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

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

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

Code: Select all

``16G synth``
Using a TL-block constellation brings it down to 15G:

Code: Select all

``````x = 135, y = 427, rule = B3/S23
116b3o2\$114bo5bo\$114bo5bo\$114bo5bo2\$12b3o5bo95b3o\$14bo3bobo\$13bo5b2o2\$
22bo\$20b2o99b2o\$21b2o98b2o59\$55bo\$54bo\$54b3o\$10bo\$8bobo\$9b2o23\$134bo\$
16b3o97b3o15bo\$134bo\$14bo5bo93bo5bo\$14bo5bo93bo5bo\$14bo5bo93bo5bo2\$16b
3o97b3o5\$21b2o98b2o\$21b2o98b2o56\$64bo\$64bobo\$64b2o15\$8bobo\$9b2o\$9bo12\$
17bo96b2o\$17bo15b3o78b2o\$17bo\$118b2obo\$13b3o3b3o96bob2o2\$17bo101b5o\$
17bo99bo2bo2bo\$17bo99b2o4\$21b2o\$21b2o15\$54b2o\$54bobo\$54bo5\$5b2o\$4bobo\$
6bo58\$10bo\$11bo\$9b3o3\$14b2o\$14b2o2\$18b2obo96b2obo\$18bob2o96bob2o2\$19b
5o95b5o\$17bo2bo2bo93bo2bo2bo\$17b2o98b2o87\$2bo\$obo\$b2o6\$18b2obo96b2obo\$
18bob2o96bob2o2\$19b5o95b5o\$17bo2bo2bo96bo2bo\$17b2o99bo\$118b2o13\$9bo\$2b
2o5b2o24bo\$bobo4bobo23b2o\$3bo9b2o19bobo\$12bobo\$14bo!
``````

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote: Using a TL-block constellation brings it down to 15G:
Thanks. I guess this should give 16.713 in 11G but I'm not going to complete it until tomorrow:

Code: Select all

``````x = 52, y = 49, rule = B3/S23
o\$b2o\$2o16\$27b2o\$26bo2bo\$27b2o2\$30b2o\$30b2o2\$22bo\$21bobo\$20bo3bo\$20bo
3bo\$20b2ob2o5\$30b3o4\$50b2o\$49b2o\$51bo6\$22b3o\$24bo\$23bo!
``````

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

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

Code: Select all

``rle``
Yes, 16.713 in 11 gliders:

Code: Select all

``````x = 64, y = 61, rule = B3/S23
o\$b2o\$2o3\$58bobo\$58b2o\$59bo14\$42bobo\$42b2o\$43bo3\$35bo\$33bobo\$34b2o2\$
36b3o\$38bo\$37bo6\$24bo\$24b2o\$23bobo11bobo\$37b2o\$31bo6bo\$30b2o\$30bobo4b
2o\$36b2o\$38bo4\$62b2o\$61b2o\$63bo6\$22b3o\$24bo\$23bo!
``````
Here are some predecessors for 16.1323 that have a hope of taking only 10 gliders, which would give 16.1398 in 15 gliders:

Code: Select all

``````x = 47, y = 17, rule = B3/S23
6bo34bo\$6bo34bo\$6bo34bo3\$8bo34bo\$6b2obo31b2obo\$7bobo32bobo\$8bo34bo2\$9b
2o33b2o\$9b3o32bobo\$45bo\$2bo34bo\$bobo32bobo\$o2bo31bo2bo\$b2o33b2o!
``````

AbhpzTa
Posts: 485
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

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

Code: Select all

``16G synth``
Using a TL-block constellation brings it down to 15G:

Code: Select all

``````x = 135, y = 427, rule = B3/S23
116b3o2\$114bo5bo\$114bo5bo\$114bo5bo2\$12b3o5bo95b3o\$14bo3bobo\$13bo5b2o2\$
22bo\$20b2o99b2o\$21b2o98b2o59\$55bo\$54bo\$54b3o\$10bo\$8bobo\$9b2o23\$134bo\$
16b3o97b3o15bo\$134bo\$14bo5bo93bo5bo\$14bo5bo93bo5bo\$14bo5bo93bo5bo2\$16b
3o97b3o5\$21b2o98b2o\$21b2o98b2o56\$64bo\$64bobo\$64b2o15\$8bobo\$9b2o\$9bo12\$
17bo96b2o\$17bo15b3o78b2o\$17bo\$118b2obo\$13b3o3b3o96bob2o2\$17bo101b5o\$
17bo99bo2bo2bo\$17bo99b2o4\$21b2o\$21b2o15\$54b2o\$54bobo\$54bo5\$5b2o\$4bobo\$
6bo58\$10bo\$11bo\$9b3o3\$14b2o\$14b2o2\$18b2obo96b2obo\$18bob2o96bob2o2\$19b
5o95b5o\$17bo2bo2bo93bo2bo2bo\$17b2o98b2o87\$2bo\$obo\$b2o6\$18b2obo96b2obo\$
18bob2o96bob2o2\$19b5o95b5o\$17bo2bo2bo96bo2bo\$17b2o99bo\$118b2o13\$9bo\$2b
2o5b2o24bo\$bobo4bobo23b2o\$3bo9b2o19bobo\$12bobo\$14bo!
``````
Reduced to 13G:

Code: Select all

``````x = 65, y = 170, rule = B3/S23
58bo\$58bo\$58bo2\$54b3o3b3o2\$4bo53bo\$4b2o4bo47bo\$3bobo5b2o45bo\$10b2o2\$
12bo\$11bo50b2o\$11b3o48b2o33\$28bo\$28bobo\$28b2o2\$8bo46b2o\$8bo46b2o\$8bo\$
59b2obo\$4b3o3b3o46bob2o2\$8bo11bo39b5o\$8bo12b2o35bo2bo2bo\$8bo11b2o2b3o
31b2o\$24bo\$25bo2\$12b2o\$12b2o2\$16b3o\$18bo\$17bo30\$3bo\$bobo\$2b2o\$5b2o\$5b
2o2\$9b2obo46b2obo\$9bob2o46bob2o2\$10b5o45b5o\$8bo2bo2bo43bo2bo2bo\$8b2o
48b2o45\$bo7b2obo46b2obo\$2bo6bob2o46bob2o\$3o\$10b5o45b5o\$8bo2bo2bo46bo2b
o\$8b2o49bo\$59b2o5\$8b2o\$b3o5b2o6b2o\$3bo4bo7b2o\$2bo9b3o3bo\$14bo\$13bo!``````
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote: Yes, 16.713 in 11 gliders
Thanks!
Godltiger997 wrote: Here are some predecessors for 16.1323 that have a hope of taking only 10 gliders, which would give 16.1398 in 15 gliders:
In 12G...

Code: Select all

``````x = 73, y = 95, rule = B3/S23
3bo\$4b2o\$3b2o18\$o\$b2o\$2o25\$40bo\$28bo11bobo\$29b2o9b2o\$28b2o4\$38bo\$34bob
2o\$32bobo2b2o\$33b2o6\$41bo\$40bobo\$23b3o8b2o4bo2bo\$25bo7b2o6b2o\$24bo10bo
3\$35b2o\$34b2o\$36bo20\$71bo\$70b2o\$70bobo!
``````
Here's a quick peek at the SLs at 20G and above:

Code: Select all

``````16.1139    xs16_kq23z124871         25
16.353     xs16_321fgc453           23
16.621     xs16_g5r8jdz11           23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.1846    xs16_25a8c93zw33         22
16.2313    xs16_08u16853z32         22
16.159     xs16_2egmd1e8            21
16.218     xs16_3pajc48c            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.217     xs16_3146pajo            20
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
``````

Sokwe
Moderator
Posts: 1625
Joined: July 9th, 2009, 2:44 pm

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

16.1139 in 15G:

Code: Select all

``````x = 339, y = 34, rule = B3/S23
238bo\$236bobo29b2o28b2o\$225bo11b2o29b2o28b2o\$226bo\$224b3o10bo57b3o\$
237b2o58bo\$236bobo57bo7\$2bobo31bo29bo29bo29bo29bo29bo29bo15bo13bo29bo
29bo29bo\$3b2o29b3o27b3o27b3o27b3o27b3o27b3o27b3o16bo10b3o27b3o27b3o27b
3o\$3bo29bo29bo29bo29bo29bo29bo29bo17b3o9bo29bo29bo29bo\$33b2o24bo3b2o
27bobo27bobo27bobo27bobo27bobo27bobo29bo29bo29bo\$3o57bo32b2o28b2o28b2o
28b2o28b2o28b2o28b2o28b2o28b2o\$2bo55b3o96b2o28b2o28b2o28b2o24bo3b2o24b
o3b2o24bo3b2o\$bo155bo20bo8bo29bo29bo26bo2bo26bo2bo26bo2bo\$60b3o64b2o
26bobo21bo5bobo26b2obo26b2obo27bobo27bobo27bobo\$60bo65b2o27b2o20b3o5b
2o27bobo27bobo29bo29bo29bo\$61bo61b2o3bo\$122bobo55b3o\$124bo57bo\$181bo\$
188bo\$187b2o\$187bobo3\$247b3o\$247bo\$248bo!``````
-Matthias Merzenich

Posts: 1938
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

16.353 takes 12 (left) but might be as few as 10 (right):

Code: Select all

``````x = 47, y = 18, rule = B3/S23
11b2o\$11b2o3\$41bo2b2o\$41bo2bo\$4b3o7b2o19b2o4bo3bo\$14bo19bo2bo7b2o\$b2o
11bobo18b2o\$o2bo11b2o\$b2o2\$40bo\$39bobo\$6bo32bo2bo\$5bobo32b2o\$5bo2bo\$6b
2o!
``````
Reaction for 16.621:

Code: Select all

``````x = 111, y = 98, rule = B3/S23
96bo\$95bo\$95b3o35\$42b2o\$41bo2bo\$42b2o3\$42b2o\$41bobo\$42bo4bo\$47b2o\$46bo
bo\$46b2o\$46bo6bobo\$53b2o\$34b2o18bo\$33bo2bo10bo\$34bobo9bobo\$35bo9bo3bo\$
46bobo\$47bo35\$3o\$2bo\$bo3\$109bo\$108b2o\$108bobo!
``````
Last edited by BlinkerSpawn on April 27th, 2017, 7:22 am, edited 1 time in total.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Extrementhusiast
Posts: 1817
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

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

Code: Select all

``RLE``
Definitely ten:

Code: Select all

``````x = 18, y = 21, rule = B3/S23
15bo\$14bo\$11bo2b3o\$12bo\$10b3o3\$13bo\$13bobo\$13b2o\$6b3o\$b2o\$o2bo11bobo\$b
2o12b2o\$16bo3\$6bo4b3o\$5bobo3bo\$5bo2bo3bo\$6b2o!
``````
However, I have a strong suspicion that it can be made with even less, at least partly because of this:

Code: Select all

``````x = 6, y = 8, rule = B3/S23
2bo\$obo\$b2o2\$3b2o\$2bo2bo\$2bobo\$3bo!
``````
I Like My Heisenburps! (and others)

Sokwe
Moderator
Posts: 1625
Joined: July 9th, 2009, 2:44 pm

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

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

Code: Select all

``````x = 75, y = 24, rule = B3/S23
10bo\$9bo\$9b3o\$70bobo\$2bo34bobo30b2o\$3b2o32b2o32bo\$2b2o2bo26bo4bo30bo\$
6bobo20b2obobo24b2ob2o4b2o\$6b2o22bobobo2b2o21bobo5bobo\$29bo2b2o2b2o21b
o2bobo\$29b2o7bo20b2o2b2o8bo\$72b2o\$72bobo\$2o\$obo\$o58b2o\$58bobo\$60bo\$66b
2o\$66bobo\$66bo\$60b2o\$59bobo\$61bo!``````
-Matthias Merzenich

Posts: 1938
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

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

Code: Select all

``RLE``
Definitely ten:

Code: Select all

``````rle
``````
My estimate of ten was based upon making the sparked-R octomino in 3 gliders like the G+loaf collision does and everything else in 2, and the G+loaf collision doesn't seem to fit with 2G blinker syntheses.
Unless you can make the three-object constellation in 4G total your synthesis would still take 11 or 12 (5G + 5-6 for three objects + 1 cleanup).
Another reaction for 16.621, this time neater:

Code: Select all

``````x = 13, y = 9, rule = B3/S23
4bobo2\$5bo\$5b2ob3o\$5b2o2\$bo8b3o\$b2o\$obo!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

Sokwe wrote:16.1139 in 15G:...
Nicely done!
chris_c wrote:
Godltiger997 wrote: Here are some predecessors for 16.1323 that have a hope of taking only 10 gliders, which would give 16.1398 in 15 gliders:
In 12G...
I'll see if I can reduce it (I highly doubt I'll get it to ten though).
BlinkerSpawn wrote:16.353 takes 12 (left) but might be as few as 10 (right):

Code: Select all

``````x = 47, y = 18, rule = B3/S23
11b2o\$11b2o3\$41bo2b2o\$41bo2bo\$4b3o7b2o19b2o4bo3bo\$14bo19bo2bo7b2o\$b2o
11bobo18b2o\$o2bo11b2o\$b2o2\$40bo\$39bobo\$6bo32bo2bo\$5bobo32b2o\$5bo2bo\$6b
2o!``````
16.353 in 9 gliders:

Code: Select all

``````x = 30, y = 28, rule = B3/S23
bo\$2bo\$3o6\$27bobo\$27b2o\$28bo\$17bo\$15bobo\$11bo4b2o\$9bobo\$10b2o6b3o\$20bo
6bo\$19bo6bo\$26b3o2\$12bobo5b2o\$13b2o4bobo\$13bo7bo3\$20b2o\$19b2o\$21bo!
``````

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

Sokwe wrote:16.697 can be done in 12G by trivially modifying the synthesis of 16.698:
The same component also reduces 16.1105 and 16.1464
Goldtiger997 wrote:16.353 in 9 gliders:
This reduces 16.358 to 14G.

Here is 16.2313 in 15G:

Code: Select all

``````x = 128, y = 411, rule = B3/S23
27bo\$26bo\$26b3o\$21bo\$22bo\$20b3o\$123b2o\$123b2o3\$125b3o2\$22b2o\$23b2o\$22b
o69\$13bobo4bo13bo\$14b2o2bobo12bo\$14bo4b2o12b3o4\$120b2o2b2o\$120b2o2b2o
16\$23b2o98b2o\$23b2o98b2o3\$25b3o97b3o74\$4bo\$5b2o\$4b2o2\$122bo\$20b2o2b2o
95bobo\$20b2o2b2o95bob3o\$120b2o4bo\$121bo3b2o\$119bo\$119b2o12\$23b2o\$23b2o
3\$25b3o5\$6b2o\$7b2o\$6bo2\$2o\$b2o\$o20\$63b3o\$63bo\$64bo45\$22bo99bo\$21bobo
97bobo\$21bob3o95bob3o\$20b2o4bo93b2o4bo\$21bo3b2o94bo3b2o\$19bo99bo\$19b2o
98b2o4b2o\$124bobo\$125bo7\$15b2o\$14bobo\$16bo67\$42bo\$41bo\$16bo24b3o\$14bob
o\$15b2o12\$22bo99bo2b2o\$21bobo97bobo2bo\$21bob3o95bobobo\$20b2o4bo93b2o2b
o\$21bo3b2o94bo\$19bo99bo\$19b2o4b2o92b2o\$24bobo\$25bo9\$41bo\$40b2o\$40bobo\$
10bo\$10b2o\$9bobo!
``````
SLs at 20G or above:

Code: Select all

``````16.621     xs16_g5r8jdz11           23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.1846    xs16_25a8c93zw33         22
16.159     xs16_2egmd1e8            21
16.218     xs16_3pajc48c            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.217     xs16_3146pajo            20
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
``````
EDIT
16.621 in 14G:

Code: Select all

``````x = 120, y = 80, rule = B3/S23
47bo\$46bo\$46b3o\$19bo\$20bo\$18b3o3\$43bo\$42bo\$42b3o4\$12bo19bo\$13bo19b2o\$
11b3o18b2o4\$51bo\$35bobo12bo\$36b2o12b3o\$36bo5\$32b2o81b2ob2o\$31bobo82bob
o\$33bo81bo3bo\$116b2obo\$114bobobo\$114b2o\$20bo\$20b2o\$19bobo2\$31bo\$31b2o
75b2o\$30bobo74bo2bo\$45b2o61b2o\$45bobo\$38b2o5bo57b3o\$38bobo64bo\$38bo65b
o32\$2o\$b2o\$o!
``````
EDIT2: 16.829 in 8G:

Code: Select all

``````x = 23, y = 26, rule = B3/S23
7bo\$8bo\$6b3o10bo\$18bo\$18b3o\$11bo\$12b2o\$11b2o\$6b3o\$8bo\$7bo\$2o\$b2o\$o4\$
12bo\$12b2o7bo\$11bobo6b2o\$20bobo3\$13b3o\$15bo\$14bo!
``````
Last edited by chris_c on April 27th, 2017, 7:21 pm, edited 2 times in total.

Posts: 1938
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

Tough reaction for 16.829:

Code: Select all

``````x = 23, y = 10, rule = B3/S23
13b3o\$13b3o2\$7b2ob3o\$b2o4b2o\$o2bo\$b2ob2o\$b2ob2o14b2o\$3bo16bobo\$20bo!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

dvgrn
Moderator
Posts: 6277
Joined: May 17th, 2009, 11:00 pm
Contact:

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

chris_c wrote: SLs at 20G or above:
...
16.2309 xs16_8kk31e8z641 21
This one is an easy 14G from the first soup I tried, and can no doubt be done in less -- possibly starting from T=175 in this pattern:

Code: Select all

``````#C 16.2309 in 14G
x = 153, y = 151, rule = B3/S23
bo\$2bo\$3o6\$129bo\$127b2o\$128b2o51\$103bo\$103bobo\$103b2o14\$70b2o\$69bobo\$
71bo\$78b2o\$77b2o\$79bo2\$64b2o\$63bobo\$65bo2\$103b3o\$60b2o19b2o20bo\$59bobo
19bobo20bo\$61bo19bo3\$56bo\$56b2o\$55bobo2\$61bo26b2o\$61b2o24b2o\$60bobo26b
o29\$150b2o\$150bobo\$150bo17\$b2o\$obo\$2bo!``````
Minor apologies for the arbitrary continuous synthesis -- it's really ten separate stages.

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

Code: Select all

``````x = 26, y = 18, rule = B3/S23
14bo\$13bobo\$12bo3bo\$12bo3bo\$12bo3bo\$13bobo\$14bo2\$11b2o11bo\$11b2o4b3o3b
obo\$17b3o3bobo\$bo14bo3bo3bo\$b2o14b3o\$obo14b3o2\$21bo\$21bo\$21bo!``````

Posts: 1938
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

From 13G w/ that second reaction:

Code: Select all

``````x = 48, y = 60, rule = B3/S23
45bo\$45bobo\$45b2o13\$14bobo\$15b2o9bo\$15bo10bobo\$26b2o3\$12bo\$13b2o\$12b2o
5bo\$17bobo13bo\$18b2o11b2o\$32b2o4\$35b2o\$34b2o\$9b2o25bo\$10b2o\$9bo\$bo17b
2o\$b2o17b2o\$obo16bo10b2o\$30bobo\$30bo\$26b3o\$28bo\$27bo15\$6b2o\$5bobo\$7bo!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

Code: Select all

``````x = 23, y = 10, rule = B3/S23
13b3o\$13b3o2\$7b2ob3o\$b2o4b2o\$o2bo\$b2ob2o\$b2ob2o14b2o\$3bo16bobo\$20bo!
``````
16.829 in 9 gliders:

Code: Select all

``````x = 37, y = 31, rule = B3/S23
8\$26bo\$24b2o\$25b2o2\$4bo\$4bobo\$4b2o15bo\$2bo17bo\$obo12bo4b3o\$b2o4bobo5bo
bo\$7b2o6b2o\$8bo\$28b2o\$27b2o\$10b2o17bo\$9bobo\$11bo2\$32bo\$31b2o\$31bobo!
``````
I spent far too long on that synthesis.
Last edited by Goldtiger997 on April 28th, 2017, 8:39 am, edited 1 time in total.

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

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

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

16.1702 in 11G or less:

Code: Select all

``````x = 39, y = 27, rule = B3/S23
36bo\$36bobo\$36b2o5\$12bo\$13bo\$11b3o\$bo\$2bo\$3o\$25b2o\$17b2o6b2o\$8b3o5bo2b
o\$10bo6b2o\$9bo4\$3b3o\$5bo\$4bo12b2o\$16bobo13b2o\$18bo12b2o\$33bo!
``````

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

yootaa wrote:16.1702 in 11G or less:

Code: Select all

``````x = 39, y = 27, rule = B3/S23
36bo\$36bobo\$36b2o5\$12bo\$13bo\$11b3o\$bo\$2bo\$3o\$25b2o\$17b2o6b2o\$8b3o5bo2b
o\$10bo6b2o\$9bo4\$3b3o\$5bo\$4bo12b2o\$16bobo13b2o\$18bo12b2o\$33bo!
``````
16.1702 in 8 gliders:

Code: Select all

``````x = 46, y = 32, rule = B3/S23
43bo\$43bobo\$43b2o3\$o\$b2o\$2o2\$23bo\$24b2o\$23b2o3\$18bo\$19bo2b2o\$17b3obobo
\$23bo9\$3b2o\$4b2o\$3bo13bo\$17b2o23b2o\$16bobo23bobo\$42bo!
``````
(EDIT: I replaced a 9-glider synthesis with the above synthesis)

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

dvgrn wrote:Ooh, the next soup builds the still life in stages, starting from the eater
I did a 4G search for the necessary spark giving 16.2309 in 6G:

Code: Select all

``````x = 29, y = 31, rule = B3/S23
5\$13bo\$14bo\$12b3o\$4bo16bobo\$5bo15b2o\$3b3o16bo5\$16bo\$17bo\$15b3o3\$16b2o\$
17b2o\$16bo\$5bo\$5b2o\$4bobo!
``````
Quite often the reaction works as a simple 4G component:

Code: Select all

``````x = 18, y = 18, rule = B3/S23
bo\$2bo\$3o\$14b2obo\$14bob2o3\$13bo\$14bo\$12b3o3\$13b2o\$14b2o\$13bo\$2bo\$2b2o\$
bobo!
``````
I also found this alternative version with more clearance at the bottom in 6G:

Code: Select all

``````x = 22, y = 26, rule = B3/S23
12b2obo\$12bob2o2\$6bo\$obo4bo\$b2o2b3o\$bo4\$9b2o\$10b2obobo\$9bo3b2o\$14bo2\$
19b3o\$19bo\$20bo6\$b2o\$obo\$2bo!
``````
SLs taking 19G and above:

Code: Select all

``````16.1740    xs16_69acga6zx32         23
16.1846    xs16_25a8c93zw33         22
16.159     xs16_2egmd1e8            21
16.218     xs16_3pajc48c            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.2096    xs16_wck5b8oz311         21
16.217     xs16_3146pajo            20
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
16.18      xs16_caarzbd             19
16.131     xs16_660uhar             19
16.230     xs16_178jd2ko            19
16.801     xs16_08eharz321          19
16.1684    xs16_4aab9k8zx32         19
16.1694    xs16_4a5p6o8zx121        19
16.1912    xs16_at16426z32          19
16.1979    xs16_4ap30ga6zw121       19
16.2050    xs16_6ik8a52z065         19
16.2162    xs16_0at16426z32         19
16.2200    xs16_06agc93z2521        19
16.2307    xs16_6ik8a52z641         19
16.2316    xs16_0at16413z32         19
``````

dvgrn
Moderator
Posts: 6277
Joined: May 17th, 2009, 11:00 pm
Contact:

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

chris_c wrote:I did a 4G search for the necessary spark giving 16.2309 in 6G...
Nice! I was hoping there'd be something like that -- the spark looked like it would be small enough to show up in a 3G or 4G search.

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

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

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

dvgrn wrote:
chris_c wrote:I did a 4G search for the necessary spark giving 16.2309 in 6G...
Nice! I was hoping there'd be something like that -- the spark looked like it would be small enough to show up in a 3G or 4G search.

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

-- I'm interested in the way these kinds of searches are currently done, because of my ongoing plot to come up with an actual total count for three-glider collisions, along with the various lists of useful constellations that might come out of an exhaustive enumeration. Haven't figured out how to usefully catalogue this kind of edgy spark yet...!
The spark eventually settles into a beehive, therefore the first task was a 4G search for beehives using some old LifeAPI code. This took the longest time. I intended to post-process this with Golly but it was taking too long. Instead I wrote a LifeAPI program to analyse a series of reactions and output the RLE of the generation that is N generations before the final pattern appears. N was equal to 12 in my case. I post-processed this file in Golly looking for the desired spark. That was still quite slow.

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

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

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

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

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

Code: Select all

``````x = 29, y = 31, rule = B3/S23
5\$13bo\$14bo\$12b3o\$4bo16bobo\$5bo15b2o\$3b3o16bo5\$16bo\$17bo\$15b3o3\$16b2o\$
17b2o\$16bo\$5bo\$5b2o\$4bobo!
``````
Quite often the reaction works as a simple 4G component:

Code: Select all

``````x = 18, y = 18, rule = B3/S23
bo\$2bo\$3o\$14b2obo\$14bob2o3\$13bo\$14bo\$12b3o3\$13b2o\$14b2o\$13bo\$2bo\$2b2o\$
bobo!
``````
...
16.2801 in 8G with this reaction:

Code: Select all

``````x = 69, y = 20, rule = B3/S23
36bobo\$37b2o\$37bo\$48bo\$49b2o\$5bo42b2o\$6bo\$4b3o54b2o\$47b3o11bo\$9bo39bo
13bo\$9bobo36bo13b2o\$9b2o50bo\$27b2o23b2o8b2o3b2o\$24bobobo20bobobo10bobo
bo\$24b2o23b2o13b2o\$35b3o\$3o34bo\$2bo8b2o23bo\$bo9bobo\$11bo!
``````
Bob Shemyakin

Extrementhusiast
Posts: 1817
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

16.723 and 16.833 in at most eleven gliders each:

Code: Select all

``````x = 84, y = 28, rule = B3/S23
2o\$2o\$9bo63bo\$7b2o56bo5b2o\$8b2o56bo5b2o\$60bo3b3o\$18b2o41bo\$bo15bo2bo
38b3o\$obo15b2o2b2o\$obo19bobo\$bo20bo2\$51b3o2\$6bo\$6bo\$6bo49b3o4b2o\$63bob
o\$63bo3\$60b3o\$62bo\$61bo2b3o\$64bo16b3o\$27b3o35bo15bo\$27bo54bo\$28bo!
``````
The first soup for the latter even suggests a component:

Code: Select all

``````x = 19, y = 17, rule = B3/S23
2b2o\$bobo\$bo12bo\$2o11bobo\$2b2o8bo2bo\$2bobo8b2o\$3bo3\$15b3o\$18bo\$18bo\$
15b3o2\$12b3o2\$12bo!
``````
Also, I think it's probably about time to reveal the whole list of 16-bit SLs.

EDIT: 16.18 in nine gliders:

Code: Select all

``````x = 47, y = 49, rule = B3/S23
o\$b2o\$2o13\$22bo\$20b2o\$16bobo2b2o\$17b2o\$17bo3\$25bo\$20bo4bo\$18bobo4bo\$
19b2o4\$15b2o\$14bobo\$16bo4\$28b2o\$27b2o\$29bo9\$45b2o\$44b2o\$46bo!
``````
I Like My Heisenburps! (and others)

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

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

Code: Select all

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

Code: Select all

``````x = 116, y = 38, rule = B3/S23
bo\$2bo\$3o8\$49b2o28b2o30b2o\$49b2o28b2o30bobo\$39bo48bo24bo\$39bobo44b2o
25b2o\$39b2o46b2o22b2o2bo\$37bo72bo2bobo\$17bo17bobo29b2o28b2o11b2o2bo\$
15bobo18b2o12bo15bo2bo10bo15bo2bo\$16b2o2bo28bobo15b2o10bobo15b2o2b2o\$
20bobo26bobo27bobo19bobo\$20b2o28bo29bo20bo2\$18bo\$19b2o\$18b2o35bo29bo\$
55bo29bo\$55bo29bo8\$3b3o\$5bo100b3o\$4bo101bo\$107bo!
``````
16.833 in 11 gliders (could not find a 3G synthesis of the blinker constellation):

Code: Select all

``````x = 34, y = 25, rule = B3/S23
23bo\$15bo5b2o\$16bo5b2o\$10bo3b3o\$obo8bo\$b2o6b3o\$bo3\$2o\$b2o\$o2\$5bo\$6b2o
5b2o\$5b2o6bobo\$13bo2\$6bo\$6b2o2b3o\$5bobo4bo\$11bo2b3o\$14bo16b3o\$15bo15bo
\$32bo!``````
Extrementhusiast wrote: The first soup for the latter even suggests a component:

Code: Select all

``````x = 19, y = 17, rule = B3/S23
2b2o\$bobo\$bo12bo\$2o11bobo\$2b2o8bo2bo\$2bobo8b2o\$3bo3\$15b3o\$18bo\$18bo\$
15b3o2\$12b3o2\$12bo!``````
It reduces to this:

Code: Select all

``````x = 33, y = 27, rule = B3/S23
2b2o18b2o\$bobo2b2o13bobo2b2o\$bo3b2o14bo4bo3bo\$2o18b2o4bo3bobo\$2b2o3bob
o12b2o6b2o\$2bobo2b2o13bobo2b2o\$3bo3b2o14bo3b2o14\$2b2o18b2o\$bobo2b2o13b
obo2b2o\$bo3b2o14bo3b2o\$2o18b2o\$2b2o3bo14b2o3bobo\$2bobo2b2o13bobo2b3o\$
3bo3b3o13bo3b2o!``````
EDIT:
Extrementhusiast wrote:EDIT: 16.18 in nine gliders:

Code: Select all

``````x = 47, y = 49, rule = B3/S23
o\$b2o\$2o13\$22bo\$20b2o\$16bobo2b2o\$17b2o\$17bo3\$25bo\$20bo4bo\$18bobo4bo\$
19b2o4\$15b2o\$14bobo\$16bo4\$28b2o\$27b2o\$29bo9\$45b2o\$44b2o\$46bo!
``````
Reduced to 8 gliders:

Code: Select all

``````x = 47, y = 49, rule = B3/S23
o\$b2o\$2o13\$22bo\$20b2o\$16bobo2b2o\$17b2o12bo\$17bo11b2o\$30b2o3\$20bo\$18bob
o\$19b2o6b2o\$27bobo\$27bo8\$28b2o\$27b2o\$29bo9\$45b2o\$44b2o\$46bo!
``````
EDIT2:

16.1740 in 9 gliders:

Code: Select all

``````x = 38, y = 51, rule = B3/S23
13bo\$11bobo\$12b2o5\$18bo\$16bobo\$17b2o2\$28bo\$26bobo\$27b2o2\$23bo5bo\$13b2o
6bobo5bobo\$12bobo7b2o5b2o\$14bo6\$17b2o\$16bobo\$18bo16b3o\$35bo\$36bo20\$2o\$
b2o\$o!``````
Can anyone make a converter out of this?:

Code: Select all

``````x = 12, y = 17, rule = B3/S23
8b2o\$10b2o\$5bob2o\$3bobobo\$4b2obobo\$8bobo\$9bo2\$2bo\$obo\$b2o\$4bo\$3bobob2o
\$3bobobo\$4b2obobo\$8bobo\$9bo!``````
EDIT3:

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

16.1846 in 11 gliders:

Code: Select all

``````x = 24, y = 24, rule = B3/S23
23bo\$8bo12b2o\$6bobo13b2o\$7b2o2\$19bobo\$8bo10b2o\$6bobo11bo\$7b2o2bo\$10bo\$
10b3o4bobo\$17b2o\$11bo6bo\$10b2o\$10bobo\$2bo\$obo\$b2o2\$3b3o\$5bo3b2o\$4bo5b
2o6bo\$9bo7b2o\$17bobo!
``````
It uses this new converter:

Code: Select all

``````x = 24, y = 24, rule = B3/S23
23bo\$8bo12b2o\$6bobo13b2o\$7b2o2\$19bobo\$3b2o14b2o\$3bobo14bo\$4bobo\$5bobo\$
6bobo8bobo\$7bobo7b2o\$8bobo7bo\$9bo2\$2bo\$obo\$b2o2\$3b3o\$5bo3b2o\$4bo5b2o6b
o\$9bo7b2o\$17bobo!
``````

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

16.218 in 10G gives 16.217 in 15G:

Code: Select all

``````x = 127, y = 140, rule = B3/S23
44bo\$43bo\$43b3o9\$30bobo\$10bo20b2o\$11bo19bo\$9b3o14bo\$27b2o\$26b2o\$8bo
114bobo\$6bobo110b2obob2o\$7b2o110bob2o\$123b2obo\$31b2o90bob2o\$30bobo\$32b
o4\$12b2o4b3o\$13b2o5bo\$12bo6bo2\$19bo\$19b2o\$18bobo16b2o\$37bobo\$37bo64\$
30bobo\$o29b2o\$b2o28bo\$2o5\$bo\$2b2o\$b2o3\$bo\$2bo\$3o3\$23bobo93b2o2bobo\$19b
2obob2o93bo2bob2o\$19bob2o98b2o\$23b2obo96b2obo\$23bob2o96bob2o16\$2bo\$2b
2o\$bobo!
``````
Here are all 16-bit SLs costing at least 16G. There are currently 143:

Code: Select all

``````16.159     xs16_2egmd1e8            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.2096    xs16_wck5b8oz311         21
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.872     xs16_2lla8oz065          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
16.131     xs16_660uhar             19
16.230     xs16_178jd2ko            19
16.801     xs16_08eharz321          19
16.1684    xs16_4aab9k8zx32         19
16.1694    xs16_4a5p6o8zx121        19
16.1912    xs16_at16426z32          19
16.1979    xs16_4ap30ga6zw121       19
16.2050    xs16_6ik8a52z065         19
16.2162    xs16_0at16426z32         19
16.2200    xs16_06agc93z2521        19
16.2307    xs16_6ik8a52z641         19
16.2316    xs16_0at16413z32         19
16.155     xs16_3pabp46             18
16.600     xs16_6421344og84c        18
16.665     xs16_699mkiczx1          18
16.848     xs16_ca9b8oz0252         18
16.914     xs16_8kkja952zx1         18
16.926     xs16_3iajc4gozw1         18
16.1107    xs16_02egdbz2521         18
16.1130    xs16_oe12koz01ac         18
16.1558    xs16_3loz1226io          18
16.1711    xs16_c8idik8z023         18
16.1757    xs16_g8idik8z123         18
16.1790    xs16_178cia4z0321        18
16.1911    xs16_69q3213z32          18
16.1990    xs16_8e1tazx1252         18
16.1995    xs16_cik8a52z065         18
16.2201    xs16_0ggml96z641         18
16.2447    xs16_0g8it248cz23        18
16.2480    xs16_3iaczw1139c         18
16.15      xs16_178c1f84c           17
16.227     xs16_5b8r5426            17
16.265     xs16_259m861ac           17
16.380     xs16_4a40vh248c          17
16.616     xs16_i5pajoz11           17
16.640     xs16_c9bkkozw32          17
16.668     xs16_gbq1daz121          17
16.716     xs16_3pmk46zx23          17
16.748     xs16_39ege2z321          17
16.799     xs16_c8al56z311          17
16.803     xs16_c9bk46z311          17
16.843     xs16_4a9liczx56          17
16.875     xs16_4a5pa4z2521         17
16.1064    xs16_39m88cz6221         17
16.1073    xs16_3lkaa4z641          17
16.1097    xs16_ck0ol3z643          17
16.1276    xs16_3iakgozw1ac         17
16.1373    xs16_32q4goz4a43         17
16.1398    xs16_g88c93zc952         17
16.1685    xs16_c48n98czx23         17
16.1715    xs16_64p784czw23         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1867    xs16_069q453z311         17
16.1871    xs16_5bo8ge2z32          17
16.1882    xs16_259m453zx23         17
16.1905    xs16_8u16853z32          17
16.1991    xs16_8e1qbzx1252         17
16.2014    xs16_25a8kk8z0253        17
16.2045    xs16_25ao8ge2z032        17
16.2132    xs16_0g8it2sgz23         17
16.2356    xs16_25icggozx1ac        17
16.2467    xs16_0kc3213z34a4        17
16.2555    xs16_4a9jzxpia4          17
16.3163    xs16_wo443123zbd         17
16.3164    xs16_wo443146zbd         17
16.104     xs16_0j5ozj4pz11         16
16.115     xs16_0ol3z0mdz32         16
16.243     xs16_2egu16426           16
16.300     xs16_9fg4czbd            16
16.302     xs16_5b8o642ac           16
16.350     xs16_312461tic           16
16.360     xs16_2egu16413           16
16.593     xs16_3123c48gka4         16
16.724     xs16_j5o64koz11          16
16.762     xs16_jhke1e8z1           16
16.771     xs16_69qb8oz32           16
16.772     xs16_3h4e1daz011         16
16.810     xs16_ca9la4z311          16
16.822     xs16_8ehikozw56          16
16.836     xs16_4aajkczx56          16
16.838     xs16_ci9b8ozw56          16
16.840     xs16_c8idiczw56          16
16.856     xs16_kc32acz1252         16
16.953     xs16_0cil56z6221         16
16.995     xs16_0raik8z643          16
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1085    xs16_3h4e12koz011        16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1581    xs16_8o6413zrm           16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         16
16.1710    xs16_4a9bk46zx32         16
16.1717    xs16_4aajk46zx121        16
16.1720    xs16_4a4o79ozx121        16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1796    xs16_0bt06ioz32          16
16.1856    xs16_39u06a4z32          16
16.1857    xs16_39u0652z32          16
16.1864    xs16_31ke1e8z032         16
16.1929    xs16_0g5r8b5z121         16
16.1959    xs16_4ai31e8zx56         16
16.1994    xs16_0g9fgka4z121        16
16.2018    xs16_25a8c826zw33        16
16.2025    xs16_069q48cz2521        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2030    xs16_0i5q8a52z121        16
16.2060    xs16_69akg4czx56         16
16.2124    xs16_0g8jd2koz23         16
16.2129    xs16_0g8jt246z23         16
16.2190    xs16_032q4goz6413        16
16.2204    xs16_0gilla4z641         16
16.2214    xs16_0mq0c93z641         16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2317    xs16_cik8a52z641         16
16.2322    xs16_raak8zx1252         16
16.2323    xs16_ra248goz056         16
16.2445    xs16_ciligzx254c         16
16.2549    xs16_g4c3213zdb          16
16.2630    xs16_31e8gzxo9a6         16
16.2781    xs16_wj9c826z6221        16
16.3032    xs16_1784ozx342sg        16
``````