## 15 in 15: Efficient 15-bit Synthesis Project (DONE!)

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
Posts: 1970
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Alexey_Nigin wrote:Probably useless:

Code: Select all

``````x = 35, y = 32, rule = B3/S23
3bo\$2bobo\$2bo2bo\$3b2o3\$3o5\$8b3o\$10bo21b2o\$8b3o20bo2bo\$32b2o9\$20bo\$20bo
\$20bo\$6bo\$5bobo8b3o3b3o\$6b2o\$20bo\$20bo\$20bo!``````
Moved from >15G to precisely 15G, and begging for further improvement:

Code: Select all

``````x = 103, y = 57, rule = B3/S23
61bo\$62bo\$60b3o10\$93bo\$94b2o\$o92b2o\$b2o77bo\$2o79b2o\$80b2o19bo\$100bobo\$
53bobo44bobo\$53b2o46bo\$54bo\$96b2o\$88bo6bo2bo\$88bo7b2o\$88bo4\$7b3o70bo\$
80bo4bo\$80bo3bobo\$84bobo\$85bo\$15b3o\$17bo\$15b3o2\$87bo\$86bobo\$85bo2bo\$
84bo3b2o\$85b3o2bo\$87bobo\$88bo9bo\$91b2o3b2o\$27bo63b2o4b2o\$27bo\$27bo\$13b
o79b2o\$12bobo8b3o3b3o61b2o\$13b2o68b2o\$27bo55bobo\$27bo56bo\$27bo53b2o\$
80bobo\$82bo!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Kazyan
Posts: 989
Joined: February 6th, 2014, 11:02 pm

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Later in that reaction, we get something like this to work from:

Code: Select all

``````x = 12, y = 15, rule = B3/S23
8b2o\$7bo2bo\$8b2o4\$o10bo\$o8bobo\$b3o4b2obo\$10bo2\$8bo\$8b2o\$9b2o\$10bo!``````
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook.

Extrementhusiast
Posts: 1844
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Alexey_Nigin wrote:Probably useless:

Code: Select all

``````x = 35, y = 32, rule = B3/S23
3bo\$2bobo\$2bo2bo\$3b2o3\$3o5\$8b3o\$10bo21b2o\$8b3o20bo2bo\$32b2o9\$20bo\$20bo
\$20bo\$6bo\$5bobo8b3o3b3o\$6b2o\$20bo\$20bo\$20bo!``````
Moved from >15G to precisely 15G, and begging for further improvement:

Code: Select all

``````x = 103, y = 57, rule = B3/S23
61bo\$62bo\$60b3o10\$93bo\$94b2o\$o92b2o\$b2o77bo\$2o79b2o\$80b2o19bo\$100bobo\$
53bobo44bobo\$53b2o46bo\$54bo\$96b2o\$88bo6bo2bo\$88bo7b2o\$88bo4\$7b3o70bo\$
80bo4bo\$80bo3bobo\$84bobo\$85bo\$15b3o\$17bo\$15b3o2\$87bo\$86bobo\$85bo2bo\$
84bo3b2o\$85b3o2bo\$87bobo\$88bo9bo\$91b2o3b2o\$27bo63b2o4b2o\$27bo\$27bo\$13b
o79b2o\$12bobo8b3o3b3o61b2o\$13b2o68b2o\$27bo55bobo\$27bo56bo\$27bo53b2o\$
80bobo\$82bo!
``````
Found a better cleanup:

Code: Select all

``````x = 70, y = 51, rule = B3/S23
o\$b2o\$2o8\$14bo\$15b2o\$14b2o3\$67bobo\$67b2o\$68bo8\$21b3o5\$29b3o\$31bo\$29b3o
10\$41bo\$41bo\$41bo\$27bo\$26bobo8b3o3b3o\$27b2o\$41bo\$41bo\$41bo!
``````
EDIT: Even better, all of the blinkers can be made at once:

Code: Select all

``````x = 261, y = 63, rule = B3/S23
2bo\$obo\$b2o4\$126bobo\$127b2o\$127bo8\$140bobo\$141b2o\$141bo2\$198bo\$196b2o
33bo\$197b2o33bo\$230b3o2bo\$234bobo\$234bobo\$235bo2\$230b2o\$229bo2bo\$230b
2o2\$78b3o68b3o4\$153bo4bo\$153b2ob2o\$152bobo2b2o6\$221bo35bo\$220bobo33bob
o\$219bo2bo32bo2bo\$218bo3b2o30bo3b2o\$219b3o2bo30b3o2bo\$98bo70bo51bobo
33bobo\$98bo70bo52bo35bo\$82bobo13bo70bo55b2o3bo\$83b2o70bo69b2o2bo\$44bo
38bo10b3o3b3o51bobo8b3o3b3o55b3o\$42b2o111b2o\$43b2o38b3o12bo70bo57b2o\$
83bo14bo70bo57b2o\$84bo13bo70bo47b2o\$44b2o171bobo\$43b2o173bo\$45bo169b2o
\$214bobo\$216bo!
``````
I Like My Heisenburps! (and others)

mniemiec
Posts: 1156
Joined: June 1st, 2013, 12:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Alexey_Nigin wrote:Probably useless: ...
BlinkerSpawn wrote:Moved from >15G to precisely 15G, and begging for further improvement: ...
Extrementhusiast wrote:Found a better cleanup: ... EDIT: Even better, all of the blinkers can be made at once:
This also reduces the corresponding 20-bit mold to 20 (1 glider/bit), and two corresponding 21-bit oscillators to 18 and 17 (<1 glider/bit):

Code: Select all

``````x = 109, y = 77, rule = B3/S23
13bo29bo29bo29bo\$12bobo27bobo27bobo27bobo\$11bobbo26bobbo26bobbo26bobbo
\$10bo3boo24bo3boo24bo3boo24bo3boo\$11b3obbo8bo15b3obbo24b3obbo24b3obbo\$
13bobo8boo17bobobo25bobobobb3o20bobobbo\$14bo9bobo17bobo27bobo3bo23bo\$
18b3o24bo29bo5bo23boobo\$20bo58bo27bo\$19bo54boo3boo\$73bobobbobo\$20boo
53bo\$20bobo\$20bo8\$33bo\$32boo\$32bobo7\$13bo29bo\$12bobo27bobo\$11bobbo26bo
bbo\$10bo3boo24bo3boo\$11b3obbo24b3obbo\$13bobo8bobo16bobobbo\$14bo9boo18b
o3bo\$25bo22bo\$45bo\$22boo22boo\$21boo\$18bo4bo\$16boo\$17boo\$\$21b3o\$21bo\$
22bo3\$20b3o\$20bo\$21bo8\$10bo\$11boo\$10boo\$14bobo\$14boo\$15bo3\$40b3o\$\$obo
10bo24bo4bo\$boo9bobo23bo3bobo\$bo9bobbo23bobbobbo\$10bo3boo24bo3boo\$3boo
6b3obbo24b3obbo\$4boo7bobo27bobo\$3bo10bo29bo!
``````

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

### Re: 15 in 15: Efficient 15-bit Synthesis Project

AbhpzTa wrote: ...
=15:

Code: Select all

``````15.446  15.447  15.485  15.487  15.516  15.598  15.653  15.751  15.786  15.839
15.855  15.874  15.890  15.919  15.934  15.939  15.942  15.949  15.1024 15.1033
15.1034 15.1036 15.1060 15.1088``````
...
>15:

Code: Select all

``````15.451  15.457  15.458  15.475  15.476  15.477  15.478  15.480  15.483  15.486
15.497  15.501  15.507  15.512  15.562  15.578  15.619  15.620  15.698  15.723
15.731  15.759  15.791  15.797  15.834  15.835  15.840  15.848  15.849  15.860
15.868  15.918  15.923  15.947  15.960  15.983  15.986  15.1001 15.1012 15.1032
15.1035 15.1065``````
...
My lists differ slightly from those shown:
=15:

Code: Select all

``````15.446	15.447	15.487	15.516	15.578	15.598	15.653	15.751	15.786	15.839
15.855	15.876	15.890	15.891	15.919	15.934	15.939	15.942	15.949	15.1024
15.1033  15.1034  15.1060  15.1088``````
...
>15:

Code: Select all

``````15.451	15.457	15.475	15.476	15.477	15.478	15.480	15.483	15.486	15.497
15.501	15.507	15.512	15.562	15.619	15.620	15.723	15.731	15.759	15.791
15.797	15.835	15.840	15.848	15.849	15.860	15.868	15.918	15.923	15.947
15.960	15.983	15.986	15.1001  15.1012  15.1032  15.1065
``````
From the first list are excluded 15.485(13G) 15.874(9G) 15.1036(10G) :

Code: Select all

``````x = 171, y = 145, rule = B3/S23
121bo\$119b2o\$120b2o7\$106bo\$104b2o\$105b2o4\$98bo\$99bo\$97b3o\$48bo44b3o\$
47bo19bo27bo11bo17b2o18b2o18b2o\$47b3o16bobo25bo11bobo16bo19bo19bo\$bo
64bobo37bobo18bo2bo16bo2bo16bo2bo\$2bo47b3o14bo39bo18b5o15b5o15b5o\$3o
47bo114bo\$20b2o18b2o9bo8b2o38b2o26bo13bobo3bo17b3o\$2bo17bobo17bobo17bo
bo37bobo24bobo13b2o2bobo18bo\$b2o18bo19bo19bo39bo26bo14bo4bo\$bobo2\$142b
2o\$143b2o2b2o\$142bo4bobo\$147bo2\$87bo\$87b2o\$86bobo10\$72bo\$72b2o\$71bobo
22\$12bo\$12bobo\$b2o9b2o\$2b2o41bo\$bo3bobo36bo\$5b2o37b3o\$6bo55bo19bo19bo\$
22b2o18b2o17bobo17bobo17bobo\$22bo19bo18bo2bo16bo2bo16bo2bo\$23bo19bo18b
obo17bobo17bobo\$24bobo17bobo14b2obobo14b2obobo14b2obob2o\$25b2o18b2o18b
2o18b2o18bobo\$39b2o49bo15bo\$10bo29b2o48bobo\$9b2o28bo47b2ob2o\$9bobo31b
3o40bobo\$43bo44bo\$44bo33\$3bo\$4bo\$2b3o37bo\$41bo\$41b3o5bobo\$49b2o\$50bo\$b
o\$2bo15bobo21b2o7b2o\$3o15b2o23b2o5b2o\$19bo22bo9bo12b2o\$bo24b2o18b2o17b
obo\$b2o24bo19bo19bo\$obo23bo19bo19bo\$26b2o18b2o18b2o\$27bo2b2o15bo2b2o
15bo2b2o\$27bobobo15bobobo15bobobo\$12bobo13bo19bo19bo\$12b2o\$13bo3\$12b2o
\$12bobo\$12bo!
``````
but included still life (15.578) of 2 list and two still life (15.876 and 15.891), which in my database belong to 15G, but I have not seen in the discussion.
From the second list are excluded 15.458(10G) 15.698(12G) 15.1035(14G):

Code: Select all

``````x = 171, y = 145, rule = B3/S23
87bo\$86bo\$86b3o\$64bo\$62bobo\$63b2o\$66bo\$66bobo\$9bobo54b2o\$9b2o52bo\$10bo
45bo4b2o\$57bo4b2o\$55b3o2\$96b2o18b2o18b2o\$96bo19bo19bo\$97b3o17b3o17b3o\$
95bobo2bo14bobo2bo14bobo2bo\$30b3o27b3o32b2o2bobo13b2o2bobo13b2o2bobo\$
100bo19bo5bo13b2o\$obo121b2o\$b2o122b2o\$bo\$124bo\$b2o29b2o28b2o59b2o\$obo
29b2o28b2o59bobo\$2bo13\$5bo\$4bo\$4b3o5\$11bo3bobo\$3b2o7b2ob2o\$4b2o5b2o3bo
10b2o18b2o18b2o18b2o18b2o\$3bo24bo19bo19bo19bo19bo\$28bobo17bobo17bobo
17bobo5bo11bobo\$12b2o15b2o18b2o18b2o18b2o4bo13b2o\$13b2o16b2o18b2o18b2o
18b2o2b3o13b2o\$12bo18bobo12bo4bobo17bobo17bobo17bo\$32bo14bo4bo19bo19bo
2b3o14bo\$19bo25b3o21b3o17b3o3bo13b3o\$18b2o49bo19bo6bo12bo\$18bobo\$42bo\$
40bobo6b2o\$41b2o7b2o\$44b2o3bo\$45b2o\$44bo10\$100bo\$67bo33bo\$67bobo21bo7b
3o9bo\$67b2o2b3o16bobo17bobo\$71bo18bo2bo16bo2bo\$72bo18b2o18b2o3bo\$106bo
9bobo\$85b3o18bo9b2o\$106bo\$108b3o\$16bo5bo85bo\$17b2o3bobo84bo4bo\$16b2o4b
2o5bo84bobo\$29bobo82b2o10b2o\$29b2o95bobo\$129bo\$127b2o\$43b2ob2obo13b2ob
2obo13b2ob2obo13b2ob2obo13b2obo\$42bo2b2ob2o12bo2b2ob2o12bo2b2ob2o12bo
2b2ob2o12bo2b2o\$42b2o18b2o18b2o18b2o18b2o2\$114bo\$113b2o\$10b2o101bobo\$
9bobo2b2o\$11bo2bobo\$14bo4\$3b2o\$2bobo\$4bo!
``````
One still life (15.578) to first list and one still life (15.834) appeared later published lists.

So, left to find 61 (24 +37) still life.

Bob Shemyakin

Goldtiger997
Posts: 619
Joined: June 21st, 2016, 8:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

I've been stuck on this highly annoying predecessor of 15.446 for a long time, and have not been to use it for a synthesis

Code: Select all

``````x = 25, y = 22, rule = B3/S23
2\$3b2o\$3bo10b2o\$4bo9b2o\$5bobo\$6b2o6\$11bo\$10b3o\$9b2o2bo\$11bo2bo\$11b3o!
``````
Can anyone else...

(Here are all the 3-glider syntheses for the methulesah:

Code: Select all

``````x = 216, y = 16, rule = B3/S23
b2o98b2o99bo\$obo97bobo8bo88bobo\$2bo7b3o89bo7b2o89b2o\$10bo5b2o92bobo3b
2o\$11bo4bobo97bobo\$16bo99bo5\$214b2o\$213b2o\$215bo\$205b2o\$204bobo\$206bo!
``````
)

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

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Goldtiger997 wrote:I've been stuck on this highly annoying predecessor of 15.446 for a long time, and have not been to use it for a synthesis
I found an alternative honey-farm predecessor using 3 gliders for 11 gliders in total:

Code: Select all

``````x = 58, y = 44, rule = B3/S23
27bo\$28bo\$26b3o\$55bo\$55bobo\$55b2o4\$11bo\$11bobo\$2o9b2o\$b2o\$o3bobo\$4b2o\$
5bo\$31b2o\$31bo\$32bo\$33bobo\$34b2o\$48bobo\$9bo31b3o4b2o\$8b2o31bo7bo\$8bobo
26b3o2bo\$39bo\$38bo\$43b3o\$43bo\$44bo12\$9b3o\$11bo\$10bo!
``````

mniemiec
Posts: 1156
Joined: June 1st, 2013, 12:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

BobShemyakin wrote:... and two still life (15.876 and 15.891), which in my database belong to 15G, but I have not seen in the discussion.
I found this 9-glider synthesis of 15-876 no later than 1999-06-21:

Code: Select all

``````x = 97, y = 57, rule = B3/S23
80bobo\$80boo\$35bo45bo\$36bo\$34b3o22\$20boo28boo4bo33boo\$21bo29bo4bobo32b
o\$oo19bobo27bobobboo33boboboo\$boo19boo28boo5boo31b3obo\$o3boo53bobo\$4bo
bo52bo34boo\$4bo89boo\$\$54bobo\$54boo\$55bo\$\$54b3o\$54bo\$55bo14\$39boo\$38bob
o\$40bo!
``````
Goldtiger997 wrote:I've been stuck on this highly annoying predecessor of 15.446 for a long time, and have not been to use it for a synthesis ... (Here are all the 3-glider syntheses for the methulesah: ...
chris_c wrote:I found an alternative honey-farm predecessor using 3 gliders for 11 gliders in total: ...
By making the canoe simultaneously, one of the original predecessors works, reducing this to 10:

Code: Select all

``````x = 56, y = 47, rule = B3/S23
obo\$boo\$bo13\$31bobo\$31boo\$32bo6bobo\$39boo\$40bo3\$27bo\$25boo\$26boo\$\$31bo
\$16bo5boo6bo\$16bobo3bobo5b3o20bo\$16boo4bo29bobo\$51bobobo\$18bo32bo3bo\$
17boo33b3o\$17bobo30bobo\$50boo3\$19boo\$19bobo\$19bo5\$37boo\$36boo\$38bo!
``````

AbhpzTa
Posts: 501
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 15 in 15: Efficient 15-bit Synthesis Project

mniemiec wrote:
Goldtiger997 wrote:I've been stuck on this highly annoying predecessor of 15.446 for a long time, and have not been to use it for a synthesis ... (Here are all the 3-glider syntheses for the methulesah: ...
chris_c wrote:I found an alternative honey-farm predecessor using 3 gliders for 11 gliders in total: ...
By making the canoe simultaneously, one of the original predecessors works, reducing this to 10:

Code: Select all

``````x = 56, y = 47, rule = B3/S23
obo\$boo\$bo13\$31bobo\$31boo\$32bo6bobo\$39boo\$40bo3\$27bo\$25boo\$26boo\$\$31bo
\$16bo5boo6bo\$16bobo3bobo5b3o20bo\$16boo4bo29bobo\$51bobobo\$18bo32bo3bo\$
17boo33b3o\$17bobo30bobo\$50boo3\$19boo\$19bobo\$19bo5\$37boo\$36boo\$38bo!
``````
9 gliders: (spark + glider = block)

Code: Select all

``````x = 48, y = 39, rule = B3/S23
45bo\$43b2o\$44b2o14\$16b3o\$12b2o2bo\$13b2o2bo\$6b3o3bo\$8bo32b2o\$7bo33bo2b
2o\$16b3o23b2o2bo\$18bo24bobobo\$17bo25bo2bo\$22bo21b2o\$21b2o\$21bobo3\$17b
2o\$17bobo9b2o\$17bo10b2o\$30bo3\$bo\$b2o\$obo!``````
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: 15 in 15: Efficient 15-bit Synthesis Project

15.507 in 14G:

Code: Select all

``````x = 168, y = 48, rule = B3/S23
18\$57bo34bo\$56bo36bo\$56b3o32b3o\$75b3o17b3o\$55bo\$12bo43bo\$13b2o33bobo3b
3o5bobo\$12b2o35b2o11b2o\$49bo13bo2\$36bo8b3o8bo8b3o6b2ob2o15b2ob2o15b2ob
2o15b2ob2o15b2ob2o\$35bobo9bo7bobo7bo9bobo17bobo17bobo17bobo17bobo\$35bo
bo8bo8bobo8bo8bobo17bobo17bobo17bobo17bobo\$13bobo20bob2o16bob2o16bob2o
16bob2o16bob2o16bob2o16bob2o\$14b2o21bo2bo16bo2bo16bo2bo16bo2bo16bo2bo
16bo2bo16bo2bo\$14bo23b2o18b2o18b2o18b2o18b2o18b2o19b2o\$24bo\$15b3o5b2o
104bo\$17bo5bobo104bo\$16bo111b3o\$132b2o\$131bobo3bo\$133bo3bobo\$137b2o!
``````
15.473 in 12G:

Code: Select all

``````x = 98, y = 40, rule = B3/S23
8\$25bobo40bo\$28bo40b2o\$28bo39b2o\$25bo2bo\$26b3o45bo\$72b2o\$69bo3b2o\$70b
2o\$69b2o3\$30bo58bo\$28b2o20bo19bo17bobo\$29b2o18bobo8bo8bobo16bobo\$48bob
o10b2o5bobo15b2obo\$47bo2bobo7b2o5bo2bobo12bobobobo\$33b3o11b2o2b2o14b2o
2b2o13bo3b2o\$24bo8bo\$24b2o8bo\$23bobo\$61b3o\$63bo\$62bo3\$13bo\$13b2o\$12bob
o!
``````
Bob Shemyakin

Extrementhusiast
Posts: 1844
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 15 in 15: Efficient 15-bit Synthesis Project

BobShemyakin wrote:15.507 in 14G:

Code: Select all

``RLE``
Down to twelve gliders:

Code: Select all

``````x = 141, y = 41, rule = B3/S23
111bo\$112b2o\$94bo16b2o7bo\$93bo24b2o\$93b3o19bo3b2o\$58bo27bo29b2o\$58bobo
23bobo28b2o\$58b2o25b2o\$56bo\$54bobo30b2o\$55b2o29bo2bo23b2o19b2o\$61bo25b
2o3bo19bo2bo18bo2bo\$17bo3bo38bobo28bobo19b2obo18b2obo\$18b2obobo36bo2bo
19bo7bo2bo20bobo19bobo\$17b2o2b2o38bobo19b2o7bobo20bobo19bobo\$60b2ob2o
17bobo6b2ob2o18b2ob2o17b2ob2o18\$39b2o\$38b2o\$40bo3\$bo\$b2o\$obo!
``````
BobShemyakin wrote:15.473 in 12G:

Code: Select all

``RLE``
I Like My Heisenburps! (and others)

Goldtiger997
Posts: 619
Joined: June 21st, 2016, 8:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

15.447 in 11 gliders:

Code: Select all

``````x = 91, y = 101, rule = B3/S23
17bo\$bo16bo\$2bo13b3o\$3o19\$32bo\$33bo\$31b3o\$39bo\$37bobo\$38b2o8\$89bo\$88bo
\$88b3o8\$66bo\$65bo\$61bo3b3o\$62b2o\$61b2o\$65b3o\$67bo\$66bo15\$81b3o\$81bo\$
82bo10\$48bo\$48b2o\$47bobo17\$15b2o\$14bobo\$16bo!
``````
Last edited by Goldtiger997 on November 5th, 2016, 7:43 pm, edited 1 time in total.

mniemiec
Posts: 1156
Joined: June 1st, 2013, 12:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Goldtiger997 wrote:14.447 in 11 gliders: ...
I think you meant 15.447. By the way, thanks for all the excellent work on this project!

EDIT:
BobShemyakin wrote:15.473 in 12G: ...
You did. He improved it with a cheaper synthesis of the base still-life (12.100).

AbhpzTa
Posts: 501
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 15 in 15: Efficient 15-bit Synthesis Project

15.457 in 11G:

Code: Select all

``````x = 213, y = 32, rule = B3/S23
71bo\$72bo\$70b3o20bobo\$93b2o\$94bo\$97bobo\$67bobo27b2o\$68b2o6bo21bo\$68bo
7bobo\$76b2o4\$69bo\$67bobo\$68b2o\$126b2o38b2o38b2o\$70b2o54bobo2b2o33bobo
2b2o33bobo2b2o\$3bo67b2o55bo3bo35bo3bo35bo3bo\$2bo67bo39b2o15bob3o18b2o
15bob3o35bob3o\$2b3o105b2o15bobo20b2o15bobo37bobo\$41b3o37b3o44bo39bo39b
o\$bo145b3o\$2bo36bo39bo69bo\$3o36bo39bo68bo\$39bo39bo4\$3bo\$3b2o\$2bobo!``````
BobShemyakin wrote:From the first list are excluded 15.485(13G) 15.874(9G) 15.1036(10G) :

Code: Select all

``RLE``
but included still life (15.578) of 2 list and two still life (15.876 and 15.891), which in my database belong to 15G, but I have not seen in the discussion.
From the second list are excluded 15.458(10G) 15.698(12G) 15.1035(14G):

Code: Select all

``RLE``
One still life (15.578) to first list and one still life (15.834) appeared later published lists.
=15

Code: Select all

``````15.487  15.516  15.578  15.598  15.653  15.751  15.786  15.839  15.855  15.890
15.891  15.919  15.934  15.939  15.942  15.949  15.1024 15.1033 15.1034 15.1060
15.1088``````

Code: Select all

``````x = 98, y = 27, rule = B3/S23
2o2bo8b2o5bo5bo3b2o8b2o3bo4b2o8bo10bo9b2o7b2o\$o2bobo4bobob3o3b3o2bobo
3bo2bo5bobobobo3bobo3bo3b3o7bobo8bobo6bo2bo\$bobo2bo3b2o5bo5bo2bo4bobob
obo5b2obo6bobobo5bo2b2o3bobo2bo6bo8b4o\$2bobobo9bo5bob2o6bobob2o7bo8b2o
2bo3bo2bo2bo4b4o4bob2o11bo\$3bobo7bobo6bo11bo10bobo8bobo4b2o2bobo2bo7bo
bo2bo8bobo\$4bo8b2o6b2o10b2o11b2o8b2o10bo3bobo6bo2bobo6bobo\$73b2o10bo7b
2o4\$2o8b2o2bo5b2ob2o8bo8b2o7bo8b2o8b2o8b2o8b2o\$o2bo6bo2bobo4bob2obo5b
3o9bo6bobo7bo9bo2b2o5bo2b2o5bobobo2bo\$2b4o6b2o2bo8bo4bo5b2o4bo8bo2bo6b
o3bo5bobobo5bobobo7b5o\$6bo7b2o9b2o4bo3bobo3bo10b5o5bobobo5bo3bo5bo3bo\$
4b3o7bo11bo5bo2bo4bo5b2o9bo5b2o2bo9bo9bo7bo\$3bo11bo9bo7bobo5b3obobo6bo
bo8bobo7bobo6b3o7bobo\$3b2o9b2o9b2o7bo8b2o9b2o9b2o8b2o7bo10bo4\$o\$3o\$3bo
\$2bo\$2b2o3b2o\$4bobobo\$4b2o!
``````
>15

Code: Select all

``````15.451  15.475  15.476  15.477  15.478  15.480  15.483  15.486  15.497  15.501
15.512  15.562  15.619  15.620  15.723  15.731  15.759  15.791  15.797  15.835
15.840  15.848  15.849  15.860  15.868  15.918  15.923  15.947  15.960  15.983
15.986  15.1001 15.1012 15.1032 15.1065``````

Code: Select all

``````x = 98, y = 37, rule = B3/S23
2o8b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o2bo5b2o2b2o4b2ob
o\$obo7bo4bo4bo2bo2bo3bo2bo2bo3bo2bo2bo3bo2bo2bo3bobobobo3bo2bobo4bo2bo
bo4bob4o\$2bo8b3obo5bob2o6bob2o6b3obo5b4o7b2o8b2obo5b2o13bo\$bob2obo5bob
o7bo9bo11bo16bo11bob2o6b2o9b3o\$o2bob2o3bo12bobo4bobo10bo7b2o9bobo6bo
11bo2bo6bo\$2o8b2o12b2o4b2o11b2o6b2o10b2o6b2o12b2o6b2o5\$2ob2obo4b2o7b2o
8b2o8b2o8b2o8b2o2bo5bob2o6b2o10b2o\$bobob2o3bobo7bo2bo6bo2bo6bo9bo2bo6b
o2bobo4b2obo7bo9bobo\$bo8bobob2o6b2o2b2o3b2obo7bo4bo4b2o8b2obo8b2o2b2ob
ob2ob2o2bo\$2bo8bobo2bo6bobobo5bobobo3b2o3bobo4bob2obo6b2o9bo2bo2bob2o
2bo2b5o\$3bobo6bo2bobo5bobo7bo2b2o5b2o2bo5bobob2o6bo2bo7bobo8bobo6bo\$4b
2o10bo7b2o6b2o9bob2o7bo12b2o8bo10bo4bobo\$93b2o4\$bo9b2o8b2o8b2o8b2o7b2o
2bo5b2o2bobo4bo9bo8bo\$obo8bobo7bobo6bo2bo6bo2bob2o3bo2bobo4bo2bob2o3bo
bo7bobob2o4b3o\$bobob2o7bo9bo6b2o3bo4b2o3bo5b2o2bo5b2o7bo2bo6bo3bo7bo\$
3b2obo5b2o8b2o9b4o6b2o9b2o7bo8b2obobo4b3o7bo3b2o\$2bo8bo2b3o3bo2bobo7bo
9bo10bo7bo11bob2o6bobo5b2o2bo\$3b3o4bobo3bo3b2o2bobo7bo10bo10bo4bo12bo
10bobo6bobo\$5bo5bo13bo7b2o9b2o9b2o4b2o10b2o11bo7b2o4\$o9b2o8b2o8b2o8b2o
2bo\$3o8bo9bo2b2o4bo2b2o5bo2bobo\$3bo7bob2o6bobobo5bobo8b2obo\$2b2o2bo5bo
bo7bo3b2o4bo2bo8bo\$3bobobo6bob2o9bo5b2obo7bobo\$3bo2bo6bobobo7bo10bo8bo
bo\$2b2o10bo10b2o9b2o8bo!``````
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: 15 in 15: Efficient 15-bit Synthesis Project

Nice! 15.457 30G->11G! Now the greatest cost of the 15.759 (29G).

15.480 ->14G:

Code: Select all

``````x = 140, y = 43, rule = B3/S23
8\$25bo\$25bobo\$25b2o\$103bo\$93bo9bobo\$13bobo75bobo9b2o\$14b2o21b2o18b2o
33b2o\$8bo5bo21bobo17bobo\$9b2o26bo19bo\$8b2o44b2o\$27bobo23bobo\$27b2o11b
2o13bo4b2o18b2o10bobo5b2o\$16b3o9bo11bo3b2o14bo3b2o14bo3b2o7b2o5bo3b2o
13b2o3b2o\$16bo5bo19bo2bo16bo2bo16bo2bo7bo8bo2bo13bo2bo2bo\$17bo3bo19b4o
16b4o16b4o16b4o16b4o\$21b3o67bo\$43b2o18b2o18b2o4bobo11b2o18b2o\$43b2o18b
2o18b2o5b2o11b2o18b2o\$21b3o\$21bo70bo\$22bo69b2o\$91bobo3\$30bo\$29b2o\$29bo
bo!
``````
15.923 ->13G:

Code: Select all

``````x = 207, y = 51, rule = B3/S23
15\$57bo\$58bo\$56b3o\$119bo\$120bo\$118b3o2\$121b2o\$95bobo23b2o\$95b2o\$96bo2\$
19bo3bo\$20bobo97b2o28b2o18b2o18b2o\$18b3ob3o54b2ob2o36bo4b2o23bo4b2o6bo
6bo4b2o13bo4b2o\$79b2ob2o38bobobo25bobobo7b2o6bobobo15bobobo\$121b3o11b
2o14b3o9b2o6b3o17b3o\$92bo27bo13bobo13bo19bo19bo\$93b2obo23b2o13bo2b3o9b
2o18b2o19bo\$92b2o2bobo39bo51b2o\$96b2o41bo\$43bo58bo64b2o\$42bo59bo63bobo
\$42b3o57bo65bo\$170b2o\$170bobo\$42b2o126bo\$42bobo\$42bo!
``````
15.1012 ->11G:

Code: Select all

``````x = 77, y = 23, rule = B3/S23
9bo3bo30bo\$7bobob2o32b2o3bo\$2bo5b2o2b2o30b2o2b2o\$obo46b2o\$b2o22bo\$25bo
bo41b2o\$25b2o4bob2o11bobo2bob2o15bo2b2o\$31b2obo12b2o2b2obo15bobobo\$35b
2o10bo7b2o14bo3b2o\$36bo19bo19bo\$34bo13b3o3bo19bo\$34b2o12bo5b2o18b2o\$
49bo\$11b2o\$12b2o5bo\$11bo6b2o\$18bobo4\$14b3o\$16bo\$15bo!
``````
15.1065 ->15G:

Code: Select all

``````x = 129, y = 40, rule = B3/S23
9\$31bo\$31bobo\$23bo7b2o\$16bo4bobo\$17bo4b2o\$15b3o71bo\$90bo\$88b3o\$12b2o
84bobo\$13b2o8bo67bobo4b2o\$12bo11bo17bo19bo19bo8b2o6bo12bo\$22b3o16bobo
17bobo17bobo8bo18bobo\$37b2o3bobo12b2o3bobo17bobo27bobo\$25b2o10b2o5bo
12b2o5bo19bo11bo17bo\$18b2o5bobo15bob2obo14bob2obo14bob2obo6b2o16bob2o\$
18b2o5bo17bobob2o14bobob2o14bobob2o6bobo15bobo2bo\$44bo9b3o7bo19bo29bo
2b2o\$56bo\$55bo\$88b2o\$89b2o3b2o\$88bo5bobo\$94bo!
``````
53(22 +31) still life left.
Bob Shemyakin

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

### Re: 15 in 15: Efficient 15-bit Synthesis Project

BobShemyakin wrote:Now the greatest cost of the 15.759 (29G).
It inspired me to try to reduce it. By completing the reduction of 15.1064 suggested here I got down to 15G:

Code: Select all

``````x = 203, y = 51, rule = B3/S23
19bobo176bobo\$20b2o176b2o\$20bo178bo\$29bo\$29bobo112b2o2bo35b2o2bo11b2o\$
29b2o113bo2bobo34bo2bobo10bobo\$67b3o37b3o36b2obo36b2obo10bo\$61bo39bo
47b2o38b2o\$45b2o14bo23b2o14bo47bo39bo8bo\$44bo2bo13bo22bo2bo13bo49bo39b
o5b2o\$45b2o38b2o63b2o38b2o5bobo\$8b2o16bo\$8bobo14b2o\$8bo16bobo\$b2o\$obo
92b2o101b2o\$2bo93b2o89b2o9bobo\$95bo90bobo9bo\$188bo5\$114b3o\$114bo\$115bo
\$100b2o\$100bobo\$100bo\$86b2o\$85bobo\$87bo17\$131bo\$130b2o\$130bobo!
``````

Extrementhusiast
Posts: 1844
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 15 in 15: Efficient 15-bit Synthesis Project

BobShemyakin wrote:15.1012 ->11G:

Code: Select all

``RLE``
Unfortunately, the final step doesn't work, and we must use one more glider:

Code: Select all

``````x = 43, y = 14, rule = B3/S23
bo\$2bo6bo\$3o7b2o5bo\$9b2o4b2o\$16b2o3\$35b2o\$8bo8bob2o15bo2b2o\$9bo2bo4b2o
bo15bobobo\$7b3o2b2o7b2o14bo3b2o\$11bobo8bo19bo\$20bo19bo\$20b2o18b2o!
``````
Fortunately, this still fits well under the fifteen-glider target.
I Like My Heisenburps! (and others)

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

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Extrementhusiast wrote:
BobShemyakin wrote:15.1012 ->11G:

Code: Select all

``RLE``
Unfortunately, the final step doesn't work, and we must use one more glider:

Code: Select all

``````x = 43, y = 14, rule = B3/S23
bo\$2bo6bo\$3o7b2o5bo\$9b2o4b2o\$16b2o3\$35b2o\$8bo8bob2o15bo2b2o\$9bo2bo4b2o
bo15bobobo\$7b3o2b2o7b2o14bo3b2o\$11bobo8bo19bo\$20bo19bo\$20b2o18b2o!
``````
Fortunately, this still fits well under the fifteen-glider target.
Thanks! 15.1012 ->12G:

Code: Select all

``````x = 87, y = 25, rule = B3/S23
45bo\$46bo6bo\$9bo3bo30b3o7b2o5bo\$7bobob2o40b2o4b2o\$2bo5b2o2b2o46b2o\$obo
\$b2o22bo\$25bobo51b2o\$25b2o4bob2o17bo8bob2o15bo2b2o\$31b2obo18bo2bo4b2ob
o15bobobo\$35b2o14b3o2b2o7b2o14bo3b2o\$36bo18bobo8bo19bo\$34bo29bo19bo\$
34b2o28b2o18b2o2\$11b2o\$12b2o5bo\$11bo6b2o\$18bobo4\$14b3o\$16bo\$15bo!
``````
Extrementhusiast wrote:
BobShemyakin wrote: Now the greatest cost of the 15.759 (29G).

It inspired me to try to reduce it. By completing the reduction of 15.1064 suggested here I got down to 15G:

Code: Select all

``````x = 203, y = 51, rule = B3/S23
19bobo176bobo\$20b2o176b2o\$20bo178bo\$29bo\$29bobo112b2o2bo35b2o2bo11b2o\$
29b2o113bo2bobo34bo2bobo10bobo\$67b3o37b3o36b2obo36b2obo10bo\$61bo39bo
47b2o38b2o\$45b2o14bo23b2o14bo47bo39bo8bo\$44bo2bo13bo22bo2bo13bo49bo39b
o5b2o\$45b2o38b2o63b2o38b2o5bobo\$8b2o16bo\$8bobo14b2o\$8bo16bobo\$b2o\$obo
92b2o101b2o\$2bo93b2o89b2o9bobo\$95bo90bobo9bo\$188bo5\$114b3o\$114bo\$115bo
\$100b2o\$100bobo\$100bo\$86b2o\$85bobo\$87bo17\$131bo\$130b2o\$130bobo!``````
Nice! Now the greatest cost of the 15.868 (28G).
Bob Shemyakin

Goldtiger997
Posts: 619
Joined: June 21st, 2016, 8:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

I have not been able to synthesise 15.451 in under 15 gliders . Does anyone know cheaper converters or a different method of construction than the one below?

Code: Select all

``````x = -75, y = -35, rule = B3/S23
bbo\$3bo\$b3o\$12bo\$11bo\$11b3o\$127bo\$128bo\$3bobo120b3obbo\$4boo81bobo40bo\$
4bo10bo72boo40b3o\$14bo73bo38bo\$14b3o111bo\$86boo38b3o\$17boo68boo32bobo\$
17bobo12bobboo15bobboo15bobboo9bo5bobboo14boobboo5boo7boobboo18boo\$17b
o13bobobbo14bobobbo14bobobbo14bobobbo14bobobbo5bo8bobobbo13boobobbo\$bo
30boobo16boobo16boobo16boobo16boobo10bo5boobo14boboobo\$boo4b3o24bo19bo
19bo19bo19bo11boo6bo19bo\$obo6bo15bo8bobo17bobo17bobo17bobo17bobo8bobo
6bobo17bobo\$8bo15bo10boo18boo18boo18boo18boo18boo18boo\$24b3o\$35boo18b
oo\$35boo18boo\$10bo4b3o\$10boo5bo39b3o\$9bobo4bo40bo\$58bo9\$58bobo\$58boo\$
46bo12bo\$47boo\$46boo42bo\$88bobo39bobo\$55bo33boo39boo\$54bo76bo\$54b3o14b
oo18boo58bo\$71boobboo14boobboo18boo11bo6boo13bobobboo\$48bobo6boo17bo
19bo19bo12bo6bo14boo3bo\$49boo6bobo15bo19bo19bo11b3o5bo19bo\$49bo7bo16bo
19bo19bo19bo19bo\$74bobo17bobo17bobo9b3o5bobo17bobo\$75boo18boo18boo9bo
8boo18boo\$127bo14\$94bo\$85bobo5bo36bo\$88bo4b3o35bo\$40bo3bo43bo40b3o\$38b
oboboo41bobbo\$39boobboo17bo23b3o3bo19boo18boo\$61bobo15bobo9bobo18boo
18boo\$36b3o23bo17boo10bo\$38bo41bo\$37bo3bo19bo29bo\$40bobobboo13bobobboo
23bobobboo15bobboo15bobboo15bobboo\$41boo3bo14boo3bo24boo3bo14bobobbo
14bobobbo14bobobbo\$45bo19bo29bo16boobo16boobo16boobo\$44bo19bo14b4o11bo
19bo19bo19bo\$44bobo17bobo11bo3bo11bobo17bobo17bobo17bobo\$45boo18boo15b
o12boo18boo18boo18boo\$78bobbo5boo\$86bobo\$88bo\$\$92boo\$81boo9bobo\$82boo
8bo\$81bo\$90boo\$89bobo\$91bo!
15-451.rle
Mark D. Niemiec's life synthesis database, Thu Feb 19 02:00:41 2015
``````

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

### Re: 15 in 15: Efficient 15-bit Synthesis Project

They seem to be not bad.
15.835 15.983 15.860

Code: Select all

``````x = 72, y = 17, rule = B3/S23
15bo24bo21bobo\$14bo24bobo20b2o\$14b3o23bo22bo\$64bo\$64bo\$58bobo\$2o56bobo
\$2o59bo\$39b3o3b2o13bobo\$10bo21b2o4bo2bo3b2o13bobo\$9bobo21b2o3b3o20bo\$
2b2o6b2o21b2o\$2bo2bo27b2o35bo\$32b3o34bobo\$3bobo19b2o2b2ob2o35bobo\$5bo
19b2ob3ob2o36bo\$3o!
``````
Last edited by yootaa on November 6th, 2016, 8:36 am, edited 1 time in total.

Goldtiger997
Posts: 619
Joined: June 21st, 2016, 8:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

I wrote:I have not been able to synthesise 15.451 in under 15 gliders . Does anyone know cheaper converters or a different method of construction than the one below?

Code: Select all

``````x = -75, y = -35, rule = B3/S23
bbo\$3bo\$b3o\$12bo\$11bo\$11b3o\$127bo\$128bo\$3bobo120b3obbo\$4boo81bobo40bo\$
4bo10bo72boo40b3o\$14bo73bo38bo\$14b3o111bo\$86boo38b3o\$17boo68boo32bobo\$
17bobo12bobboo15bobboo15bobboo9bo5bobboo14boobboo5boo7boobboo18boo\$17b
o13bobobbo14bobobbo14bobobbo14bobobbo14bobobbo5bo8bobobbo13boobobbo\$bo
30boobo16boobo16boobo16boobo16boobo10bo5boobo14boboobo\$boo4b3o24bo19bo
19bo19bo19bo11boo6bo19bo\$obo6bo15bo8bobo17bobo17bobo17bobo17bobo8bobo
6bobo17bobo\$8bo15bo10boo18boo18boo18boo18boo18boo18boo\$24b3o\$35boo18b
oo\$35boo18boo\$10bo4b3o\$10boo5bo39b3o\$9bobo4bo40bo\$58bo9\$58bobo\$58boo\$
46bo12bo\$47boo\$46boo42bo\$88bobo39bobo\$55bo33boo39boo\$54bo76bo\$54b3o14b
oo18boo58bo\$71boobboo14boobboo18boo11bo6boo13bobobboo\$48bobo6boo17bo
19bo19bo12bo6bo14boo3bo\$49boo6bobo15bo19bo19bo11b3o5bo19bo\$49bo7bo16bo
19bo19bo19bo19bo\$74bobo17bobo17bobo9b3o5bobo17bobo\$75boo18boo18boo9bo
8boo18boo\$127bo14\$94bo\$85bobo5bo36bo\$88bo4b3o35bo\$40bo3bo43bo40b3o\$38b
oboboo41bobbo\$39boobboo17bo23b3o3bo19boo18boo\$61bobo15bobo9bobo18boo
18boo\$36b3o23bo17boo10bo\$38bo41bo\$37bo3bo19bo29bo\$40bobobboo13bobobboo
23bobobboo15bobboo15bobboo15bobboo\$41boo3bo14boo3bo24boo3bo14bobobbo
14bobobbo14bobobbo\$45bo19bo29bo16boobo16boobo16boobo\$44bo19bo14b4o11bo
19bo19bo19bo\$44bobo17bobo11bo3bo11bobo17bobo17bobo17bobo\$45boo18boo15b
o12boo18boo18boo18boo\$78bobbo5boo\$86bobo\$88bo\$\$92boo\$81boo9bobo\$82boo
8bo\$81bo\$90boo\$89bobo\$91bo!
15-451.rle
Mark D. Niemiec's life synthesis database, Thu Feb 19 02:00:41 2015
``````
The equivalent with a python has 1 soup on catalogue (the original had none). Here are two reductions:

Code: Select all

``````x = 60, y = 25, rule = B3/S23
2b3o2\$o5bo45b3o\$o5bo45bobo\$o5bo45b3o2\$2b3o2\$2bo\$2bo48bo\$2b2o46bobo\$2b
3o3b2o39bo2bo5b2o\$2b2o4b2o40b2o6b2o2\$4bo42b2o\$46b2o\$5bo34b2o5bobo\$3b3o
33bo2bo5b2o\$40b2o12bo\$53b3o\$52b5o\$51b2o3b2o\$52b5o\$53b3o\$54bo!
``````
If anyone can use either of those to make a synthesis in 11 gliders or less, we can use the following converter to synthesise 15.451 in under 15 gliders.

Code: Select all

``````x = 16, y = 12, rule = B3/S23
4bo\$5bo\$3b3o3\$8b2o4b2o\$2bo5bobobo2bo\$obo8b2obo\$b2o10bo\$4b2o7bobo\$5b2o
7b2o\$4bo!
``````
This is quite a hard one!

Sokwe
Moderator
Posts: 1669
Joined: July 9th, 2009, 2:44 pm

### Re: 15 in 15: Efficient 15-bit Synthesis Project

yootaa wrote:They seem to be not bad.
15.835 15.938 15.860
That last one (15.860) is just part of loafer along with a traffic light and beehive:

Code: Select all

``````x = 29, y = 32, rule = B3/S23
2bo\$obo\$b2o2\$26bo\$26bobo\$26b2o8\$11bo\$11bobo\$11b2o2\$10bo\$8bobo\$5bo3b2o\$
5b2o\$4bobo6\$24bo\$23bobo\$23bobo\$24bo!``````
-Matthias Merzenich

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

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Sokwe wrote:
yootaa wrote:They seem to be not bad.
15.835 15.938 15.860
That last one (15.860) is just part of loafer along with a traffic light and beehive:

Code: Select all

``````x = 29, y = 32, rule = B3/S23
2bo\$obo\$b2o2\$26bo\$26bobo\$26b2o8\$11bo\$11bobo\$11b2o2\$10bo\$8bobo\$5bo3b2o\$
5b2o\$4bobo6\$24bo\$23bobo\$23bobo\$24bo!``````
Thank you!
15.860 in 9G:

Code: Select all

``````x = 48, y = 60, rule = B3/S23
2bo\$obo\$b2o4\$11bo\$9bobo\$10b2o2\$35bo\$35bobo\$35b2o8\$20bo\$20bobo\$20b2o2\$
19bo\$17bobo\$14bo3b2o\$14b2o\$13bobo5\$34bo\$34bobo\$34b2o2\$37b2o\$37bobo\$37b
o18\$46b2o\$45b2o\$47bo!
``````

Sokwe
Moderator
Posts: 1669
Joined: July 9th, 2009, 2:44 pm

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Goldtiger997 wrote:If anyone can use either of those to make a synthesis in 11 gliders or less, we can use the following converter to synthesise 15.451 in under 15 gliders.
15.451 in 14:

Code: Select all

``````x = 231, y = 25, rule = B3/S23
2bo\$obo\$b2o5\$38b2o28b2o135bo\$38b2o28b2o34b2o28b2o28b2o28b2o7b2o19b2o\$
104bobo27bobo27bobo27bobo7b2o18bobo\$11bo94bo29bo29bo29bo10b2o17bo\$10bo
22b2o21bo6b2o12bo27bob2o26bob2o26bob2o26bob2o8bobo15bob2obo\$10b3o19bo
2bo21b2o3bo2bo11bobo24bo2bobobo22bo2bobobo22bo2bobobo22bo2bobobo5bo16b
o2bob2o\$7b2o24b2o21b2o5b2o12b2o2b2o21b2o4b2o22b2o4b2o22b2o4b2o22b2o4b
2o22b2o\$6bobo30b3o27b3o9bobo\$8bo72bo26bo29bo\$107bobo27bobo64b3o\$65b2o
40bobo27bobo64bo\$19bo40b2o2bobo41bo29bo66bo\$18b2o41b2o3bo\$18bobo39bo
77b2o\$138bobo\$66bo71bo\$65b2o\$65bobo!``````
-Matthias Merzenich

AbhpzTa
Posts: 501
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 15 in 15: Efficient 15-bit Synthesis Project

yootaa wrote:They seem to be not bad.
15.835 15.983 15.860

Code: Select all

``````x = 72, y = 17, rule = B3/S23
15bo24bo21bobo\$14bo24bobo20b2o\$14b3o23bo22bo\$64bo\$64bo\$58bobo\$2o56bobo
\$2o59bo\$39b3o3b2o13bobo\$10bo21b2o4bo2bo3b2o13bobo\$9bobo21b2o3b3o20bo\$
2b2o6b2o21b2o\$2bo2bo27b2o35bo\$32b3o34bobo\$3bobo19b2o2b2ob2o35bobo\$5bo
19b2ob3ob2o36bo\$3o!
``````
15.983 in 9G:

Code: Select all

``````x = 61, y = 68, rule = B3/S23
59bo\$58bo\$58b3o4\$55bo\$54bo\$54b3o6\$39bo\$38bo\$15bo22b3o\$13bobo\$14b2o18\$
20bo16b2o\$21b2o14bobo\$20b2o3bo11bo\$23b2o\$24b2o32bo\$57b2o\$57bobo23\$3o\$
2bo\$bo!``````
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).