15_0ggmp3z346                          7   116028915.968     xs15_0g8ka96z3421                        7   106973412.55      xs12_3542ako                             7   81215414.16      xs14_0gbaa4z343                          7   74944316.736     xs16_2ege96z321                          10  71562214.587     xs14_08u1acz321                          10  695637`

For example the still life 12.103 that I mentioned previously is the 120th most common still life that does not have any known synthesis in 5 gliders.
chris_c

Posts: 868
Joined: June 28th, 2014, 7:15 am

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

Just started a new thread on enumerating three-glider collisions, as a starting point for a (maybe somewhat) more exhaustive 5G search... or at least a better prebuilt database of small constellations.

I don't think I'll have time to work on any search code for the next few months at least -- too many other things on my To-Do list right now, and I'm trying not to have it be a LIFO stack...! But I do want to pick this topic up again eventually, if no one else gets to it first.

Maybe let's move any future progress on collision enumeration to that thread, to avoid polluting this thread any further...?

chris_c wrote:-Bonus points if the program is clever enough to realise that the active reaction has settled down to an oscillator or still life so that trying arbitrarily distant gliders is futile.

-Bonus points if the program is clever enough to recognise interesting objects that appear in the soup for a limited number of ticks before being destroyed.

The first item I think happens automatically if we keep a list of hashes of each "final initial" state of the 2G collision plus glider #3, at the last generation before they interact. Once we've backed off the T=0 position of glider #3 far enough that the new pre-collision picture is already in the hash table, we can stop investigating that glider lane and move to the next one.

... Unless there's some kind of spark that curls around behind the glider but dies before the glider reaches the stabilized constellation. Bother. To be safe, maybe we have to keep backing the glider off for some number of extra ticks proportional to the size of the 2G collision's total reaction envelope...? Or we could track cells lining the incoming glider's lane and move on to the next lane only if the hash value is in the table AND those lane cells are all undisturbed.

The interesting-objects-for-a-limited-time bonus points are going to be a lot harder to get, I think. For stabilized ash we have code lying around, like recognizer.py and the various apgsearches. It's going to slow things down a lot if we have to hunt through an active reaction every tick, or even every ten ticks or hundred ticks, looking for interesting still-life islands.

We'd also want to look for much more interesting things than still lifes -- things like a temporary loafer, which there really might be one of, out there somewhere unnoticed in an already-censused Catagolue soup. It's so much easier to run through a pattern and recognize-and-remove everything as we get to it, than to have to check every cell against a huge list of interesting stuff, and end up ignoring most cells because they're still active but not recognizable yet.

chris_c wrote:EDIT:Oh there's something I forgot that occurred to me recently. The above method only catches cases where every new glider added interacts with the main part of the pattern. It would not catch reactions like below where both gliders would miss the block on their own...

Good point. A clearer example for me would be something like this:

`x = 11, y = 41, rule = B3/S232bo\$obo\$b2o17\$bo6bobo\$b2o5b2o\$obo6bo17\$8b2o\$8bobo\$8bo!`

This constellation can't be found by adding a fourth glider to my proposed three-glider collision database, because none of the subsets of three out of the four gliders are valid three-glider collisions. So if we ever, Heaven forbid, get to the stage of trying to enumerate all four-glider collisions, we can start with the three-glider-database-plus-one-glider approach, but then as you say we'll have to add all two-glider-collision interactions with other-two-glider-collisions.

But for just three gliders I think this isn't a problem yet. There's no way to set up three gliders such that no two of them interact, but the combination of all three does interact. (Right?) So with a decent 3G database we could kinda sorta reach up to 6G before we start missing huge classes of reactions.

-- I'm sure people have thought of all these problems before, and maybe more, and that's why the collision census hasn't been done yet for more than two gliders. It still seems as if an exhaustive 3G search is a lot closer to being possible than 4G and above, though.

dvgrn
Moderator

Posts: 5080
Joined: May 17th, 2009, 11:00 pm

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

16.623 in 9 gliders:

`x = 26, y = 24, rule = B3/S2311bo\$10bo\$10b3o\$bo\$2bo\$3o7bo\$11b2o\$10b2o2\$20bo\$18b2o\$19b2o3\$23bo\$23bobo\$23b2o\$10b2o\$10bobo7b3o\$10bo9bo\$15b2o4bo\$6b2o7bobo\$5bobo7bo\$7bo!`

dvgrn wrote:... or at least a better prebuilt database of small constellations...

I would find such a thing very useful, as it can take an hour for my computer to find a 3-glider collision to make the constellation I need, with my very slow clumsy method.

EDIT:

16.828 in 12 gliders (ugly):

`x = 125, y = 148, rule = B3/S23obo\$b2o\$bo65\$77bobo\$78b2o\$78bo2\$51bo\$52bo\$50b3o6bo18b2o\$37bo22b2o15b2o\$35bobo21b2o18bo\$36b2o15b2o\$33b2o19b2o4bo\$32bobo18bo6b2o\$34bo24bobo2b2o\$63b2o\$65bo37\$116b2o\$116bobo\$116bo25\$122b2o\$122bobo\$122bo!`

16.930 in 10 gliders:

`x = 49, y = 62, rule = B3/S2322bo\$20b2o\$21b2o6\$48bo\$46b2o\$47b2o8\$3bo\$bobo\$2b2o\$15bo\$13b2o\$14b2o2\$5b2o9bo\$4bobo8b2o\$6bo8bobo2\$o\$b2o\$2o3\$12b2o\$3b2o8b2o\$4b2o6bo\$3bo22\$35bo\$34b2o\$34bobo!`
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 467
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

chris_c wrote:...
Now the maximum cost is 25G:

`16.623 xs16_o5r8jdz01 2516.828 xs16_4alhe8z0641 2516.930 xs16_3iaj21e8zw1 2516.1139 xs16_kq23z124871 2516.1398 xs16_g88c93zc952 2516.706 xs16_39s0qmz023 2416.713 xs16_o8bap3z23 2416.1034 xs16_3lkaa4z065 2416.1323 xs16_031e8gzc9311 2416.353 xs16_321fgc453 2316.621 xs16_g5r8jdz11 2316.829 xs16_0md1e8z1226 2316.1702 xs16_4a5p68ozx121 2316.1740 xs16_69acga6zx32 2316.825 xs16_4alhe8zw65 2216.1846 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 2016.1073 xs16_3lkaa4z641 2016.1127 xs16_giligoz104a4 2016.1739 xs16_g88r2qkz121 2016.1791 xs16_03lkaa4z3201 2016.1962 xs16_4a9eg8ozw65 2016.2058 xs16_69akg4czx146 20`

...

Don't miss this 16.1034 synthesis.
`x = 62, y = 65, rule = B3/S2360bo\$59bo\$59b3o12\$33bo\$34bo\$32b3o\$37bo\$26b2o7b2o\$25bobo8b2o\$27bo\$29b2o\$29bobo\$29bo9\$36bobo\$36b2o\$37bo2\$27bo7b2o\$28b2o5bobo\$27b2o6bo3\$24b3o\$26bo\$25bo13bo\$38bo\$38b3o3\$38b2o\$38bobo\$38bo12\$bo\$b2o\$obo!`

This might be useful for 16.1073 and 16.1791 synthesis.

yootaa

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

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

16.706 in 11:
`x = 40, y = 54, rule = B3/S235bobo\$6b2o\$6bo8\$23bo\$24b2o\$23b2o\$14bo\$12bobo\$13b2o2\$15b3o\$17bo\$16bo\$22b2o\$21bobo\$23bo2\$38bo\$37b2o\$37bobo2\$32b3o\$32bo\$27b2o4bo\$26bobo\$28bo3\$17b2o\$16bobo\$18bo2\$28b2o\$28bobo\$28bo10\$bo\$b2o\$obo!`
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1809
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

Goldtiger997 wrote:16.828 in 12 gliders (ugly):

Reduced to 11 which gives 16.825 in 15:

`x = 156, y = 228, rule = Life134b2o\$33b2o99b2o\$34b2o\$33bo4bo\$37b2o\$37bobo23\$obo\$b2o\$bo61\$75bo\$73bobo\$74b2o3\$46bobo\$47b2o7bo\$47bo9bo94b2o\$55b3o17b3o73bo2bo\$34b2o39bo74bobobo\$34b2o40bo74bo2b2o\$49b3o100b2o\$51bo4b2o95bo\$50bo4bobo93bo\$57bo3b3o87b2o\$61bo\$62bo64\$120b2o\$119b2o\$121bo25\$52b2o98b2o\$51bo2bo96bo2bo\$50bobobo95bobobo\$51bo2b2o95bo2b2o\$52b2o98b2o\$53bo99bo\$51bo100bo\$51b2o99b2o12\$63b2o\$37b2o23b2o\$38b2o6b2o16bo\$37bo7bobo\$47bo4\$44b2o\$45b2o\$44bo!`

Goldtiger997 wrote:16.930 in 10 gliders

Reduced to 9:

`x = 123, y = 150, rule = Life13bo\$11bobo\$12b2o103bo\$116bobo\$15b2o99bobo\$14bobo100bo\$16bo59\$56bo\$55bo\$55b3o22\$10bobo\$11b2o\$11bo6\$4bo35bo\$5bo32b2o\$3b3o33b2o3\$17bo\$16bobo\$16bobo\$17bo97bo2bobo\$115b5obo\$121bo\$117bo3b2o\$116bobo\$117bo16\$38bo\$37b2o\$37bobo2\$3o\$2bo\$bo15\$45bo\$44b2o\$44bobo!`

yootaa wrote:Don't miss this 16.1034 synthesis.
`x = 62, y = 65, rule = B3/S2360bo\$59bo\$59b3o12\$33bo\$34bo\$32b3o\$37bo\$26b2o7b2o\$25bobo8b2o\$27bo\$29b2o\$29bobo\$29bo9\$36bobo\$36b2o\$37bo2\$27bo7b2o\$28b2o5bobo\$27b2o6bo3\$24b3o\$26bo\$25bo13bo\$38bo\$38b3o3\$38b2o\$38bobo\$38bo12\$bo\$b2o\$obo!`

This might be useful for 16.1073 and 16.1791 synthesis.

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.

`x = 40, y = 54, rule = B3/S235bobo\$6b2o\$6bo8\$23bo\$24b2o\$23b2o\$14bo\$12bobo\$13b2o2\$15b3o\$17bo\$16bo\$22b2o\$21bobo\$23bo2\$38bo\$37b2o\$37bobo2\$32b3o\$32bo\$27b2o4bo\$26bobo\$28bo3\$17b2o\$16bobo\$18bo2\$28b2o\$28bobo\$28bo10\$bo\$b2o\$obo!`

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

`x = 135, y = 432, rule = Life11bo\$9bobo\$10b2o3\$116b3o2\$114bo5bo\$114bo5bo\$114bo5bo\$16bo\$14bobo99b3o\$15b2o2\$6b2o\$5bobo\$7bo113b2o\$121b2o2\$17b3o\$19bo\$18bo55\$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!`

Still lifes at 20G or above:

`16.1139    xs16_kq23z124871         2516.1398    xs16_g88c93zc952         2516.713     xs16_o8bap3z23           2416.1323    xs16_031e8gzc9311        2416.353     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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Joined: June 28th, 2014, 7:15 am

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