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

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
BobShemyakin
Posts: 214
Joined: June 15th, 2014, 6:24 am

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

Chris_c is seriously engaged in this task. He has already had some success and published a list of outstanding SL16.
Let's wish him good luck and help him.
Looking through my database I have found 10 still lifes from his list:

Code: Select all

x = 244, y = 506, rule = B3/S23
10bo$11bo$9b3o$20bo$19bo$19b3o3$11bobo$12b2o$12bo10bo$22bo95bo$22b3o
93bobo$118b2o$25b2o$25bobo22bo2b2o15bo2b2o15bo2b2o15bo2b2o2b2o11bo$25b
o23bobo2bo14bobo2bo14bobo2bo14bobo2bo2bobo9bobobo2bo$9bo40b2obo16b2obo 16b2obo16b2obo3bo12b2ob4o$9b2o4b3o34bo19bo19bo19bo19bo$8bobo6bo15bo18b obo17bobo17bobo17bobo17bobo$16bo15bo20b2o18b2o18b2o18b2o18b2o$32b3o$
53b2o18b2o$53b2o18b2o$18bo4b3o$18b2o5bo49b3o$17bobo4bo50bo$76bo32$130b
o$128b2o$129b2o5$118bo$119b2o$118b2o2$101bobo$102b2o$102bo2$132bo$130b
2o$116bo14b2o$116b2o$115bobo$109b2o$66bo43b2o$65bo43bo$17bobo45b3o155b o$18b2o51b2o87bo39bo22bobo14bo$18bo51b2o86b3o37b3o22b2o13b3o$20bo13b2o
bo16b2obo6b3o5bo11b2obo3bo22b2obo3bo19bo12b2obo3b2o17b2o12b2obo3b2o17b
2o12b2obo3b2o$15b2o2bo14bob2o16bob2o6bo19bob2o2bobo21bob2o2bobo13b2o2b o13bob2o2bo2bo16b2o12bob2o2bo2bo16b2o12bob2o2bo2bo$14b2o3b3o43bo25b2o
28b2o14b2ob3o18b2o38b2o38b2o$16bo119bo$11b2o$12b2o$11bo33$106bo$104b2o
61bo$105b2o59bo$166b3o$21bo78bo15bo$21bobo35bo41b2o12bo28b2o18b2o$21b 2o34bobo40b2o3bo4bobo2b3o26b2o18b2o$58b2o43b2o5b2o$11bo52bo39b2o5bo3bo$12bo49b2o50b2o$10b3o50b2o49bobo$66b2o21bo19bo24b2o18b2o18b2o$34bo3b2o 14bo3b2o6bobo15bo3bobo13bo3bobo22bo2bo16bo2bo16bo2bo$33bobobobo13bobob
obo6bo16bobobobo13bobobobo23bobo2bo14bobo2bo14bobo2bo$15bo18b2obo16b2o bo26b2obo16b2obo26b2ob2o15b2ob2o15b2ob2o$16bo20bo19bo29bo19bo29bo19bo
19bo$14b3o20bobo17bobo27bobo17bobo27bobo17bobo17bobo$21bo16b2o18b2o28b
2o18b2o28b2o18b2o18b2o$20b2o$15bo4bobo$15b2o$14bobo24$174bo$173bo$173b 3o$123bo$56bo51bo13bo28b2o18b2o$54bobo52bo7bobo2b3o26b2o18b2o$55b2o50b 3o7b2o$15bo45bo56bo3bo$14bo44b2o60b2o$14b3o43b2o44b2o13bobo$7bobo53b2o 21bo18bobo8bo25bo19bo19bo$8b2o25b2o18b2o6bobo19bobo19bo7bobo23bobo17bo
bo17bobo$8bo7b2o13b2obobo14b2obobo6bo17b2obobo24b2obobo23bobo2bo14bobo 2bo14bobo2bo$15b2o13bobobo15bobobo25bobobo25bobobo25bobob2o14bobob2o
14bobob2o$13bo3bo13bo2bo16bo2bo26bo2bo26bo2bo26bo2bo16bo2bo16bo2bo$11b
obo20bobo17bobo27bobo27bobo27bobo17bobo17bobo$12b2o21b2o18b2o28b2o28b 2o28b2o18b2o18b2o30$173bo$172bo$172b3o19bo$122bo71bobo$55bo51bo13bo28b
2o18b2o22b2o$53bobo52bo7bobo2b3o26b2o18b2o20bo$54b2o50b3o7b2o75bo$14bo 45bo56bo3bo69b3o$13bo44b2o60b2o$13b3o43b2o44b2o13bobo$6bobo53b2o21bo
18bobo8bo25bo19bo19bo18bo19bo$7b2o25b2o18b2o6bobo19bobo19bo7bobo23bobo 17bobo17bobo7b3o6bobo17bobo$7bo7b2o13b2obobo14b2obobo6bo17b2obobo24b2o
bobo23bobo2bo14bobo2bo14bobo2bo5bo7bobo2bo16bo2bo$14b2o13bobobo15bobob o25bobobo25bobobo25bobob2o14bobob2o14bobob2o6bo6bobob2o14bobob2o$12bo
3bo13bo2bo16bo2bo26bo2bo26bo2bo26bo2bo16bo2bo16bo2bo15bo2bo15b2o2bo$10bobo20bobo17bobo27bobo27bobo27bobo17bobo17bobo16bobo17bobo$11b2o21b
2o18b2o28b2o28b2o28b2o18b2o18b2o17b2o18b2o29$61bo$59bobo$60b2o2$15bobo
43bo19b2o18b2o$16b2o43b2o17bo2bo16bo2bo47bobo$16bo43bobo17bo2bo16bo2bo
43bo3b2o$81b2o18b2o45b2o2bo$7bo8b3o17bo29bo19bo10bo8bo19bo20b2o7bo19bo
$7b2o9bo17b3o27b3o17b3o9bo2bo4b3o17b3o27b3o17b3o$6bobo8bo21bo29bo19bo
6b3o2b2o6bo14b2o3bo24b2o3bo14b2o3bo$36b2obo26b2obo16b2obo10bobo3b2obo 14bo2bobo24bo2bobo13bo3bobo$36b2ob2o25b2ob2o15b2ob2o15b2ob2o15b2ob2o
25b2ob2o12b2ob2ob2o$152bo$147bo3b2o$145bobo3bobo$146b2o3$26bo$25b2o$25bobo24$33bobo$33b2o$34bo4$11bo5bo$12bo5bo$10b3o3b3o37b2o3bo$56bo2b3o
$18b2o37b2o$5bo12bobo38b3o$6b2o10bo40bo2bo$5b2o53b2o7$38bo$37b2o$30bo 6bobo$29b2o$29bobo$42b3o$42bo$43bo2$27bo$26b2o$26bobo2$33b3o$33bo$34bo
25$12bo$11bo$11b3o7$3bo$bobo$2b2o6$8bo$7bo6b3o$7b3o4bo12b2o3b2o$15bo
11bobobobo$3bo21bobobobo$4bo4b3o13b2o3b2o$2b3o6bo$10bo6$15b2o$15bobo$15bo7$5b3o$7bo$6bo24$2bo$3bo$b3o2$132bo$13bobo56bo13bo43bobo$13b2o58bo
12bobo42b2o2bo$14bo56b3o12b2o46bo$134b3o$112bo19bo$27b2o18b2o28b2o27bo
b2obobo12bob2obobo12bob2ob2o$3b2o22bobo17bobo18b3o6bobo26b2obob2o13b2o bob2o13b2obob2o$2bobo24bo19bo20bo8bo29bo19bo19bo$4bo9b2o13bob2o16bob2o 16bo9bob2o26bob2o16bob2o16bob2o$14bobo13bo2bo16bo2bo26bo2bo26bobo17bob
o17bobo$10bo3bo17b2o18b2o28b2o4bo$10b2o76bobo$9bobo76b2o2$85b3o$85bo$
86bo24$19bo$20bo$18b3o$obo$b2o$bo32bo$33bo$33b3o2$16bo$16bobo$16b2o$6b
o21bo20b2o$4bobo21bobo17bobo$5b2o9b3o9b2o16b3o$b2o13bo15b2o11bo3bo$obo
14bo14bobo11b3o$2bo29bo15bobo$49b2o5$33b3o$33bo$bo32bo$b2o$obo$18b3o$20bo$19bo!

1 row 16.871 in 13G
2 row 16.406 in 16G
3row 16.1801 in 15G
4 row 16.1805 in 13G
5 row 16.1810 in 16G
6 row 16.235 in 12G
7 row 16.736 in 10G
8 row 16.14 in 8G
9 row 16.158 in 12G
10 row 16.747 in 12G

Bob Shemyakin

BlinkerSpawn
Posts: 1974
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

16.1805 reduced by 2, which in turn reduces 16.1810 to 14G:

Code: Select all

x = 140, y = 15, rule = B3/S23
106bobo$107b2o$49bo51bo5bo$47bobo52bo7bobo$48b2o50b3o7b2o$8bo45bo56bo$
7bo44b2o$7b3o43b2o44b2o$obo53b2o21bo18bobo8bo25bo$b2o25b2o18b2o6bobo 19bobo19bo7bobo23bobo$bo7b2o13b2obobo14b2obobo6bo17b2obobo24b2obobo23b
obo2bo$8b2o13bobobo15bobobo25bobobo25bobobo25bobob2o$6bo3bo13bo2bo16bo
2bo26bo2bo26bo2bo26bo2bo$4bobo20bobo17bobo27bobo27bobo27bobo$5b2o21b2o
18b2o28b2o28b2o28b2o!

LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

AbhpzTa
Posts: 504
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

16.406 reduced to 15G, 16.1801 reduced to 14G:

Code: Select all

x = 232, y = 78, rule = B3/S23
51bobo$52b2o35bo$2bo20b2o18b2o7bo10b2o18b3ob2o14b2o38b2o38b2o38b2o$obo 2b2o16bobo17bobo8bo8bobo2b2obo13bo2b2o13bobo2b2obo12b2o16bo2bo2b2obo 12b2o16bo2bo2b2obo30bo2bo2b2obo$b2ob2o18bo19bo4b2o2bo10bo3bob2o12bo19b
o3bob2o12b2o17b2o3bob2o12b2o17b2o3bob2o31b2o3bob2o$6bo41b2o3b3o89b3o 13b2o22b3o37b3o$50bo94bo14bobo22bo39bo$45b2o115bo$46b2o68bo$45bo68b2o$
115b2o$108bobo$108b2o$93b2o14bo$94b2o$93bo2$123bo$122b2o$122bobo2$106b 2o$105b2o$107bo5$95b2o$96b2o$95bo10$6bo$6bobo$2bo3b2o$obo$b2o4bo25b2o 28b2o28b2o28b2o28b2o$6b2o25bobo27bobo27bobo27bobo27bobo$6bobo26bo29bo 29bo29bo29bo$35bob2o26bob2o26bob2o26bob2o25b2ob2o$33bobobobo16bo6bobob obo23bobobobo23bobobobo24bo2bobo$33b2o3bo15bobo6b2o3bo23bobo3bo23bobo
3bo27bo2bo$11bo43b2o36bo29bo33b2o$10b2o46b2o51b2o2b2o$10bobo46b2o49bob ob2o$58bo53bo3bo$63b2o$2o61bobo$b2o60bo$o12$105b2o4b3o$104bobo6bo$106b o5bo33b3o$146bo$147bo2$110b3o$112bo$111bo!
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).

chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

I pushed an update containing everything in this thread, all of Goldtiger's 14-bit SL reductions and many of Bob's converters. I didn't include any of Bob's converters that reduced the population and I didn't include any that looked inapplicable to 16-bit SL lifes. If this means that I have missed out something important then please point it out.

The new stats are: 3123 out 3286 synthesised, 2874 less than 16G, 89 equal to 16G, 163 unknown syntheses, 126 hard classes:

Code: Select all

x = 106, y = 2508, rule = B3/S23
3bobo15b2ob2o$2bob2o15b2obo$2bo22bo$b2ob2o15b4o$2bob2o16bo$o19bo$2o18b
2o14$4bo$3bobo$bo2bobo$b2obobo$2bob2o$o$2o14$2b2o$3bo$bo2b2o$b2obobo$
2bo2bo$obo$2o14$3b2o$4bo2bo$4bobobo$2bobo2bo$bob2o$bo$2o14$5b2o18b2o$6bo19bo$3b3o17b3o$3bo19bo$b2o18b2o$o19bo$b2o18b2o$2bo19bo$bo18bo$b2o 17b2o11$3b2o17b2o20bo19bo18bo19bo$2bo2bo16bo2bo17bobo17bobo16bobo17bob o$3b2obo16b2obo15bobobo15bobo16bobobo15bobo$5bo19bo16bobobo15bobobo14b obobo15bobobo$b4o16b4o16b2o2bo15b2o2b2o13b2o2bo15b2o2b2o$2bo19bo19bo 19bo18bo19bo$o19bo19bo19bo19bo19bo$2o18b2o18b2o18b2o18b2o18b2o13$2b2o
2b2o14b2o$2bobo2bo14bobob2o$4b2o18b2obo$3bo19bo$b3o17b3o$o19bo$2o18b2o
14$b2o18b2o$bo19bo$2bo2b2o15bo$3bo2bo16bob2o$bob2o16bob2obo$obo17bobo$obo17bobo$bo19bo13$bo3b2o$b3o2bo$4b2o$3bo$b3o$o$2o14$2ob2o$bobobo$bo2b
obo$2bobo2bo$3bo2b2o16$2ob2ob2o$bobo3bo$bo2b3o$2bobo$3bo16$2ob2o$bobo$
bo2b3o$2bobo2bo$3bo2b2o16$2ob2o$bobobobo$bo2bob2o$2bobo$3b2o16$4b2o$2o bo2bo$bob2obo$bo2bob2o$2b2o16$2o2bobo13b2obo$o2bob2o13bob2o$2b2o20b2ob o$4b2obo13b2obob2o$4bob2o13bobo16$2o2bo$o2bobo$2b2o2bo$4b2o$2b2o$bobo$
2bo14$2o$o2b2o$2b2o$5bo$2b4o$2bo$3bo$2b2o13$2o2b2o$o2bobo$2b2o$4bo$2b 3o$bo$b2o14$o2b2o$4o$5bo$2b4o$2bo$3bo$2b2o14$o2bob2o13b2o$4obo2bo12bo$4bo2b2o12bob2o$2bo17b2o2bo$2b2o18bo$20b2o$20bo$21bo$20b2o12$o2bob2o$5o bo2$2bob2o$2b2obo16$o2bo2b2o$4o3bo$4b3o$2bobo$2b2o16$o3b2o$3o2bo$3b2o$
2bo2b3o$2b2o3bo16$2ob2obo17bobo14b2ob2obo17bobo$2obob2o13b2obob2o13bob obob2o13b2obob2o$3bo16b2obo17bo2bo15bobobo$3bob2o16bob2o17bob2o13bo2bo b2o$4bobo16b2obo18bobo16b2obo16$2o18b2o$o2b2o15bo2b2o$b2obo16b2obo$2bo
19bo$2bo19bo$2o18b2o$o19bo$2bo18bo$b2o17b2o12$o2bo$6o$6bo$2bo2bobo$bob
o2bo$2bo15$o2bo$4o$4b2o$2bo2bo$bob2o$bo$2o14$2o2bo$o2bobo$b2o2bo$3b2o$b2o$obo$bo14$2o18b2o$o19bo$b3o17b3o$3bo19bo$b2o18b2o$o19bo$b2o18b2o$2b o19bo$bo18bo$b2o17b2o11$2o3bo$o2b3o$b2o$3bo$b3o$o$2o14$2obo$ob4o$6bo$b
2o2bo$bo2bo$2b2o15$2ob2o$ob2o2bo$5b2o$b4o$bo2bo16$2obo$ob4o$6bo$b2o2b 2o$bobo$2bo15$2o$o3b2o$2bo2bo$b2obo$bo2b2o$3bo$2b2o14$2o21b2o$obo17b2o
2bo$2b3o2b2o11bob2o$bo3bo2bo13bo$b2o2b2o15bo$20b2o$20bo$21bo$20b2o12$
2o$obo2bo$2b4o$bo$b3o$4bo$3b2o14$2ob2o$ob2obo$5bo$b2obo$b2ob2o16$2b2o$bo2bo$ob2o2bo$bo2b3o$3bo$4bo$3b2o14$2bo$bobo$o2bo$b3ob2o$4bobo$3bo$2bo$2b2o13$2b2o$bobo$o2bob2o$b3o2bo$4bo$3bo$3b2o14$2b2o$bobo$o3b2o$b2obob o$3bo2bo$3bobo$4bo14$2b2o$bo2bo$o2b2o$b2o2b2o$3bobo$3bobo$4bo14$2b2o$b o2bo$o2bo$b2ob3o$3bo2bo$3bobo$4bo14$2bo$bobo2bo$o2b4o$b2o$3b2o$3bobo$4bo14$2b2obo$bob2obo$o5bo$b3obo$3bob2o16$2b2ob2o$bobobo$o5bo$b4obo$3bo bo16$3b2o$b3o$o4bo$b5o2$3bo$2bobo$3bo13$3b2o$b3o$o4bo$b4obo$5bo$3bo$3b 2o14$3bo$b3o2bo$o3b3o$b2o$3b2o$3bobo$4bo14$3bobo$b4obo$o5bo$b3obo$3bob 2o16$3b2o$b3obo$o5bo$bo5bo$2bob3o$3b2o15$2b2o$bobo2b2o$o6bo$b2o3bo$2bo
2bo$2bobo$3bo14$2bo$bobo$o2b3o$b2o3bo$2bo2b2o$o$2o14$2b2o$bobo$o2bobo$b2ob2o$2bo$obo$2o14$3b2o$b3obo$o4bo$b4o$2bo$o$2o14$3b2o$3bobo$2obo2bo$bobob2o$bobo$2b2o15$3b2o$3bobo$2obobo$bobob2o$bobo$2b2o15$2ob2o$bobo$o
3bo$b3obo$4bo$3bo$3b2o14$2ob2o$bobobo$o5bo$b4obo$3bobo16$2obobo$bob2ob o$o5bo$b5o$3bo16$2obo$bob3o$o5bo$b4obo$3bobo16$2ob2obo13b2ob2o15b2ob2o
15bobo$bobob2o14bobo2bo14bobo2bo13b2obob2o$o19bo4b2o13bo4b2o16b2obo$b 2o18b2o18b2o17b2o$2bo19bo19bo17bo$o20bo18bo20bo$2o19b2o17b2o18b2o14$2b 2ob2o$o2bobo$2obo3bo$3bo2b2o$3b2o16$3b2obo$obo2b2o$2obo$3bob2o$3b2obo
16$3bo$o2b3o$3o3bo$3bob2o$2bo$bo$b2o14$3bobo$o2b2obo$3o3bo$3bobo$2b2ob
2o16$2b2o17b2o19b2o18b2o$o2bo16bo2bo18bo19bo$3o17b3o20bo19bo$5bo19bo
14b4o16b4o$2b4o16b4o14bo19bo$2bo19bo20b3o17b3o$3bo19bo19bo2bo16bo2bo$
2b2o18b2o21b2o17b2o13$b2obo$o2b2o$2o3b2o$2b2o2bo$2bob2o16$b2o$o2bo$ob
2o2bo$bo2b3o$3bo$4bo$3b2o14$b2o$o2bo$obo2bo$bob2obo$3bo2bo$3bobo$4bo 14$bo19bo$obob2o14bobob2o$ob2obo14bob2obo$bo19bo$3b2o18b2o$4bo19bo$2bo
20bo$2b2o19b2o13$bo$obo2b2o$obo3bo$bob3o$3bo$2bo$2b2o14$bob2o$ob2obo$o 5bo$b4obo$3bobo16$bobobo$ob3obo$o5bo$b5o$3bo16$bobobo$ob3obo$o5bo$b3ob
o$3b2o16$b2o$ob3o$o4bo$b3obo$4bo$3bo$3b2o14$b2o$obo2bo$o2b3o$b2o$3bo$o
bo$2o14$b2o20b2o$obo20bobo$o2b2o16b2o2bo$b2o2bo14bo2b2o$3b2o16b2o$3bo 18bo$4bo15bo$3b2o15b2o13$bob2o$ob2obo$o5bo$bob2obo$2b2obo16$b2ob2o$obo
bo$o5bo$bo3b2o$2bobo$3b2o15$b2o$o2bo$obo$bob3o$2bo2bo$obo$2o14$b2ob2o$obobo$obo2bo$bobobo$2bobo$3bo15$b2o$obo$o2b2o$b2o2bo$2bob2o$2bo$b2o14$b2o$ob3o$o4bo$b4o$2bo$o$2o14$2b2o$o2b3o$2o4bo$bob3o$bobo$2bo15$2b2o$bo bo$bo2b2o$2o4bo$4b3o$3bo$3b2o14$3bobo$3b2obo$b2o3bo$o2bobo$bobob2o$2bo
15$2b2o$3bo$bo2b2o$ob2o2bo$bo2b2o$3bo$2b2o14$b2o$o2bo$bobo$2obobo$2bob
2o$2bo$b2o14$2b2o$3bo$3o3bo$o2b4o$3bo$4bo$3b2o14$3b2o$3bo$2obo2bo$obob 3o$3bo$4bo$3b2o14$4b2o$3bo2bo$2o2b2o$ob2o$3bo$obo$2o14$2b2o$3bo$3o$o2b 3o$2bo2bo$obo$2o14$2b2obo14bob2o$2bob2o14b2obo$obo20bobo$2o2b2o14b2o2b
2o$5bo14bo$3bo17bo$3b2o15b2o14$2b2o$2bo2bo$obob2o$2obo$3bo$3o$o14$b2o$
2b3o$o4bo$4obo$4bo$2bo$2b2o14$b2o$2bo$o2b2o$3o2bo$3b3o$2bo$2b2o14$4b2o$b2o2bo$o2b2o$2obo$3bo$3o$o14$2b2o$bo2bo$ob2obo$2o2bo$3bo$3o$o14$2b2o$
bobo$o$6o$5bo$2bo$bobo$2bo13$2b2o$bo2bo$o2bobo$4obo$4bo$2bo$2b2o14$3bo
$b3o$o$6o$5bo$2bo$bobo$2bo13$2b2o18b2o$bo2bo16bo2bo$o2bobo14bo2bo$2obo bo14b2obobo$2bobo17bob2o$2bo19bo$b2o18b2o14$3bo$b3o$o$ob2o$bobo$3bob2o
$3b2obo14$2bo19bo$bobo17bobo$obo17bobo$o2b3o14bo2b3o$b2o2bo15b2o2bo$2b o19bo$bo18bo$b2o17b2o13$2bo$bobo$obo$o4bo$b5o2$3bo$2bobo$3bo12$4b2o$b 2o2bo$ob3o$o$b2o$2bo$o$2o13$2b2o$2bobo$2o3bo$o5bo$bo3b2o$2bobo$3b2o14$2bo$2b3o$2o3bo$o2b2o$b2o$2bo$o$2o13$2b2o$3bo$3o$o$b2o$3bo$3b3o$6bo$5b 2o12$4b2o$4bo$2o3bo$o5bo$bo3b2o$2bo2bo$3bobo$4bo13$3bo$2bobo$o2bobo$2o bobo$bob2o$bo$2o14$b2ob2o$2bobo$bo3bo$2b2obo$obobo$2o15$4bo19bo$3bobo
17bobo$3bo2bo16bo2bo$b2o2b2o14b2o2b2o$o19bo$b2o18b2o$2bo19bo$bo18bo$b 2o17b2o12$4bo$3bobo$3bo2bo$b2o2b2o$o$3o$3bo$2b2o13$3bo$2bobo$3bobo$bob obo$obobo$obo$bobo$2bo13$2bo$bobo$2bo$5bo$6o$o$3bo$2bobo$3bo12$2b2o17b 2o$bo2bo16bo2bo$2b2obo16b2obo$4bo19bo$4o16b4o$o19bo$bo19bo$2o18b2o13$4bo$2b3o$bo$bo2b3o$2obo2bo$3bo$3b2o14$b2obo$o2b2o$bo$2b2obo$obob2o$2o 15$2obo$ob2o$4b2o$b2o2bo$o2b2o$2o15$2bo$2b3o$2o3bo$bo2bo$o3b2o$b3o$3bo
14$3b2o$3bobo$bobo2bo$obobobo$obob2o$bo15$2b2o$2bo$3bo$3o2bo$o2b3o$2bo
$3bo$2b2o13$4b2o$5bo$2b3o$2bo2b3o$3bo3bo$3o$o14$4bo$3bobo$3bo2bo$2b2o 3bo$2bo3b2o$3bo$3o$o!  Extrementhusiast Posts: 1850 Joined: June 16th, 2009, 11:24 pm Location: USA ### Re: 16 in 16: Efficient 16-bit Synthesis Project From the original list: Code: Select all x = 205, y = 2828, rule = B3/S23 102b2o$103bo$101bo$100bob4o$101bo3bo$102bo$99b3o$99bo13$102bobo15b2ob 2o$101bob2o15b2obo$101bo22bo$100b2ob2o15b4o$101bob2o16bo$99bo19bo$99b 2o18b2o10$67bo$68bo2bo$66b3obo$70b3o$100b2o$101bo$70b2o2b2o25bob2o$70b obo2bo24b2o2bo$73b2o27b2o$71b2o27b2o$70bobo26bobo$71bo28bo13$101b2o17b
2o$102bo18bo$100bo19bo$100b2o18b2o$102bo19bo$102bo19bo$100bob2o16bob2o
$99bobo17bobo$99bobo17bobo$100bo19bo11$103b2o$102bo2bo$100bo2bobo$100b 2ob2o$101bo$99bobo$99b2o14$103bo19bo$102bobo17bobo$100bo2bobo14bo2bo$
100b2obobo14b2obobo$101bo2bo16bo2b2o$99bobo17bobo$99b2o18b2o14$103bo$102bobo$100bo2bobo$100b2obobo$101bob2o$99bo$99b2o14$101b2o$102bo$100bo 2b2o$100b2obobo$101bo2bo$99bobo$99b2o14$102b2o$103bo2bo$103bobobo$101b obo2bo$100bob2o$100bo$99b2o14$104b2o18b2o$105bo19bo$102b3o17b3o$102bo
19bo$100b2o18b2o$99bo19bo$100b2o18b2o$101bo19bo$100bo18bo$100b2o17b2o
11$102b2o17b2o20bo19bo18bo19bo$101bo2bo16bo2bo17bobo17bobo16bobo17bobo
$102b2obo16b2obo15bobobo15bobo16bobobo15bobo$104bo19bo16bobobo15bobobo
14bobobo15bobobo$100b4o16b4o16b2o2bo15b2o2b2o13b2o2bo15b2o2b2o$101bo
19bo19bo19bo18bo19bo$99bo19bo19bo19bo19bo19bo$99b2o18b2o18b2o18b2o18b
2o18b2o13$101b2o2b2o14b2o$101bobo2bo14bobob2o$103b2o18b2obo$102bo19bo$100b3o17b3o$99bo19bo$99b2o18b2o8$67bo$66bo$66b3o2$64b3o$66bo$65bo34b2o 18b2o$100bo19bo$101bo2b2o15bo$62b2o38bo2bo16bob2o$61bobo5b2o29bob2o16b ob2obo$63bo3bo2bo28bobo17bobo$67b2o30bobo17bobo$65b2o33bo19bo$64bobo$
60bo4bo$60b2o$59bobo$65b3o$65bo$66bo6$100bo3b2o$100b3o2bo$103b2o$102bo$100b3o$99bo$99b2o14$99b2ob2ob2o$100bobo3bo$100bo3b2o$101b3o$103bo16$
99b2ob2o$100bobobo$100bo2bobo$101bobo2bo$102bo2b2o13$13bo$11b2o$8bo3b 2o$9b2o88b2ob2ob2o$8b2o90bobo3bo$100bo2b3o$15b2o84bobo$10bo4bo86bo$9bo bo4bo$10b2o2bobo$14b2o$10b2o$3b2o4bobo$4b2o4bo$3bo$8b2o$7bobo$9bo6$99b 2ob2o$100bobo$100bo2b3o$101bobo2bo$102bo2b2o16$99b2ob2o$100bobobobo$
100bo2bob2o$101bobo$102b2o7$50bo$49bo$49b3o7$103b2o18bo$34b2ob2o60b2ob obo14b2obobo$35bobo62bobo17bobobo$35bobo62bob2o16bob2o$36bo64bo19bo$99bobo17bobo$47b3o49b2o18b2o$47bo5b3o$48bo4bo$54bo3$40b2o$26bo9b2o2bob o$26b2o7bobo2bo$25bobo9bo5$103b2o$99b2obo2bo$100bob2obo$100bo2bob2o$
101b2o$42b3o$42bo$43bo13$99b2o2bobo13b2obo$99bo2bob2o13bob2o$101b2o20b
2obo$103b2obo13b2obob2o$103bob2o13bobo16$99b2o3b2o$99bobobobo$101bobob obo$101b2o3b2o17$99b2o2bo$99bo2bobo$101b2o2bo$103b2o$101b2o$100bobo$101bo14$99b2o$99bo2b2o$101b2o$104bo$101b4o$101bo$102bo$101b2o13$99b2o
2b2o$99bo2bobo$101b2o$103bo$101b3o$100bo$100b2o8$52bo13bo$53bo12bobo$51b3o12b2o3$57b2o$48b3o6bobo39bob2ob2o$50bo8bo39b2obob2o$49bo9bob2o39b o$60bo2bo38bob2o$62b2o4bo34bobo$68bobo$68b2o2$65b3o$65bo$66bo7$50bo$
51bo$49b3o6bo$58bobo38bo2b2o$58b2o39b4o$104bo$101b4o$101bo$47bo2bo51bo$47b4o50b2o2$49b4o$49bo2bo$50b2o3$58b2o$58bobo$58bo$50b2o$41b2o6b2o$42b2o7bo$41bo3b3o$45bo53bo2bob2o13b2o$46bo52b4obo2bo12bo$103bo2b2o12bo b2o$101bo17b2o2bo$101b2o18bo$119b2o$119bo$120bo$119b2o12$99bo2bob2o$99b5obo2$101bob2o$101b2obo16$99bo2bo2b2o$99b4o3bo$103b3o$101bobo$101b
2o16$99bo3b2o$99b3o2bo$102b2o$101bo2b3o$101b2o3bo16$99b2ob2obo17bobo
14b2ob2obo17bobo$99b2obob2o13b2obob2o13bobobob2o13b2obob2o$102bo16b2ob
o17bo2bo15bobobo$102bob2o16bob2o17bob2o13bo2bob2o$103bobo16b2obo18bobo
16b2obo16$99b2o18b2o$99bo2b2o15bo2b2o$100b2obo16b2obo$101bo19bo$101bo 19bo$45bo15bo37b2o18b2o$46bo13bo38bo19bo$44b3o6bo6b3o38bo18bo$51bobo 46b2o17b2o$52b2o2$54bo$54bobo$54b2o7$39b3o23b3o31b2o3b2o$41bo23bo33bo 2bo2bo$40bo25bo33b2ob2o$101bobo$52b3o46bobo$102bo8$54b2o$54bobo$54bo2$42bo9b2o10bo$42b2o7bobo9b2o$41bobo9bo9bobo$99b2obo16b2o$99bob2o16bo3b 2o$121bo2bo$100b5o15b2obo$101bo2bo16bob2o$99bo21bo$99b2o19b2o14$99bo2b o$99b6o$105bo$101bo2bobo$100bobo2bo$101bo15$99bo2bo$99b4o$103b2o$101bo
2bo$100bob2o$100bo$99b2o14$99b2o2bo$99bo2bobo$100b2o2bo$102b2o$100b2o$99bobo$100bo14$99b2o18b2o$99bo19bo$100b3o17b3o$102bo19bo$100b2o18b2o$
99bo19bo$100b2o18b2o$101bo19bo$100bo18bo$100b2o17b2o11$99b2o3bo$99bo2b
3o$100b2o$102bo$100b3o$99bo$99b2o14$99b2o$99bo$100bo2b2o$101bo2bo$100b
2obo$102bo$99bobo$99b2o13$99b2obo$99bob4o$105bo$100b2o2bo$100bo2bo$101b2o15$99b2ob2o$99bob2o2bo$104b2o$100b4o$100bo2bo16$99b2obo$99bob4o$105bo$100b2o2b2o$100bobo$101bo15$99b2o$99bo3b2o$101bo2bo$100b2obo$100b o2b2o$102bo$101b2o14$99b2o21b2o$99bobo17b2o2bo$101b3o2b2o11bob2o$100bo 3bo2bo13bo$100b2o2b2o15bo$119b2o$119bo$120bo$119b2o12$99b2o$99bobo2bo$101b4o$100bo$100b3o$103bo$102b2o14$99b2ob2o$99bob2obo$104bo$100b2obo$
100b2ob2o16$101b2o$100bo2bo$99bob2o2bo$100bo2b3o$102bo$103bo$102b2o14$
101bo$100bobo$99bo2bo$100b3ob2o$103bobo$102bo$101bo$101b2o13$101b2o$100bobo$99bo2bob2o$100b3o2bo$103bo$102bo$102b2o14$101b2o$100bobo$99bo 3b2o$100b2obobo$102bo2bo$102bobo$103bo14$101b2o$100bo2bo$99bo2b2o$100b 2o2b2o$102bobo$102bobo$103bo14$101b2o$100bo2bo$99bo2bo$100b2ob3o$102bo 2bo$102bobo$103bo14$101bo$100bobo2bo$99bo2b4o$100b2o$102b2o$102bobo$
103bo14$101b2obo$100bob2obo$99bo5bo$100b3obo$102bob2o16$101b2ob2o$100b obobo$99bo5bo$100b4obo$102bobo16$102b2o$100b3o$99bo4bo$100b5o2$102bo$
101bobo$102bo13$102b2o$100b3o$99bo4bo$100b4obo$104bo$102bo$102b2o14$102bo$100b3o2bo$99bo3b3o$100b2o$102b2o$102bobo$103bo14$102bobo$100b4ob o$99bo5bo$100b3obo$102bob2o16$102b2o$100b3obo$99bo5bo$100bo5bo$101bob 3o$102b2o15$101b2o$100bobo2b2o$99bo6bo$100b2o3bo$101bo2bo$101bobo$102b o14$101bo$100bobo$99bo2b3o$100b2o3bo$101bo2b2o$99bo$99b2o14$101b2o$
100bobo$99bo2bobo$100b2ob2o$101bo$99bobo$99b2o14$102b2o$100b3obo$99bo
4bo$100b4o$101bo$99bo$99b2o14$102b2o$102bobo$99b2obo2bo$100bobob2o$100bobo$101b2o15$102b2o$102bobo$99b2obobo$100bobob2o$100bobo$101b2o15$99b2ob2o$100bobo$99bo3bo$100b3obo$103bo$102bo$102b2o14$99b2ob2o$100bob obo$99bo5bo$100b4obo$102bobo16$99b2obobo$100bob2obo$99bo5bo$100b5o$102bo16$99b2obo$100bob3o$99bo5bo$100b4obo$102bobo16$99b2ob2obo13b2ob2o 15b2ob2o15bobo$100bobob2o14bobo2bo14bobo2bo13b2obob2o$99bo19bo4b2o13bo 4b2o16b2obo$100b2o18b2o18b2o17b2o$101bo19bo19bo17bo$99bo20bo18bo20bo$99b2o19b2o17b2o18b2o6$60bo$58bobo$59b2o$68bobo$61bo6b2o$61bobo5bo$61b
2o2$51b2ob2o45b2ob2o$49bo2bob2o43bo2bobo$49b2obo46b2obo3bo$52bo49bo2b
2o$52b2o48b2o5$63b2o$63bobo$63bo9$102b2obo$99bobo2b2o$99b2obo$102bob2o
$102b2obo16$102bo$99bo2b3o$99b3o3bo$102bob2o$101bo$100bo$100b2o14$102b obo$99bo2b2obo$99b3o3bo$102bobo$101b2ob2o9$37bo$38bo$36b3o$67bobo$59bo
bo5b2o$60b2o6bo$47bobo10bo$40bobo4b2o15bobo34b2o17b2o19b2o18b2o$41b2o
5bo16b2o32bo2bo16bo2bo18bo19bo$41bo23bo33b3o17b3o20bo19bo$104bo19bo14b
4o16b4o$101b4o16b4o14bo19bo$101bo19bo20b3o17b3o$47bo23bo30bo19bo19bo2b o16bo2bo$45b3o21b3o29b2o18b2o21b2o17b2o$44bo23bo$44b2o22b2o3$41b2o22b 2o$40bobo21bobo$42bo23bo$44b2o22b2o$44bobo21bobo$44bo23bo3$100b2obo$
99bo2b2o$99b2o3b2o$101b2o2bo$101bob2o16$100b2o$99bo2bo$99bob2o2bo$100b o2b3o$102bo$103bo$102b2o14$100b2o$99bo2bo$99bobo2bo$100bob2obo$102bo2b o$102bobo$103bo14$100bo19bo$99bobob2o14bobob2o$99bob2obo14bob2obo$100b o19bo$102b2o18b2o$103bo19bo$101bo20bo$101b2o19b2o13$62bo37bo$61bobo2b 2o31bobo2b2o$61bobo3bo31bobo3bo$62bob3o33bob3o$64bo37bo$62bobo36bo$62b
2o37b2o2$69b2o$58b2o5bo2b2o$59b2o4b2o3bo$58bo5bobo9$100bob2o$99bob2obo
$99bo5bo$100b4obo$102bobo16$100bobobo$99bob3obo$99bo5bo$100b5o$102bo
16$100bobobo$99bob3obo$99bo5bo$100b3obo$102b2o16$100b2o20b2o$99bobo20b obo$99bo24bo$100b4o16b4o$104bo14bo$102b2o16b2o$102bo18bo$103bo15bo$
102b2o15b2o12$100b2o$99bob3o$99bo4bo$100b3obo$103bo$102bo$102b2o14$
100b2o$99bobo2bo$99bo2b3o$100b2o$102bo$99bobo$99b2o14$100b2o20b2o$99bo
bo20bobo$99bo2b2o16b2o2bo$100b2o2bo14bo2b2o$102b2o16b2o$102bo18bo$103b o15bo$102b2o15b2o13$100bob2o$99bob2obo$99bo5bo$100bob2obo$101b2obo16$
100b2ob2o$99bobobo$99bo5bo$100bo3b2o$101bobo$102b2o15$100b2o$99bo2bo$
99bobo$100bob3o$101bo2bo$99bobo$99b2o14$100b2ob2o$99bobobo$99bobo2bo$
100bobobo$101bobo$102bo15$100b2o$99bobo$99bo2b2o$100b2o2bo$101bob2o$
101bo$100b2o14$100b2o$99bob3o$99bo4bo$100b4o$101bo$99bo$99b2o14$101b2o$99bo2b3o$99b2o4bo$100bob3o$100bobo$101bo15$101b2o$100bobo$100bo2b2o$
99b2o4bo$103b3o$102bo$102b2o14$102bobo$102b2obo$100b2o3bo$99bo2bobo$
100bobob2o$101bo15$101b2ob2o$102bobo$100bo3bo$99bob3o$100bo$101bo$100b
2o14$101b2o$102bo$100bo2b2o$99bob2o2bo$100bo2b2o$102bo$101b2o14$102b2o
$101bobo$100bo$99bob5o$100bo4bo$102bo$101b2o14$103bo$101b3o$100bo$99bo
b5o$100bo4bo$102bo$101b2o8$54bo$54bobo$54b2o$48bo$46bobo$43bo3b2o$38bo
2bobo56b2o$38b2o2b2o55bo2bo$37bobo60bobo$52bobo44b2obobo$51bob2o46bob
2o$51bo49bo$42bo7b2o48b2o$42b2o$41bobo3$36b2o$35bobo$37bo$17bobo$17b2o$18bo2$19b2o$19bobo$7b2o10bo81b2o$8bo93bo$5b3o9bo81b3o3bo$5bo2b3o5b2o
81bo2b4o$8bo2bo4bobo83bo$2bo6b2o92bo$obo99b2o$b2o2$17bo$16b2o$16bobo$
10b3o$10bo$3b2o6bo$4b2o$3bo4$102b2o$102bo$99b2obo2bo$99bobob3o$102bo$
103bo$102b2o14$103b2o$102bo2bo$99b2o2b2o$99bob2o$102bo$99bobo$99b2o14$101b2o$102bo$99b3o$99bo2b3o$101bo2bo$99bobo$99b2o14$101b2obo14bob2o$101bob2o14b2obo$99bobo20bobo$99b2o2b2o14b2o2b2o$104bo14bo$102bo17bo$
102b2o15b2o14$101b2o$101bo2bo$99bobob2o$99b2obo$102bo$99b3o$99bo14$
100b2o$101b3o$99bo4bo$99b4obo$103bo$101bo$101b2o14$100b2o$101bo$99bo2b 2o$99b3o2bo$102b3o$101bo$101b2o14$103b2o$100b2o2bo$99bo2b2o$99b2obo$
102bo$99b3o$99bo14$101b2o$100bo2bo$99bob2obo$99b2o2bo$102bo$99b3o$99bo 14$101b2o$100bobo$99bo$99b6o$104bo$101bo$100bobo$101bo13$101b2o$100bo 2bo$99bo2bobo$99b4obo$103bo$101bo$101b2o14$102bo$100b3o$99bo$99b6o$104bo$101bo$100bobo$101bo8$60bo$58bobo3bo$59b2ob2o$63b2o2$101b2o18b2o$
59b2o39bo2bo16bo2bo$57bo2bo38bo2bobo14bo2bo$57b2obobo36b2obobo14b2obob
o$59bob2o38bobo17bob2o$59bo41bo19bo$58b2o40b2o18b2o14$102bo$100b3o$99b
o$99bob2o$100bobo$102bob2o$102b2obo14$101bo19bo$100bobo17bobo$99bobo 17bobo$99bo2b3o14bo2b3o$100b2o2bo15b2o2bo$101bo19bo$100bo18bo$100b2o
17b2o13$101bo$100bobo$99bobo$99bo4bo$100b5o2$102bo$101bobo$102bo12$103b2o$100b2o2bo$99bob3o$99bo$100b2o$101bo$99bo$99b2o13$101b2o$101bobo
$99b2o3bo$99bo5bo$100bo3b2o$101bobo$102b2o14$101bo$101b3o$99b2o3bo$99b o2b2o$100b2o$101bo$99bo$99b2o13$101b2o$102bo$99b3o$99bo$100b2o$102bo$
102b3o$105bo$104b2o12$103b2o$103bo$99b2o3bo$99bo5bo$100bo3b2o$101bo2bo
$102bobo$103bo13$102bo$101bobo$99bo2bobo$99b2obobo$100bob2o$100bo$99b 2o14$100b2ob2o$101bobo$100bo3bo$101b2obo$99bobobo$99b2o15$103bo19bo$102bobo17bobo$102bo2bo16bo2bo$100b2o2b2o14b2o2b2o$99bo19bo$100b2o18b2o$101bo19bo$100bo18bo$100b2o17b2o12$103bo$102bobo$102bo2bo$100b2o2b2o$99bo$99b3o$102bo$101b2o13$102bo$101bobo$102bobo$100bobobo$99bobobo$99b
obo$100bobo$101bo13$101bo$100bobo$101bo$104bo$99b6o$99bo$102bo$101bobo
$102bo12$101b2o17b2o$100bo2bo16bo2bo$101b2obo16b2obo$103bo19bo$99b4o
16b4o$99bo19bo$100bo19bo$99b2o18b2o13$103bo$101b3o$100bo$100bo2b3o$99b
2obo2bo$102bo$102b2o14$100b2obo$99bo2b2o$100bo$101b2obo$99bobob2o$99b
2o15$99b2obo$99bob2o$103b2o$100b2o2bo$99bo2b2o$99b2o15$101bo$101b3o$99b2o3bo$100bo2bo$99bo3b2o$100b3o$102bo14$102b2o$102bobo$100bobo2bo$99bobobobo$99bobob2o$100bo15$101b2o$101bo$102bo$99b3o2bo$99bo2b3o$101b o$102bo$101b2o13$103b2o$104bo$101b3o$101bo2b3o$102bo3bo$99b3o$99bo14$103bo$102bobo$102bo2bo$101b2o3bo$101bo3b2o$102bo$99b3o$99bo!

Some of these may have been solved already with the update.
I Like My Heisenburps! (and others)

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

Here are two syntheses in under 16 gliders for still-lifes that appeared on the list:

16.709 in 9 gliders:

Code: Select all

x = 18, y = 29, rule = B3/S23
8bobo6bo$bobo5b2o4b2o$2b2o5bo6b2o$2bo4$2o$b2o$o$9bobo$9b2o$10bo2$9b2o$9bobo$9bo3$2b3o4b2o$4bo4bobo$3bo5bo5$16b2o$15b2o$17bo!

16.811 in 14 gliders:

Code: Select all

x = 103, y = 56, rule = B3/S23
90bo$89bo$89b3o10bo$100b2o$101b2o2$84bo$82b2o$83b2o10$2bo$obo$b2o4$92b o$92bobo$92b2o16$39bo22bo$37bobo22bobo$38b2o22b2o2$49bo$37b3o8bo13b3o$39bo8b3o11bo$38bo24bo$47b2o9b3o$46bobo5b2o2bo$48bo4bobo3bo$37b2o16bo$36bobo$38bo!


AbhpzTa
Posts: 504
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

Goldtiger997 wrote:16.811 in 14 gliders:

Code: Select all

x = 103, y = 56, rule = B3/S23
90bo$89bo$89b3o10bo$100b2o$101b2o2$84bo$82b2o$83b2o10$2bo$obo$b2o4$92b o$92bobo$92b2o16$39bo22bo$37bobo22bobo$38b2o22b2o2$49bo$37b3o8bo13b3o$39bo8b3o11bo$38bo24bo$47b2o9b3o$46bobo5b2o2bo$48bo4bobo3bo$37b2o16bo$36bobo$38bo!
Reduced to 11G:

Code: Select all

x = 73, y = 66, rule = B3/S23
52bo$52bobo$52b2o2b3o$56bo$57bo2$61bobo$61b2o$62bo5$47bo$47b2o12bobo$
46bobo12b2o$62bo9$40b2o$41b2o$40bo7$60b2o$59b2o$61bo$37bo$37b2o18b2o$
36bobo17b2o$58bo18$b2o$obo$2bo3$71b2o$70b2o$72bo! 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). BobShemyakin Posts: 214 Joined: June 15th, 2014, 6:24 am ### Re: 16 in 16: Efficient 16-bit Synthesis Project 16.44 in 11G Code: Select all x = 178, y = 28, rule = B3/S23 6$139bobo$139b2o$140bo2$14bobo133bo$15b2o40bo90b2o$15bo41bobo17bo19bo 3b3o13b2o18b2o10b2o14bo3b2o$17bo13b2obo16b2obo2b2o12b2obobobo12b2obobo
bo2bo9b2obobo2bo11b2obobo2bo3bo17b2obobobobo$12b2o2bo14bob2o16bob2o16b ob2ob2o13bob2ob2o4bo8bob2obobo12bob2obobo2b2o18bob2obobo$11b2o3b3o81bo
16bo19bo4b2o23b2o$13bo86b2o44b2o$8b2o89bobo43b2o$9b2o136bo$8bo!

16.757 in 8G

Code: Select all

x = 102, y = 33, rule = B3/S23
6$11bo$9bobo$10b2o$34b2o3b2o23b2o3b2o18b2o3b2o$24bo9bobobobo23bobobobo 18bobobobo$23bo12bobo27bobo22bobo$23b3o10bobo27bobo22b2obo$21bo13b2obo
bo24b2obobo23bo$20b2o17b2o28b2o23b2o$20bobo38bo$62b2o$61b2o3bo$58bo6b 2o$58b2o5bobo$12b2o7b2o34bobo$13b2o6bobo$12bo8bo!  Bob Shemyakin Extrementhusiast Posts: 1850 Joined: June 16th, 2009, 11:24 pm Location: USA ### Re: 16 in 16: Efficient 16-bit Synthesis Project Major improvement to 16.406: Code: Select all x = 18, y = 28, rule = B3/S23 9bo$8bo$8b3o2$o$b2o$2o4$8b2o$8bobo2b2obo$9bo3bob2o4$3o$2bo$bo7b3o$11bo$10bo2$10b2o$10bobo$10bo$16bo$15b2o$15bobo!

I Like My Heisenburps! (and others)

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

16.1797 in 12 gliders:

Code: Select all

x = 51, y = 40, rule = B3/S23
bo$2bo$3o46bo$48bo$48b3o4$30bo$28b2o$29b2o$22bo$20bobo$21b2o4bo5bobo$28b2o4b2o$27b2o5bo6$26bo$26b2o9bo$25bobo9bobo2b2o$37b2o2b2o$35bo7bo$
34b2o$34bobo4$39b2o$39bobo$39bo4$48b3o$48bo$49bo!  I tried for a long time to use the following predecessor for a different 16-bit still-life without success: Code: Select all x = 9, y = 15, rule = B3/S23 bo$obo$obo$bo4$2b2o3bo$b2obobobo$bo2bobobo$b3o3bo$2b2o3$3b3o!

Can anyone else?

chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote:16.1797 in 12 gliders:
Reduced the cleanup by one glider:

Code: Select all

x = 139, y = 26, rule = B3/S23
88bo$86b2o30bo$87b2o30bo$80bo36b3o$78bobo$79b2o4bo$86b2o$85b2o36b2o$
40bobo80b2o$41b2o$3bo37bo$3bobo89b2o$3b2o89bo2bo34b2o$bo82bo10bobo34bo 2b2o$2o82b2o6bo3bo37b2o$obo80bobo6bo44bo$92bo41b3obo$41bo92bo2bo$41bo
7b2o37b3o44b2o$5b2o34bo6b2o$5bobo42bo$5bo31b3o2$91b2o$92b2o$91bo!

Goldtiger997 wrote: I tried for a long time to use the following predecessor for a different 16-bit still-life without success:

Code: Select all

x = 9, y = 15, rule = B3/S23
bo$obo$obo$bo4$2b2o3bo$b2obobobo$bo2bobobo$b3o3bo$2b2o3$3b3o!  Can anyone else? 11 gliders: Code: Select all x = 93, y = 34, rule = B3/S23 3bo$4b2o$3b2o$71bo$72bo$70b3o$30bo$28b2o$29b2o43b2o$74b2o4$91bo$8bo81b
o$9b2o71b2o6b3o$8b2o3bo67bobo$14b2o62bo2bo6bo$2o11b2o62bobob2o4bobo$b 2o75b2o2bo4b2o$o79bo$80b2o2$10b2o$11b2o13b2o$10bo14b2o$27bo4$28b2o$6b 3o19bobo$8bo19bo$7bo!  I'll try to update my lists within 24 hours. EDIT: Pushed another update. Now there are 3146 16-bit SLs with synthesis, 2895 less than 16G, 90 equal to 16G, 140 unknown in 111 equivalence classes: Code: Select all x = 106, y = 2208, rule = Life 3b2o$4bo2bo$4bobobo$2bobo2bo$bob2o$bo$2o14$5b2o18b2o$6bo19bo$3b3o17b3o
$3bo19bo$b2o18b2o$o19bo$b2o18b2o$2bo19bo$bo18bo$b2o17b2o11$3b2o17b2o
20bo19bo18bo19bo$2bo2bo16bo2bo17bobo17bobo16bobo17bobo$3b2obo16b2obo
15bobobo15bobo16bobobo15bobo$5bo19bo16bobobo15bobobo14bobobo15bobobo$b
4o16b4o16b2o2bo15b2o2b2o13b2o2bo15b2o2b2o$2bo19bo19bo19bo18bo19bo$o19b
o19bo19bo19bo19bo$2o18b2o18b2o18b2o18b2o18b2o13$2b2o2b2o14b2o$2bobo2bo 14bobob2o$4b2o18b2obo$3bo19bo$b3o17b3o$o19bo$2o18b2o14$bo3b2o$b3o2bo$4b2o$3bo$b3o$o$2o14$2ob2o$bobobobo$bo2bob2o$2bobo$3b2o16$4b2o$2obo2bo$bob2obo$bo2bob2o$2b2o16$2o2bobo13b2obo$o2bob2o13bob2o$2b2o20b2obo$4b2o bo13b2obob2o$4bob2o13bobo16$2o2bo$o2bobo$2b2o2bo$4b2o$2b2o$bobo$2bo14$
2o$o2b2o$2b2o$5bo$2b4o$2bo$3bo$2b2o13$2o2b2o$o2bobo$2b2o$4bo$2b3o$bo$b
2o14$o2bob2o13b2o$4obo2bo12bo$4bo2b2o12bob2o$2bo17b2o2bo$2b2o18bo$20b
2o$20bo$21bo$20b2o12$o2bob2o$5obo2$2bob2o$2b2obo16$o2bo2b2o$4o3bo$4b3o
$2bobo$2b2o16$o3b2o$3o2bo$3b2o$2bo2b3o$2b2o3bo16$2ob2obo17bobo14b2ob2o
bo17bobo$2obob2o13b2obob2o13bobobob2o13b2obob2o$3bo16b2obo17bo2bo15bob
obo$3bob2o16bob2o17bob2o13bo2bob2o$4bobo16b2obo18bobo16b2obo16$2o18b2o$o2b2o15bo2b2o$b2obo16b2obo$2bo19bo$2bo19bo$2o18b2o$o19bo$2bo18bo$b2o 17b2o12$o2bo$6o$6bo$2bo2bobo$bobo2bo$2bo15$o2bo$4o$4b2o$2bo2bo$bob2o$b o$2o14$2o2bo$o2bobo$b2o2bo$3b2o$b2o$obo$bo14$2obo$ob4o$6bo$b2o2bo$bo2b
o$2b2o15$2ob2o$ob2o2bo$5b2o$b4o$bo2bo16$2obo$ob4o$6bo$b2o2b2o$bobo$2bo
15$2o$o3b2o$2bo2bo$b2obo$bo2b2o$3bo$2b2o14$2o21b2o$obo17b2o2bo$2b3o2b
2o11bob2o$bo3bo2bo13bo$b2o2b2o15bo$20b2o$20bo$21bo$20b2o12$2o$obo2bo$2b4o$bo$b3o$4bo$3b2o14$2ob2o$ob2obo$5bo$b2obo$b2ob2o16$2b2o$bo2bo$ob2o 2bo$bo2b3o$3bo$4bo$3b2o14$2bo$bobo$o2bo$b3ob2o$4bobo$3bo$2bo$2b2o13$2b
2o$bobo$o2bob2o$b3o2bo$4bo$3bo$3b2o14$2b2o$bobo$o3b2o$b2obobo$3bo2bo$
3bobo$4bo14$2b2o$bo2bo$o2b2o$b2o2b2o$3bobo$3bobo$4bo14$2b2o$bo2bo$o2bo$b2ob3o$3bo2bo$3bobo$4bo14$2bo$bobo2bo$o2b4o$b2o$3b2o$3bobo$4bo14$2b2o bo$bob2obo$o5bo$b3obo$3bob2o16$2b2ob2o$bobobo$o5bo$b4obo$3bobo16$3b2o$
b3o$o4bo$b5o2$3bo$2bobo$3bo13$3b2o$b3o$o4bo$b4obo$5bo$3bo$3b2o14$3bo$b
3o2bo$o3b3o$b2o$3b2o$3bobo$4bo14$3bobo$b4obo$o5bo$b3obo$3bob2o16$3b2o$
b3obo$o5bo$bo5bo$2bob3o$3b2o15$2b2o$bobo2b2o$o6bo$b2o3bo$2bo2bo$2bobo$3bo14$2bo$bobo$o2b3o$b2o3bo$2bo2b2o$o$2o14$2b2o$bobo$o2bobo$b2ob2o$2bo$obo$2o14$3b2o$b3obo$o4bo$b4o$2bo$o$2o14$3b2o$3bobo$2obo2bo$bobob2o$bo bo$2b2o15$3b2o$3bobo$2obobo$bobob2o$bobo$2b2o15$2ob2o$bobo$o3bo$b3obo$4bo$3bo$3b2o14$2ob2o$bobobo$o5bo$b4obo$3bobo16$2obobo$bob2obo$o5bo$b5o
$3bo16$2obo$bob3o$o5bo$b4obo$3bobo16$2ob2obo13b2ob2o15b2ob2o15bobo$bob
ob2o14bobo2bo14bobo2bo13b2obob2o$o19bo4b2o13bo4b2o16b2obo$b2o18b2o18b
2o17b2o$2bo19bo19bo17bo$o20bo18bo20bo$2o19b2o17b2o18b2o14$3b2obo$obo2b 2o$2obo$3bob2o$3b2obo16$3bo$o2b3o$3o3bo$3bob2o$2bo$bo$b2o14$3bobo$o2b 2obo$3o3bo$3bobo$2b2ob2o16$b2obo$o2b2o$2o3b2o$2b2o2bo$2bob2o16$b2o$o2b o$ob2o2bo$bo2b3o$3bo$4bo$3b2o14$b2o$o2bo$obo2bo$bob2obo$3bo2bo$3bobo$4bo14$bo19bo$obob2o14bobob2o$ob2obo14bob2obo$bo19bo$3b2o18b2o$4bo19bo$
2bo20bo$2b2o19b2o13$bo$obo2b2o$obo3bo$bob3o$3bo$2bo$2b2o14$bob2o$ob2ob
o$o5bo$b4obo$3bobo16$bobobo$ob3obo$o5bo$b5o$3bo16$bobobo$ob3obo$o5bo$b
3obo$3b2o16$b2o$ob3o$o4bo$b3obo$4bo$3bo$3b2o14$b2o$obo2bo$o2b3o$b2o$3b o$obo$2o14$b2o20b2o$obo20bobo$o2b2o16b2o2bo$b2o2bo14bo2b2o$3b2o16b2o$3bo18bo$4bo15bo$3b2o15b2o13$bob2o$ob2obo$o5bo$bob2obo$2b2obo16$b2ob2o$
obobo$o5bo$bo3b2o$2bobo$3b2o15$b2o$o2bo$obo$bob3o$2bo2bo$obo$2o14$b2ob
2o$obobo$obo2bo$bobobo$2bobo$3bo15$b2o$obo$o2b2o$b2o2bo$2bob2o$2bo$b2o
14$b2o$ob3o$o4bo$b4o$2bo$o$2o14$2b2o$o2b3o$2o4bo$bob3o$bobo$2bo15$2b2o
$bobo$bo2b2o$2o4bo$4b3o$3bo$3b2o14$3bobo$3b2obo$b2o3bo$o2bobo$bobob2o$
2bo15$2b2o$3bo$bo2b2o$ob2o2bo$bo2b2o$3bo$2b2o14$3b2o$3bo$2obo2bo$obob 3o$3bo$4bo$3b2o14$4b2o$3bo2bo$2o2b2o$ob2o$3bo$obo$2o14$2b2o$3bo$3o$o2b 3o$2bo2bo$obo$2o14$2b2obo14bob2o$2bob2o14b2obo$obo20bobo$2o2b2o14b2o2b
2o$5bo14bo$3bo17bo$3b2o15b2o14$2b2o$2bo2bo$obob2o$2obo$3bo$3o$o14$b2o$
2b3o$o4bo$4obo$4bo$2bo$2b2o14$b2o$2bo$o2b2o$3o2bo$3b3o$2bo$2b2o14$4b2o$b2o2bo$o2b2o$2obo$3bo$3o$o14$2b2o$bo2bo$ob2obo$2o2bo$3bo$3o$o14$2b2o$
bobo$o$6o$5bo$2bo$bobo$2bo13$2b2o$bo2bo$o2bobo$4obo$4bo$2bo$2b2o14$3bo
$b3o$o$6o$5bo$2bo$bobo$2bo13$3bo$b3o$o$ob2o$bobo$3bob2o$3b2obo14$2bo 19bo$bobo17bobo$obo17bobo$o2b3o14bo2b3o$b2o2bo15b2o2bo$2bo19bo$bo18bo$
b2o17b2o13$2bo$bobo$obo$o4bo$b5o2$3bo$2bobo$3bo12$4b2o$b2o2bo$ob3o$o$b 2o$2bo$o$2o13$2b2o$2bobo$2o3bo$o5bo$bo3b2o$2bobo$3b2o14$2bo$2b3o$2o3bo
$o2b2o$b2o$2bo$o$2o13$2b2o$3bo$3o$o$b2o$3bo$3b3o$6bo$5b2o12$4b2o$4bo$2o3bo$o5bo$bo3b2o$2bo2bo$3bobo$4bo13$3bo$2bobo$o2bobo$2obobo$bob2o$bo$2o14$b2ob2o$2bobo$bo3bo$2b2obo$obobo$2o15$4bo19bo$3bobo17bobo$3bo2bo
16bo2bo$b2o2b2o14b2o2b2o$o19bo$b2o18b2o$2bo19bo$bo18bo$b2o17b2o12$4bo$
3bobo$3bo2bo$b2o2b2o$o$3o$3bo$2b2o13$3bo$2bobo$3bobo$bobobo$obobo$obo$bobo$2bo13$2bo$bobo$2bo$5bo$6o$o$3bo$2bobo$3bo12$2b2o17b2o$bo2bo16bo2b o$2b2obo16b2obo$4bo19bo$4o16b4o$o19bo$bo19bo$2o18b2o13$4bo$2b3o$bo$bo 2b3o$2obo2bo$3bo$3b2o14$b2obo$o2b2o$bo$2b2obo$obob2o$2o15$2obo$ob2o$4b 2o$b2o2bo$o2b2o$2o15$2bo$2b3o$2o3bo$bo2bo$o3b2o$b3o$3bo14$3b2o$3bobo$b
obo2bo$obobobo$obob2o$bo15$2b2o$2bo$3bo$3o2bo$o2b3o$2bo$3bo$2b2o13$4b
2o$5bo$2b3o$2bo2b3o$3bo3bo$3o$o14$4bo$3bobo$3bo2bo$2b2o3bo$2bo3b2o$3bo
$3o$o!


Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

I've been trying to synthesise 16.2446:

Code: Select all

x = 9, y = 7, rule = B3/S23
3b2o$4bo2bo$4bobobo$2bobo2bo$bob2o$bo$2o!

There are no soups on catalogue so I tried synthesising it via this 14-bit still-life which can be made in 9 gliders:

Code: Select all

x = 9, y = 5, rule = B3/S23
3b2o$4bo2bo$4bobobo$b2obo2bo$bob2o!

I could not find any converters for this. Does anyone know of one?

Otherwise...is there an alternate still-life 16.2446 could be converted from?

EDIT:

16.2663 in 10 gliders:

Code: Select all

x = 32, y = 27, rule = B3/S23
bo$2bo$3o$13bo3bo$14bo2bobo$12b3o2b2o$30bo$23bo5bo$22bo6b3o$11bo10b3o$
12b2o$11b2o$26b3o$10bo15bo$10b2o15bo$9bobo7$19bo$18b2o$11b2o5bobo$10bo bo$12bo!

Last edited by Goldtiger997 on December 27th, 2016, 11:53 pm, edited 1 time in total.

Hdjensofjfnen
Posts: 1590
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

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

No. But while I was hunting for it:

Code: Select all

x = 18, y = 18, rule = B3/S23
13bo$bo11bobo$2bo10b2o$3o4bo$8bo$6b3o4$3b3o8b2obo$5bo8bob2o$4bo$8b2o$
7bobo$9bo$3b3o$5bo$4bo!


Code: Select all

x = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo! Code: Select all x = 7, y = 5, rule = B3/S2-i3-y4i 4b3o$6bo$o3b3o$2o$bo!  BobShemyakin Posts: 214 Joined: June 15th, 2014, 6:24 am ### Re: 16 in 16: Efficient 16-bit Synthesis Project 16.787 in12G: Code: Select all x = 163, y = 47, rule = B3/S23 6$19bo$17bobo94bobo$18b2o95b2o$115bo$22bo94bo$11bobo6b2o94bo$12b2o7b2o
26b2o18b2o18b2o18b2o5b3o10b2o$12bo36bo2b2o15bo2b2o15bo2b2o15bo2b2o15bo 2b2o$50bob2o16bob2o16bob2o16bob2o16bobobo$11b3o5bo29b2o18b2o18b2o18b2o 6bo11b2o2bo$13bo4b2o5b2o20bo2bo10b3o3bo2bo19bo19bo5b2o12bo$12bo5bobo3b 2o21b2o14bo3b2o21bobo17bobo3bobo11bobo$26bo35bo12b2o14b2o18b2o18b2o$74b2o$70b3o3bo$72bo$71bo!

16.2192 in 9G:

Code: Select all

x = 120, y = 22, rule = B3/S23
40bo$41bo$39b3o$99bobo$23b2o28b2o18b2o18b2o5b2o11b2o$23bobo27bobo17bob o17bobo4bo12bobo$25bo29bo19bo19bo6bo12bo2bo$2bo22bobo27bobo17bobo17bob o3bo13bobobo$obo23bobo27bobo17bobo17bobo2b3o12bobo$b2o24bo29bo19bo19bo 19bo$74b3o17b3o17b3o$74bo19bo19bo2$3o$2bo2bobo$bo3b2o$6bo2$5b2o49bo$4b 2o47bo2bobo$6bo44bobo2b2o$52b2o!  Bob Shemyakin Goldtiger997 Posts: 627 Joined: June 21st, 2016, 8:00 am ### Re: 16 in 16: Efficient 16-bit Synthesis Project How many gliders does it take to convert this 17-bit still life... Code: Select all x = 7, y = 9, rule = B3/S23 2b2o$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!

... into 16.2446...

Code: Select all

x = 7, y = 9, rule = B3/S23
2bo$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!  ...? A for awesome Posts: 2103 Joined: September 13th, 2014, 5:36 pm Location: Pembina University, Home of the Gliders Contact: ### Re: 16 in 16: Efficient 16-bit Synthesis Project Goldtiger997 wrote:How many gliders does it take to convert this 17-bit still life... Code: Select all x = 7, y = 9, rule = B3/S23 2b2o$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!

... into 16.2446...

Code: Select all

x = 7, y = 9, rule = B3/S23
2bo$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!  ...? Two: Code: Select all x = 9, y = 16, rule = B3/S23 6bo$6bobo$6b2o$2bobo$3b2o$3bo2$2b2o$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!

praosylen#5847 (Discord)

x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

A for awesome wrote:
Goldtiger997 wrote:How many gliders does it take to convert this 17-bit still life...

Code: Select all

16.2446 but with boat instead of tub

... into 16.2446...

Code: Select all

16.2446

...?
Two:

Code: Select all

x = 9, y = 16, rule = B3/S23
6bo$6bobo$6b2o$2bobo$3b2o$3bo2$2b2o$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!  Oh sorry, I looked for a long time at two different databases of converters and neither of them had it. From that, here is 16.2446 in 15 gliders!: (EDIT: this is now incorrect, see below) Code: Select all x = 291, y = 34, rule = B3/S23 250bo$250bobo$250b2o$246bobo$247b2o$247bo$98bo$96b2o28b2o38b2o38b2o38b
2o38bo$97b2o26bobo37bobo37bobo37bobo37bobo$126bo39bo39bo39bo39bo2$124b 5o35b5o35b5o35b5o35b5o$124bo3bo35bo3bo35bo3bo35bo3bo35bo3bo$37b2o38b2o 48bo39bo39bo39bo39bo$37b2o38b2o11bo37b3o37b3o37b3o37b3o37b3o$90bobo37b o39bo39bo39bo39bo$2bo2bo84b2o6bo$obo2bobo89b2o$b2o2b2o80bobo7bobo$88b 2o$88bo47bo39bo$4b2o39bo39bo33b2o15bo22b2o15bo$3bobo38bobo37bobo32b2o
15bo22b2o15bo$5bo38bobo37bobo$45bo39bo91b3o$121b3o3b3o31b3o3b3o7bo$78b
3o90b2o5bo$80bo44bo39bo4b2o$79bo6b2o37bo39bo6bo$87b2o36bo39bo$86bo$101b3o11b2o$101bo12b2o$102bo13bo!  EDIT: See AbptzTa's post below; there was a mistake in my synthesis because the glider would have to pass through the block. Here is the complete version of AbptzaTa's (Nice Work!) corrected synthesis from below: Code: Select all x = 291, y = 34, rule = B3/S23 250bo$250bobo$250b2o$246bobo$247b2o$247bo2$126b2o38b2o38b2o38b2o38bo$
125bobo37bobo37bobo37bobo37bobo$126bo39bo39bo39bo39bo2$98bo25b5o35b5o
35b5o35b5o35b5o$77bo19bo26bo3bo35bo3bo35bo3bo35bo3bo35bo3bo$75bobo19b
3o27bo39bo39bo39bo39bo$76b2o12bo37b3o37b3o37b3o37b3o37b3o$73b2o15bobo
37bo39bo39bo39bo39bo$72bobo15b2o$74bo$87bobo$88b2o$4bo83bo47bo39bo$5bo
39bo39bo33b2o15bo22b2o15bo$3b3o38bobo37bobo32b2o15bo22b2o15bo$44bobo
37bobo$3o42bo39bo91b3o$2bo118b3o3b3o31b3o3b3o7bo$bo76b3o90b2o5bo$80bo
44bo39bo4b2o$79bo6b2o37bo39bo6bo$87b2o36bo39bo$86bo$101b3o11b2o$101bo 12b2o$102bo13bo!

Last edited by Goldtiger997 on January 11th, 2017, 7:52 pm, edited 1 time in total.

AbhpzTa
Posts: 504
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

Goldtiger997 wrote:
A for awesome wrote:
Goldtiger997 wrote:How many gliders does it take to convert this 17-bit still life...

Code: Select all

16.2446 but with boat instead of tub

... into 16.2446...

Code: Select all

16.2446

...?
Two:

Code: Select all

x = 9, y = 16, rule = B3/S23
6bo$6bobo$6b2o$2bobo$3b2o$3bo2$2b2o$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!  Oh sorry, I looked for a long time at two different databases of converters and neither of them had it. From that, here is 16.2446 in 15 gliders!: Code: Select all x = 291, y = 34, rule = B3/S23 250bo$250bobo$250b2o$246bobo$247b2o$247bo$98bo$96b2o28b2o38b2o38b2o38b
2o38bo$97b2o26bobo37bobo37bobo37bobo37bobo$126bo39bo39bo39bo39bo2$124b 5o35b5o35b5o35b5o35b5o$124bo3bo35bo3bo35bo3bo35bo3bo35bo3bo$37b2o38b2o 48bo39bo39bo39bo39bo$37b2o38b2o11bo37b3o37b3o37b3o37b3o37b3o$90bobo37b o39bo39bo39bo39bo$2bo2bo84b2o6bo$obo2bobo89b2o$b2o2b2o80bobo7bobo$88b 2o$88bo47bo39bo$4b2o39bo39bo33b2o15bo22b2o15bo$3bobo38bobo37bobo32b2o
15bo22b2o15bo$5bo38bobo37bobo$45bo39bo91b3o$121b3o3b3o31b3o3b3o7bo$78b
3o90b2o5bo$80bo44bo39bo4b2o$79bo6b2o37bo39bo6bo$87b2o36bo39bo$86bo$101b3o11b2o$101bo12b2o$102bo13bo!  Error: Code: Select all x = 40, y = 28, rule = LifeHistory 21.A$19.2A$20.2A$.DBD$.B2DB$2.D3B$3.4B$2C2.4B$2C3.4B4.A$6.4B3.A.A$7. 4B2.2A6.A$8.4B8.2A$9.BCBC7.A.A$10.B2C$11.C$8.A$7.A.A$7.A.A$8.A2$.3A$3.A$2.A6.2A$10.2A$9.A$24.3A11.2A$24.A12.2A$25.A13.A! Pi + blinker = pi + glider: (16.2446 in 15G) Code: Select all x = 45, y = 23, rule = B3/S23 26bo$5bo19bo$3bobo19b3o$4b2o12bo$b2o15bobo$obo15b2o$2bo$15bobo$16b2o$
16bo$13bo$12bobo$12bobo$13bo2$6b3o$8bo$7bo6b2o$15b2o$14bo$29b3o11b2o$29bo12b2o$30bo13bo!
or suitable "pi+G" pattern synth?

Code: Select all

x = 106, y = 28, rule = LifeHistory
61.D3.2D$60.2D2.D2.D$61.D3.2D$61.D2.D2.D$60.3D2.2D2$10.3D67.3C$2A7.D
3.D56.2A7.C3.C$2A6.D61.2A6.C$7.D69.C$7.D69.C$7.D.D67.C.C$8.2D68.2C2$
76.3A$8.A66.2A.2A$7.A.A65.A2.2A$7.A.A66.2A6.A$8.A75.2A$83.A.A$.3A86.
2A12.A$3.A86.A.A10.2A$2.A6.2A79.A12.A.A$10.2A$9.A$24.3A11.2A$24.A12.
2A$25.A13.A! Alternative: (at most 15G) Code: Select all x = 59, y = 43, rule = B3/S23 40bo$39bo$39b3o3$32bo$30b2o$31b2o5$9b2o$9b2o7$20b2o$20b2o12$5b3o$7bo$3o3bo$2bo$bo39b2o$40b2o$42bo$5b3o49b2o$7bo48b2o$6bo51bo!
I couldn't find any synthesis of these blocks in 3G.
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).

Gamedziner
Posts: 795
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

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

AbhpzTa, don't forget, cleanup is part of the synthesis.

Code: Select all

x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27. A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!  BlinkerSpawn Posts: 1974 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: 16 in 16: Efficient 16-bit Synthesis Project Gamedziner wrote:AbhpzTa, don't forget, cleanup is part of the synthesis. And I'm sure it would have been included if it wasn't the exact same cleanup as already posted. LifeWiki: Like Wikipedia but with more spaceships. [citation needed] Goldtiger997 Posts: 627 Joined: June 21st, 2016, 8:00 am ### Re: 16 in 16: Efficient 16-bit Synthesis Project 16.2688 in 12 gliders: Code: Select all x = 63, y = 55, rule = B3/S23 2bo$obo$b2o$12bobo$13b2o$13bo10$47bo$46bo$46b3o4$37bo$38b2o$37b2o9bo7b
o$49bo6bobo$36bo10b3o6b2o$36b2o$35bobo12bo$50bobo$50b2o6$52bo$51b2o$51bobo2$41b2o$40bobo$42bo5$58b2o$57b2o$59bo4$60b2o$60bobo$60bo!


chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

I pushed an update to my glider_synth repo on github based on Bob's recent 16G collection (and hopefully all of the new syntheses in this thread). It contains 225 improvements including 65 SLs that appear for the first time. Many of the most complicated syntheses look to have come via Mark Niemiec's collection.

There are now 3212 SLs with synthesis, 2933 in less than 16 gliders, 85 in 16 gliders, 74 unknown SLs and 61 hard equivalence classes.

My lists are behind Bob's in 101 cases. It looks like the biggest single reason is that Bob uses many converters that reduce the bit count of the object. Bob hasn't yet posted the syntheses for all of the necessary still lifes of bit count greater than 16 and for me to extend to 17 or 18 bit still lifes using my own system it would probably best to do a rewrite in C. Whether this will actually happen is debatable.

Nevertheless, I hope we can work out most of the other discrepancies starting with the 12-14 bit still lifes listed here.

PHPBB12345
Posts: 776
Joined: August 5th, 2015, 11:55 pm
Contact:

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

16.???:

Code: Select all

x = 8, y = 5, rule = B3/S23
4b2o$4bobo$5bobo$2obobobo$ob2ob2o!


Code: Select all

x = 7, y = 6, rule = B3/S23
3b2o$3bobo$bobo2bo$obobobo$obob2o$bo!  Goldtiger997 Posts: 627 Joined: June 21st, 2016, 8:00 am ### Re: 16 in 16: Efficient 16-bit Synthesis Project PHPBB12345 wrote:16.???: Code: Select all x = 8, y = 5, rule = B3/S23 4b2o$4bobo$5bobo$2obobobo$ob2ob2o!  Code: Select all x = 7, y = 6, rule = B3/S23 3b2o$3bobo$bobo2bo$obobobo$obob2o$bo!

16.186 and 16.643 respectively.

I did this by first finding the apgcode, then I converted it into its still life number using chris_c's "still16.txt" file which can be found here: https://github.com/ceebo/glider_synth/b ... till16.txt

Why do you want to know?

...

Anyway, I looked at the largest row of hard equivalence cases:

Code: Select all

x = 116, y = 16, rule = B3/S23
2$5b2o17b2o20bo19bo18bo19bo$4bo2bo16bo2bo17bobo17bobo16bobo17bobo$5b2o bo16b2obo15bobobo15bobo16bobobo15bobo$7bo19bo16bobobo15bobobo14bobobo
15bobobo$3b4o16b4o16b2o2bo15b2o2b2o13b2o2bo15b2o2b2o$4bo19bo19bo19bo
18bo19bo$2bo19bo19bo19bo19bo19bo$2b2o18b2o18b2o18b2o18b2o18b2o!

I looked through all the soups for each of those still-lifes. Here are all the reductions of soups I found that at least have a hope of being under 16 gliders:

Code: Select all

x = 192, y = 62, rule = B3/S23
11$105bo$106bo$104b3o$177b2o$177b2o$57b3o$56bo3bo$56bo3bo$54b2o5b2o43b 3o$53bo4bo4bo42bo$17bo35bo3bobo3bo41b3o$17b3o33bo4bo4bo$8b2o6bo2bo34b 2o5b2o$8bobo5bo39bo3bo56b2o$9bo6b3o37bo3bo50bo5b2o$18bo38b3o51bo$61bo 49bo$22bo37bobo$22b2o23bo11bo2b2o51b2o$20b2obo23bo14bo52bobo52b3o$21b 2o24bo11bo2bo53b2o52bo2bo$59b2o91b2o3b2o15bo$152b2o2bo2bo10bo2bo$121bo
34bobo11b3o$121bo35bo$52b3o4b2o60bo$53bobo3b2o99bo$54b2o103bobo$159bob o$160bo!

The block in the last one can be replaced by a glider.

EDIT: I'll do these myself

16.2205 in 15 gliders:

Code: Select all

x = 167, y = 36, rule = B3/S23
126bo$127bo$125b3o$99b2o28b2o$98bo2bo26bo2bo$99b2o20bo7b2o$105b2o15bo
12b2o28b2o$74bo31bo13b3o13bo29bo$70bo3bobo27bo29bo6bo22bo$71bo2b2o17b 2o7b4o17b2o7b4o4bo21b4o$69b3o21b2o6bo21b2o6bo8b3o18bo$100bob2o4bo21bob 2o4bo21bob2o$80bo20bo2bo2bobo21bo2bo2bobo21bo2bo$79bo23b2o3b2o23b2o3b 2o23b2o$79b3o4$bo30bo29bo$2bo29bo29bo$3o29bo29bo3$b2o102bo29bo$obo101b obo27bobo$2bo41b2o28b2o6b2o21bo29bo$13b3o28b2o28b2o5b2o$15bo67bo$14bo 120b3o$16b3o46b2o68bo$16bo47bobo69bo$17bo48bo$60b2o$59bobo7b2o$61bo7bo bo$69bo!

16.2208 in 13 gliders:

Code: Select all

x = 280, y = 35, rule = B3/S23
167bo$168bo$166b3o7$232bo$230bobo$4bobo224b2o$4b2o166bo$5bo167bo29bo4b 2o23bo4b2o$166b2o3b3o28bobo2bo2bo6bo14bobo2bo2bo6bo29bo$bo4b2o159b2o 34b2o3b2o6bobo14b2o3b2o6bobo27bobo$2bo4b2o23b2o28b2o5bo22b2o28b2o28b2o
12bo15b2o31bobo27bobo27bobo$3o3bo19bo5b2o22bo5b2o4bo17bo5b2o22bo5b2o 22bo5b2o17bo4bo5b2o31bobobo25bobobo25bobobo$26bo29bo11b3o15bo29bo29bo
24b2o3bo37b2o2b2o24b2o2b2o24b2o2b2o$26bo29bo29bo29bo29bo23bobo3bo38bo 29bo29bo$36b2o28b2o145bo29bo29bo$30b2o4b2o22b2o4b2o22b2o28b2o28b2o28b 2o31b2o28b2o28b2o$30bobo27bobo27bobo27bobo27bobo27bobo21b3o27b3o$31b2o 28b2o28b2o28b2o28b2o28b2o$202bo5bo23bo5bo$202bo5bo23bo5bo$127bo28bo29b
o15bo5bo23bo5bo$34b3o27b3o59bo29bo29bo$126b3o27bo29bo17b3o27b3o$68b2o$
68bobo$68bo57b2o$126bobo100b2o$126bo76b2o25b2ob2o$203b2o24bo3b2o!

From that synthesis 16.2207 in 15 gliders:

Code: Select all

x = 340, y = 35, rule = B3/S23
167bo$168bo$166b3o7$232bo$230bobo$4bobo224b2o$4b2o166bo$5bo167bo29bo4b 2o23bo4b2o$166b2o3b3o28bobo2bo2bo6bo14bobo2bo2bo6bo29bo29bo29bo$bo4b2o 159b2o34b2o3b2o6bobo14b2o3b2o6bobo27bobo27bobo27bobo$2bo4b2o23b2o28b2o
5bo22b2o28b2o28b2o12bo15b2o31bobo27bobo27bobo27bobo27bobobo$3o3bo19bo 5b2o22bo5b2o4bo17bo5b2o22bo5b2o22bo5b2o17bo4bo5b2o31bobobo25bobobo25bo bobo25bobobo4bo20bobobo$26bo29bo11b3o15bo29bo29bo24b2o3bo37b2o2b2o24b
2o2b2o24b2o2b2o24b2o2b2o4bobo17b2o2bo$26bo29bo29bo29bo29bo23bobo3bo38b o29bo29bo29bo8b2o19bo$36b2o28b2o145bo29bo29bo29bo29bo$30b2o4b2o22b2o4b 2o22b2o28b2o28b2o28b2o31b2o28b2o28b2o28b2o6b3o19b2o$30bobo27bobo27bobo
27bobo27bobo27bobo21b3o27b3o74bo$31b2o28b2o28b2o28b2o28b2o28b2o129bo$
202bo5bo23bo5bo$202bo5bo23bo5bo$127bo28bo29bo15bo5bo23bo5bo$34b3o27b3o 59bo29bo29bo$126b3o27bo29bo17b3o27b3o$68b2o$68bobo$68bo57b2o$126bobo
100b2o$126bo76b2o25b2ob2o$203b2o24bo3b2o!

16.1110 in 8 gliders with no cleanup (I wasn't satisfied with any of the cleanups I found):

Code: Select all

x = 63, y = 68, rule = B3/S23
19bobobobo5bobobo3bobo2bo5bobo3bobobo2$12bo6bo5bo5bo6bo3bobobo3bobo3bo bo3bo2$10bobobo4bo5bo5bobobo2bobobobo2bo2bobo3bobo3bo$60bo$12bo6bo5bo
5bo6bo3bobo3bobobo3bobo2$19bobobobobobobobobo2bo3bobo5bo2bobo2bo13$43b
obo$43b2o$44bo32$6bo$6bobo$obo3b2o8bo$2o12b2o$bo13b2o$4b2o12b3o$3b2o6b o6bo$5bo4bo8bo$10b3o2$7b3o$7bo$8bo!

From that synthesis 16.1109 in 10 gliders without cleanup:

Code: Select all

x = 138, y = 68, rule = B3/S23
19bobobobo5bobobo3bobo2bo5bobo3bobobo2$12bo6bo5bo5bo6bo3bobobo3bobo3bo bo3bo2$10bobobo4bo5bo5bobobo2bobobobo2bo2bobo3bobo3bo$60bo$12bo6bo5bo
5bo6bo3bobo3bobobo3bobo2$19bobobobobobobobobo2bo3bobo5bo2bobo2bo13$43b
obo$43b2o$44bo26$104bo$105bo$103b3o$107bo$107bobo$107b2o$6bo$6bobo64b
2o28b2o27b2o$obo3b2o8bo54bo2bo26bo2bo26bo2bo$2o12b2o54bob2o26bob2o26bo
b2o$bo13b2o54bo29bo29bo$4b2o12b3o51b4obo24b4obo24b4obo$3b2o6bo6bo55bob 2o26bob2o26bob2o$5bo4bo8bo$10b3o2$7b3o$7bo$8bo!

Unfortunately, 16.2204 costs 17 gliders:

Code: Select all

x = 228, y = 36, rule = B3/S23
126bo$127bo$125b3o$99b2o28b2o$98bo2bo26bo2bo$99b2o20bo7b2o$105b2o15bo
12b2o28b2o29b2o28b2o$74bo31bo13b3o13bo29bo30bo29bo$70bo3bobo27bo29bo6b
o22bo30bo29bo$71bo2b2o17b2o7b4o17b2o7b4o4bo21b4o27b4o26b4o$69b3o21b2o
6bo21b2o6bo8b3o18bo30bo29bo$100bob2o4bo21bob2o4bo21bob2o27bob2o26bob2o$80bo20bo2bo2bobo21bo2bo2bobo21bo2bo27bo2bo26bo2bo$79bo23b2o3b2o23b2o 3b2o23b2o29b2o27b2o$79b3o$199bo$198b2o$198bobo$bo30bo29bo131b2o$2bo29b o29bo132b2o$3o29bo29bo131bo3$b2o102bo29bo$obo101bobo27bobo$2bo41b2o28b 2o6b2o21bo29bo$13b3o28b2o28b2o5b2o$15bo67bo$14bo120b3o$16b3o46b2o68bo$
16bo47bobo69bo$17bo48bo$60b2o$59bobo7b2o$61bo7bobo$69bo!  Last edited by Goldtiger997 on March 17th, 2017, 7:49 pm, edited 1 time in total. Goldtiger997 Posts: 627 Joined: June 21st, 2016, 8:00 am ### Re: 16 in 16: Efficient 16-bit Synthesis Project 16.2318 in 12 gliders (bad cleanup): Code: Select all x = 171, y = 55, rule = B3/S23 123bo$122bo$122b3o20$148bo$148bobo$148b2o2$116bo29bo$75bo5bo3bobo28bo
29bo$75b2o5b2ob2o29bo29bo$74bobo4b2o3bo3$109b2o28b2o28b2o$10bo30bo39bo
28bo29bo29bo$11bo29bo39bo25b3o27b3o27b3o$9b3o29bo39bo25bo29bo29bo$105b 2o28b2o28b2o$103bo2bobo24bo2bobo24bo2bobo$10b2o91b2o2b2o24b2o2b2o24b2o 2b2o$bo7bobo$2bo8bo75b2o$3o32bo39bo11bobo20bo29bo$34bobo37bobo10bo22bo 29bo$3b3o28bobo37bobo33bo29bo$5bo29bo39bo$4bo137b2o$142bobo$142bo2$100b2o28b2o$100b2o28b2o2$106b2o23bo4b2o$105bobo23b2o2bobo$106bo23bobo 3bo!  16.2182 also in 12 gliders (can be improved through constellations): Code: Select all x = 168, y = 35, rule = B3/S23 102b2o28b2o28b2o$102bobob2o24bobob2o24bobob2o$8bo3bo91b2obo26b2obo26b 2obo$9bo2bobo88bo29bo29bo$7b3o2b2o28b3o27b3o26b3o27b3o27b3o$100bo29bo
29bo$100b2o28b2o28b2o3$79bo$78bo$7bo30b2o28b2o8b3o$5bobo2b2o26bobo27bo bo$6b2ob2o28bo29bo$11bo2$99bo29bo$61bo37bo29bo$59bobo37bo29bo$60b2o18b 2o13bo29bo$80bobo11bobo27bobo$32b2o28b2o16bo13b2o28b2o$b2o28bo2bo26bo
2bo$obo29b2o28b2o$2bo96b2o28b2o4bo$4b2o92bo2bo26bo2bo2bo$4bobo91bobo
27bobo3b3o$4bo94bo29bo$42b2o28b2o28b2o28b2o$12b3o27b2o28b2o27bo2bo26bo 2bo$12bo89b2o28b2o$13bo$9b3o$11bo$10bo!