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16 in 16: Efficient 16-bit Synthesis Project

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

16 in 16: Efficient 16-bit Synthesis Project

Postby BobShemyakin » December 20th, 2016, 3:38 pm

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

Postby BlinkerSpawn » December 20th, 2016, 4:54 pm

16.1805 reduced by 2, which in turn reduces 16.1810 to 14G:
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!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby AbhpzTa » December 21st, 2016, 11:36 am

16.406 reduced to 15G, 16.1801 reduced to 14G:
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).
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby chris_c » December 21st, 2016, 12:41 pm

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:

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!
chris_c
 
Posts: 743
Joined: June 28th, 2014, 7:15 am

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

Postby Extrementhusiast » December 21st, 2016, 5:06 pm

From the original list:
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)
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Extrementhusiast
 
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Goldtiger997 » December 22nd, 2016, 7:25 am

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

16.709 in 9 gliders:
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:
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!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby AbhpzTa » December 22nd, 2016, 12:48 pm

Goldtiger997 wrote:16.811 in 14 gliders:
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:
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).
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby BobShemyakin » December 22nd, 2016, 2:20 pm

16.44 in 11G
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
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!

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

Postby Extrementhusiast » December 22nd, 2016, 8:31 pm

Major improvement to 16.406:
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)
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Goldtiger997 » December 26th, 2016, 12:04 am

16.1797 in 12 gliders:
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:

x = 9, y = 15, rule = B3/S23
bo$obo$obo$bo4$2b2o3bo$b2obobobo$bo2bobobo$b3o3bo$2b2o3$3b3o!


Can anyone else?
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby chris_c » December 26th, 2016, 8:12 am

Goldtiger997 wrote:16.1797 in 12 gliders:

Reduced the cleanup by one glider:
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:

x = 9, y = 15, rule = B3/S23
bo$obo$obo$bo4$2b2o3bo$b2obobobo$bo2bobobo$b3o3bo$2b2o3$3b3o!


Can anyone else?


11 gliders:

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:

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

Postby Goldtiger997 » December 27th, 2016, 8:28 am

I've been trying to synthesise 16.2446:

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:

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:

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

Postby Hdjensofjfnen » December 27th, 2016, 9:40 pm

No. But while I was hunting for it:

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

Pattern of the month (September 2017):
#C [[ AUTOFIT ]]
x = 7, y = 9, rule = B34tw/S23
2o$2o$4b2o$6bo$3bo2bo$6bo$4b2o$2o$2o!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby BobShemyakin » January 2nd, 2017, 2:44 pm

16.787 in12G:
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:
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!



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

Postby Goldtiger997 » January 9th, 2017, 10:05 pm

How many gliders does it take to convert this 17-bit still life...

x = 7, y = 9, rule = B3/S23
2b2o$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!


... into 16.2446...

x = 7, y = 9, rule = B3/S23
2bo$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!


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

Postby A for awesome » January 9th, 2017, 10:10 pm

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

x = 7, y = 9, rule = B3/S23
2b2o$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!


... into 16.2446...

x = 7, y = 9, rule = B3/S23
2bo$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!


...?

Two:
x = 9, y = 16, rule = B3/S23
6bo$6bobo$6b2o$2bobo$3b2o$3bo2$2b2o$bobo$2bo2$5o$o3bo$3bo$4b3o$6bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

http://conwaylife.com/wiki/A_for_all

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

Postby Goldtiger997 » January 9th, 2017, 11:38 pm

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

16.2446 but with boat instead of tub


... into 16.2446...

16.2446


...?

Two:
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)

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:

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

Postby AbhpzTa » January 11th, 2017, 12:33 pm

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

16.2446 but with boat instead of tub


... into 16.2446...

16.2446


...?

Two:
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!:

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:
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)
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?
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)
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).
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Gamedziner » January 12th, 2017, 7:45 am

AbhpzTa, don't forget, cleanup is part of the synthesis.
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby BlinkerSpawn » January 12th, 2017, 8:20 am

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

Postby Goldtiger997 » January 15th, 2017, 6:39 am

16.2688 in 12 gliders:

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

Postby chris_c » January 15th, 2017, 10:27 am

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

Postby PHPBB12345 » January 16th, 2017, 4:05 am

16.???:
x = 8, y = 5, rule = B3/S23
4b2o$4bobo$5bobo$2obobobo$ob2ob2o!

x = 7, y = 6, rule = B3/S23
3b2o$3bobo$bobo2bo$obobobo$obob2o$bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Goldtiger997 » January 16th, 2017, 4:31 am

PHPBB12345 wrote:16.???:
x = 8, y = 5, rule = B3/S23
4b2o$4bobo$5bobo$2obobobo$ob2ob2o!

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/blob/master/still16.txt

Why do you want to know?

...

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

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:

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:

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:

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:

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):

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:

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:

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

Postby Goldtiger997 » January 19th, 2017, 9:42 pm

16.2318 in 12 gliders (bad cleanup):

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):

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!
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Goldtiger997
 
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