## Soup search results

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

### Re: Soup search results

Here's 6 15-bit still lifes
15.647:
x = 129, y = 22, rule = B3/S23$95bobo$96b2o$96bo3bo$100bobo$100b2o$2bobo52bo$3b2o53bo$3bo10bo41b3o62b2o$12b2o107bo$5b3o5b2o12b2o18b2o6b3o9b2o18b2o12bo15b2o3bo$7bo19bo2bo16bo2bo4bo11bo2bob2o13bo2bob2o6b2o15bo2bobo$6bo22b2o18b2o5bo12b2obobo14b2obobo5bobo16b2obobo$73bo19bo29b2o$10bo42bo$9b2o42b2o$9bobo40bobo!

15.652:
x = 155, y = 17, rule = B3/S2385bo$86bo$84b3o$o45bobo19b2o18b2o$b2o3bobo5bo18b2o12b2o4b2o12bo2bo2b2o12bo2bo2b2o14b2o2b2o14b2o2b2o14b2o2b2o$2o5b2o4bo17bo2bo12bo3bo2bo13b2obo2bo13b2obo2bo14bobo2bo14bobo2bo14bobo2bo$7bo5b3o15b2o18b2o18b2o18b2o18b2o18b2o18b2o$28b2obo13bo2b2obo19bo19bo19bo19bo19bo$14bo13b2o2bo10bobo2b2o2bo19bo19bo19bo19bo19bo$4b2o7b2o16b2o11b2o5b2o18b2o18b2o18b2o18b2o3bo16bo$5b2o6bobo31bo87bo18bo$4bo42b2o86b3o15b2o$46bobo82b2o$7b2o41b2o78bobo$7bobo40bobo79bo3b2o$7bo42bo86b2o$136bo!

15/658:
x = 112, y = 31, rule = B3/S23$83bo$84bo$82b3o2$80bo17bo$81bo16bobo$79b3o16b2o5$97bo$54bo40b2o$15bo36b2o42b2o$13b2o38b2o$14b2o83bo$56bo12bo19bo8b2o8b2o$55b2o12bo19bo8bobo7bo$55bobo11bo19bo19bo$23b2o18b2o18b2o18b2o18b2o3b2o$22bo2bobo14bo2bobo14bo2bobo14bo2bobo14bo2bobo$3b2o2b3o12b2o2b2o14b2o2b2o14b2o2b2o14b2o2b2o14b2o2b2o$2bobo2bo$4bo3bo3$9b2o$8b2o$10bo!

15.668:
x = 119, y = 34, rule = B3/S235$87bo$54bo33bo$54bobo21bo7b3o9bo$54b2o2b3o16bobo17bobo$58bo18bo2bo16bo2bo$59bo18b2o18b2o3bo$93bo9bobo$72b3o18bo9b2o$93bo$95b3o$95bo$96bo4bo$101bobo$11bo89b2o10b2o$10bo8bo93bobo$10b3o5bo9b2o18b2o18b2o18b2o18b2o6bo$18b3o7bobo17bobo17bobo17bobo17bobo3b2o$4bobo24bob2obo14bob2obo14bob2obo14bob2obo14bobo$5b2o8bo16b2ob2o15b2ob2o15b2ob2o15b2ob2o15b2o$5bo8b2o6bo$14bobo4b2o$3b3o15bobo77bo$5bo5b3o86b2o$4bo8bo86bobo$12bo! 15.708: x = 96, y = 45, rule = B3/S2312$57bo$58b2obo$50bobo4b2o2bobo$6b2o43b2o8b2o4bo$5bobo2b2o39bo14bo$7bo2bobo46bo6b3o$10bo38b2o6b2o3b3o$50b2o6b2o2bo13bo$49bo13bo11bobo$34b2o18b2o18bobo$34bo19bo19bo$35bo19bo19bo$32b4o16b4o16b4o$32bo19bo19bo$33bo19bo19bo$32b2o18b2o18b2o$9b2o$9bobo$5b2o2bo$4bobo$6bo$12b3o$12bo$13bo4$27b2o$27bobo$27bo!

15.712:
x = 117, y = 36, rule = B3/S236$8bo$7bo$7b3o51bo$62bo$60b3o2$63bobo$14bo3bobo36bo5b2o$6b2o7b2ob2o35bobo6bo$7b2o5b2o3bo10b2o18b2o4b2o17b2o18b2o$6bo24bo19bo24bo19bo$31bobo17bobo7bobo12bobo3b2o12bobo3b2o$15b2o15b2o18b2o7b2o14b2o3bo14b2o3bo$16b2o16b2o18b2o6bo16b2obo16b2obo$15bo18bobo17bobo22bobo17bobo$35bo19bo24bo$22bo$21b2o55b2ob2o$21bobo53bobobobo$79bobo! Bob Shemyakin BobShemyakin Posts: 208 Joined: June 15th, 2014, 6:24 am ### Re: Soup search results BobShemyakin wrote:Here's 6 15-bit still lifes ... These syntheses yield a few others as well. Row 1: 15.649 from 8. Row 2: 15.652: The base 13.212 can be made from 9 reducing this to 12, which also gives 15.431 from 13 Row 3: 15.652 and 15.925 can also be made from related 13.211 from 12. Row 4: 15.658 from 10. EDIT: Row 5: From the converter used in 15.668, we also get 15.1035 from 12: x = 147, y = 176, rule = B3/S23obo$boo$bo$$95bo96bo4bobo94b3o4boo102bo$$103b3o$103bo$104bo$34bo19bo19bo19bo18boo$33bobo17bobo17bobo17bobo17bo$34boo18boo18boo18boo18b3obo$18bobo96boo$18boo14boo18boo18boo18boo18boo$19bo14bo19bo19bo19bo19bo$35bo19bo19bo19bo19bo$34boo18boo18boo18boo18boo3$12bo$11bo$11b3o3$10b3o20boo18boo$10bo22boo18boo$11bo37b3o$51bo$50bo12$23bo$21boo$22boo$32bo$30boo$31boo3$o$boo$oo3$58boo$57bobo3bo37bobo$25bo33boboo34bo3boo$26bo35boo34boobbo$24b3o21boo18boo12boo4boo7boo9boo18boo$10boo37bo10bo8bo12bobo4bo19bo19bo$9bobo32boobo12boobboobo17bobo16boobo16boobo$11bo11b3o18bob3o10bobobbob3o17b3o15bob3o14bobb3o$25bo23bo19bo19bo19bo13boo4bo$24bo23boo18boo18boo12bo5boo18boo$97bo3boo$95bobo3bobo$96boo3$3boo19b3o$bbobo19bo$4bo20bo5$28boo$27boo$29bo11$bbobo$3boo$3bo8bo$10bobo88bobo$11boo89boo$102bo$19bo41bobo$6bo13boo35bo3boo37boo$7bo11boo4bo32boobbo38boo20boo$5b3o17bobo20boo7boo9boo12boo4boo10bo7boo13bo4boo$b3o21boo17boo3bo14boo3bo12bobo4bo14boo3bo14bo4bo$3bo40bobbo16bobbo17bobo16bobbo17bobo$bbo43b3o17b3o17b3o17b3o17b3o$31bo17bo19bo19bo19bo19bo$30boo16boo18boo18boo18boo18boo$30bobo4$27b3o$27bo$28bo$3boo8b3o$bbobo10bo$4bo9bo15$93bo$92bo$92b3o$44bo45bo$43bo44bobo$obo40b3o43boo$boo38bo$bo37bobo42bo$40boo40bobo$83boo$13bobo48bo29bo$8bo4boo49bo29bo20boo$8bobo3bo49bo29bo18bobbo$8boo17boo18boo18boo28boo14boobboo$28bo19bo19bo29bo19bo$27bo19bo19bo29bo19bo$8b3o15bo19bo19bo29bo19bo$8bo17bobo17bobo17bobo27bobo17bobo$9bo17boo18boo18boo28boo18boo4$94bo$93boo$93bobo5$132boo$128bobboo$46bo79bobo4bo$o3bobo39bobo78boo$booboo14boobo16boobobboo12booboboo13booboboo13booboo15booboo15booboobo$oo3bo13bobboo15bobboo5boo8bobbooboo12bobbooboo6boo4bobboobo13bobboobo13bobbooboo$19boo18boo8bobo7boo18boo8boobbobo3boo5bo12boo5bo12boo$49bo40boobo13bo19bo$3o86bo16boo18boo$bbo$bo4bo118bo$5boo117boo$5bobo116bobo$$78bo78boo77bobo! mniemiec Posts: 929 Joined: June 1st, 2013, 12:00 am ### Re: Soup search results Great Job! Which still-lifes are still left? I've got stuck on 15.310. I couldn't synthesise it, or some smaller still-lifes that can be used to make it (in a 16 glider sythesis) in few enough gliders. x = 14, y = 8, rule = B3/S23210b2o2b2o3bobobo3bo3b2o3bob2o4bobo! Things to work on: • Work on the snowflakes orthogonoid Goldtiger997 Posts: 446 Joined: June 21st, 2016, 8:00 am Location: 11.329903°N 142.199305°E ### Re: Soup search results Goldtiger997 wrote:I've got stuck on 15.310. ... By doing it in a different order, it can be done with 15: x = 155, y = 18, rule = B3/S2382bo4bo76bobbobo32bo43b3o3boo33boo37boo10bobo26bobo49boo28boo5bo50bo28bo6bobo22bo19bo5bo37boo8bo12bobo17bobo3boo5bo18boo18boo18boo18boo18boobo5boo11bobo17bobo4bobo3boo15bobobo5bobo7bobobo10boo3bobobo10boo3bobobo10boo3bobobobboo3bobo10boo18boo11bobo14boo9boo7boo14bo3boo14bo3boo14bo3booboo15boo18boo28boo11bo6boo16boboo16boboo16boboo17bobo17bobo27bobo17bobo17bobo17bobo17bobo18bo19bo29bo19bo19bo19booo3bobooboo120boobooo3bobo118bobobobo127bobo! mniemiec Posts: 929 Joined: June 1st, 2013, 12:00 am ### Re: Soup search results mniemiec wrote:Row 2: 15.652: The base 13.212 can be made from 9 reducing this to 12, which also gives 15.431 from 13 Actually, the base (as well as a variant with mango) can be made from only seven gliders: x = 48, y = 44, rule = B3/S2320bo3bo21b2obobo17b2o20b2o2b2o19bo2bo37b2oboobo37bob3ob2o42bo24b2o3bo14b2o24b2o2bo28b3o231b3o25b2o4bo9b3o12bo2bo4bo9bo15b2o10bo28b2o9b2o8bo1120bo3bo12bo8b2obobo17b2o11bo8b2o2b2o19bo11b3o26b2obo9bo30bob3o10bo34bo8b3o13b2o3bo14bobo24b2o2bo15bo2bo28b3o14bobo46bo31b3o31bo25bo6bo25b2o24bobo! I Like My Heisenburps! (and others) Extrementhusiast Posts: 1707 Joined: June 16th, 2009, 11:24 pm Location: USA ### Re: Soup search results I wrote:Row 2: 15.652: The base 13.212 can be made from 9 reducing this to 12, which also gives 15.431 from 13 Extrementhusiast wrote:Actually, the base (as well as a variant with mango) can be made from only seven gliders: ... This then also reduces 15.926 to 11: x = 31, y = 14, rule = B3/S23bbo3bob3o$$6bo$5bo$bo3b3o$bboo20boo$boo6boo13bo4boo$10bo14bo4bo$5boobo17bobo$bbobbob3o17b3o$obo7bo19bo$boo6boo18boo! mniemiec Posts: 929 Joined: June 1st, 2013, 12:00 am ### Re: Soup search results mniemiec wrote: Goldtiger997 wrote:I've got stuck on 15.310. ... By doing it in a different order, it can be done with 15: x = 155, y = 18, rule = B3/S2382bo$4bo76bo$bbobo32bo43b3o$3boo33boo$37boo10bobo26bobo$49boo28boo5bo$50bo28bo6bobo$22bo19bo5bo37boo$8bo12bobo17bobo3boo5bo18boo18boo18boo18boo18boo$bo5boo11bobo17bobo4bobo3boo15bobobo5bobo7bobobo10boo3bobobo10boo3bobobo10boo3bobobo$bboo3bobo10boo18boo11bobo14boo9boo7boo14bo3boo14bo3boo14bo3boo$boo15boo18boo28boo11bo6boo16boboo16boboo16boboo$17bobo17bobo27bobo17bobo17bobo17bobo17bobo$18bo19bo29bo19bo19bo19bo$oo3bo$booboo120booboo$o3bobo118bobobobo$127bobo!

Due to that alternate order, here is a 13 glider synthesis

x = 61, y = 57, rule = B3/S23bo$2bo$3o4$54bo$53bo$53b3o3$58bo$45bo12bobo$43b2o13b2o$27bo16b2o$28b2o$27b2o4$27bo$25bobo$26b2o3bo15bo$29b2o15b2o$30b2o14bobo$41b2o$41bobo$41bo6$38b2o$37b2o$39bo15$3o$2bo$bo48b2o$49b2o$51bo3b2o$54b2o$56bo! Things to work on: • Work on the snowflakes orthogonoid Goldtiger997 Posts: 446 Joined: June 21st, 2016, 8:00 am Location: 11.329903°N 142.199305°E ### Re: Soup search results Goldtiger997 wrote: mniemiec wrote: Goldtiger997 wrote:I've got stuck on 15.310. ... By doing it in a different order, it can be done with 15: ... Due to that alternate order, here is a 13 glider synthesis ... here is a 11 glider synthesis: x = 115, y = 30, rule = B3/S233$15bo$15bobo$15b2o3$39bo$38bo$38b3o2$35bobo$4bo4bo26b2o5bo$5b2o2bobo24bo6bobo$4b2o3b2o32b2o$30b2o18b2o18b2o18b2o18b2o$27bobobo5bobo7bobobo10b2o3bobobo10b2o3bobobo10b2o3bobobo$27b2o9b2o7b2o14bo3b2o14bo3b2o14bo3b2o$7b2o6b3o7b2o11bo6b2o16bob2o16bob2o16bob2o$8b2o5bo8bobo17bobo17bobo17bobo17bobo$7bo8bo8bo19bo19bo19bo2$83b2ob2o$82bobobobo$84bobo!

Bob Shemyakin
BobShemyakin

Posts: 208
Joined: June 15th, 2014, 6:24 am

### Re: Soup search results

Here's another 15-bit still-life

x = 101, y = 94, rule = B3/S235bobo$6b2o$6bo$bo90bo$2bo88bo$3o88b3o18$91bo$90bo$90b3o12$55bobo$51b2o2b2o$51bobo2bo$51bo4$52b3o$52bo$53bo$61b2o$44bo16bobo$42bobo16bo$43b2o13b2o$57bobo$59bo4$53b2o$52b2o$54bo$46b2o$47b2o$46bo16$98b2o$98bobo$98bo12$3b2o$4b2o$3bo! @ mniemiec & BobShemyakin: How many are left? I haven't found a suitable glider synthesis for 15.337 yet, so is there an alternative way of using smaller still-lifes to construct it, other than the one below? x = 148, y = 17, rule = B3/S2339bo42bobo$40bo41b2o$38b3o42bo$76bo$3bo38bo34bo$bobo5bo30b2o33b3o$2b2o3b2o32b2o$8b2o50b2o10b3o5b2o17bobo14bo2bobo19bo$11b2o13b2o18b2o12bobo3b2o6bo5bobo3b2o11b2obo3b2o6bobo2b2obo3b2o12bobo3b2o$11bobo9bobobo10bobo2bobobo14bo2bobo5bo8bo2bobo14bo2bobo3b2o2b2o5bo2bobo9bobo2bo2bobo$b2o8bo11b2o14b2o2b2o17bobo17bobo17bobo7b2o8bobo12b2o3bobo$obo36bo23bo19bo19bo7bo7bo3bo19bo$2bo115b2o$40b3o75bobo$40bo74b2o$41bo72bobo$116bo! Things to work on: • Work on the snowflakes orthogonoid Goldtiger997 Posts: 446 Joined: June 21st, 2016, 8:00 am Location: 11.329903°N 142.199305°E ### Re: Soup search results Goldtiger997 wrote:Here's another 15-bit still-life x = 101, y = 94, rule = B3/S235bobo$6b2o$6bo$bo90bo$2bo88bo$3o88b3o18$91bo$90bo$90b3o12$55bobo$51b2o2b2o$51bobo2bo$51bo4$52b3o$52bo$53bo$61b2o$44bo16bobo$42bobo16bo$43b2o13b2o$57bobo$59bo4$53b2o$52b2o$54bo$46b2o$47b2o$46bo16$98b2o$98bobo$98bo12$3b2o$4b2o$3bo!

@ mniemiec & BobShemyakin: How many are left?

I haven't found a suitable glider synthesis for 15.337 yet, so is there an alternative way of using smaller still-lifes to construct it, other than the one below?

x = 148, y = 17, rule = B3/S2339bo42bobo$40bo41b2o$38b3o42bo$76bo$3bo38bo34bo$bobo5bo30b2o33b3o$2b2o3b2o32b2o$8b2o50b2o10b3o5b2o17bobo14bo2bobo19bo$11b2o13b2o18b2o12bobo3b2o6bo5bobo3b2o11b2obo3b2o6bobo2b2obo3b2o12bobo3b2o$11bobo9bobobo10bobo2bobobo14bo2bobo5bo8bo2bobo14bo2bobo3b2o2b2o5bo2bobo9bobo2bo2bobo$b2o8bo11b2o14b2o2b2o17bobo17bobo17bobo7b2o8bobo12b2o3bobo$obo36bo23bo19bo19bo7bo7bo3bo19bo$2bo115b2o$40b3o75bobo$40bo74b2o$41bo72bobo$116bo!

If you remove 4 glider get 13.214 (11G-> 10G):
x = 77, y = 67, rule = B3/S237$52bo$51bo$51b3o12$16bobo$12b2o2b2o$12bobo2bo$12bo4$13b3o$13bo$14bo$22b2o$5bo16bobo$3bobo16bo$4b2o13b2o50b2o$18bobo50bo$20bo51bo$69b3o$68bo$69bo$14b2o54bobo$13b2o56b2o$15bo$7b2o$8b2o$7bo16$59b2o$59bobo$59bo!

15.337 replace last converter:
x = 148, y = 16, rule = B3/S2339bo42bobo$40bo41b2o$38b3o42bo$76bo$3bo38bo34bo$bobo5bo30b2o33b3o$2b2o3b2o32b2o72bo$8b2o50b2o10b3o5b2o17bobo14bo2bobo19bo$11b2o13b2o18b2o12bobo3b2o6bo5bobo3b2o11b2obo3b2o6b3o2b2obo3b2o12bobo3b2o$11bobo9bobobo10bobo2bobobo14bo2bobo5bo8bo2bobo14bo2bobo14bo2bobo9bobo2bo2bobo$b2o8bo11b2o14b2o2b2o17bobo17bobo17bobo17bobo12b2o3bobo$obo36bo23bo19bo19bo13b2o4bo19bo$2bo109bobo2bobo$40b3o70b2o2bo$40bo72bo$41bo! The same applies to 15,320 from 13G: x = 130, y = 62, rule = B3/S23$31bo$30bo$30b3o73bo$102bo2b2o$19bobo78bobo2bobo$20b2o54bo19bo4b2o13bo$20bo54bobo17bobo17bobo3b2o$74bo2bo16bo2bo16bo2bo2bobo$73bo3bob2o12bo3bob2o2b3o7bo3bobo$40b3o30b2o3bobo12b2o3bobo2bo9b2o3bo$23bo11b2o5bo61bo$23b2o9bobo4bo$22bobo11bo$42b2o$41b2o$29bo13bo$30bo$28b3o2$31b3o$33bo$32bo27$55b2o$55bobo$55bo6$b3o$3bo$2bo!

And 15.345 from 14G:
x = 166, y = 20, rule = B3/S2398bobo$98b2o$99bo$obo88bo57bo$b2o86bobo53bo2b2o$bo88b2o10bo40bobo2bobo$102bobo2bo36b2o$102b2o2b2o56b2o$25b2o18b2o8bo9b2o18b2o19bobo6b2o18b2o18b2o6bobo$26bo19bo8bobo8bo19bo29bo5b2o12bo5b2o2b3o7bo5bo$7bo18bob2o16bob2o5b2o9bob2ob2o13bob2ob2o23bob2obobo12bob2obobo2bo9bob2obo$6bo20bobo17bobo2b2o13bobob2o14bobob2o5b2o17bob2o16bob2o6bo9bob2o$6b3o43bobo42b2o$52bo46bo$8bo$7b2o$7bobo$b2o$2b2o$bo! More 15.503 from 14G on base 14.558 by Goldtiger997: x = 106, y = 45, rule = B3/S232$26bobo$26b2o27b2o18b2o18b2o$27bo28bo2bo16bo2bo16bo2bo$40b2o2b3o9bobobo15bobobo15bobobo$24b2o15b2obo10b2o2bo15b2o2bo15b2o2b2o$25b2o13bo4bo10bo19bo5b2o12bo$24bo30bo19bo5bobo3bo7bo$16bobo36b2o18b2o6bo2b2o7b2o$17b2o67bobo$17bo3$28b2o$27bobo2b3o$14bo14bo2bo$14b2o17bo$13bobo2b3o2b2o$20bo2bobo$19bo3bo10$18b2o$19b2o$18bo8$4b2o$3bobo$5bo!

According to my data passed over a quarter (the easiest) way. Left 76 still lifes cost > 1glider/bit and 39 cost = 1glider/bit. The biggest cost 15.441 = 31/15glider/bit.

Bob Shemyakin
BobShemyakin

Posts: 208
Joined: June 15th, 2014, 6:24 am

### Re: Soup search results

GoldTiger997 wrote:Here's another 15-bit still-life ...

BobShemyakin wrote:If you remove 4 glider get 13.214 (11G-> 10G): ...

One cleanup glider can be shaved off both syntheses: 13.234 (not 13.214) and 15.320:
x = 135, y = 45, rule = B3/S2351bo65boo$51bobo59bo3bobo$51boo61boobo$43bo44bo19bo4boo13bo$44boo41bobo17bobo17bobo3boo$43boo41bobbo16bobbo6bo9bobbobbobo$30boo28boo23bo3boboo12bo3boboobboo8bo3bobo$12b3o15boo14boo12boo23boo3bobo12boo3bobobbobo7boo3bo$7boo5bo32boo$6bobo4bo32bo$8bo$14boo$13boo$bo13bo$bbo$3o22bo7bo21bo7bo$24bobo6bo20bobo6bo$3b3o18bobo6bo20bobo6bo$5bo19bo29bo$4bo23$74bo$73boo$73bobo!

BobShemyakin wrote:More 15.503 from 14G on base 14.558 by Goldtiger997: ...

I had added this improvement to my database on 2016-10-04, in the process of adding 14.558; also, 15.502 (with boat flipped the other way)
GoldTiger997 wrote:@ mniemiec & BobShemyakin: How many are left?

BobShemyakin wrote:According to my data passed over a quarter (the easiest) way.
Left 76 still lifes cost > 1glider/bit and 39 cost = 1glider/bit.

I haven't yet included Bob Shemyakin's completed list of 15-bit still-lifes (except for a few that improve older ones), but from the others, I have 12 =15 gliders and 72 >15 gliders:
Equals: 15.369 15.386 15.405 15.406 15.440 15.447 15.485 15.487 15.598 15.653 15.873 15.1060
Greater: 15.297 15.359 15.370 15.371 15.373 15.376 15.377 15.379 15.381 15.382
15.383 15.385 15.388 15.389 15.390 15.391 15.395 15.402 15.403 15.407
15.410 15.413 15.417 15.418 15.435 15.438 15.441 15.445 15.446 15.451
15.455 15.458 15.470 15.473 15.475 15.476 15.477 15.478 15.480 15.483
15.486 15.489 15.494 15.497 15.501 15.506 15.512 15.544 15.619 15.624
15.731 15.759 15.834 15.835 15.839 15.840 15.845 15.860 15.866 15.868
15.869 15.887 15.918 15.919 15.928 15.929 15.952 15.986 15.1001 15.1013
15.1032 15.1064
mniemiec

Posts: 929
Joined: June 1st, 2013, 12:00 am

### Re: Soup search results

We interrupt your regular scheduled glider syntheses for an unrelated question... does anybody recognize this xp6, which just showed up for the second time in D8_1? (EricABQ saw the first occurrence on Catagolue back in April 2015.)

Sample soups:

Eric's:

x = 31, y = 31, rule = B3/S23obbobboobobbooobooobboboobbobbo$bbbobooooooooobbbooooooooobobbb$bbobooobbbobobooobobobbbooobobb$oobobbbbobbooboboboobbobbbboboo$bbobooobbbbooobbbooobbbbooobobb$booboooobbooooooooooobbooooboob$oooboobbbbbbooboboobbbbbboobooo$oobbbobobboobobbboboobbobobbboo$bobobbbbobobobooobobobobbbbobob$oobbbbbbbbbboobbboobbbbbbbbbboo$boobboboobbbbooboobbbboobobboob$bobooobobbbbbbbobbbbbbbobooobob$oooooooboobbooooooobboobooooooo$oobbooooboobooobooobooboooobboo$oboobobbobobooboboobobobboboobo$bbobboobobbooboooboobboboobbobb$oboobobbobobooboboobobobboboobo$oobbooooboobooobooobooboooobboo$oooooooboobbooooooobboobooooooo$bobooobobbbbbbbobbbbbbbobooobob$boobboboobbbbooboobbbboobobboob$oobbbbbbbbbboobbboobbbbbbbbbboo$bobobbbbobobobooobobobobbbbobob$oobbbobobboobobbboboobbobobbboo$oooboobbbbbbooboboobbbbbboobooo$booboooobbooooooooooobbooooboob$bbobooobbbbooobbbooobbbbooobobb$oobobbbbobbooboboboobbobbbboboo$bbobooobbbobobooobobobbbooobobb$bbbobooooooooobbbooooooooobobbb$obbobboobobbooobooobboboobbobbo!

Mine:

x = 31, y = 31, rule = B3/S23obbobbboobbbobobobobbboobbbobbo$bbobbbbbbobobbobobbobobbbbbbobb$boobbobobbooobbobbooobbobobboob$obboboobobbboobbboobbboboobobbo$bbbbbbbbbobbbbobobbbbobbbbbbbbb$bboobbbbbbobooooooobobbbbbboobb$bbbobbbbobbooobbbooobbobbbbobbb$obobbbbobobbbooooobbbobobbbbobo$obbobbobboboobbbbboobobbobbobbo$bobbobboobbbbobbbobbbboobbobbob$bbobbobbbbobbbobobbbobbbbobbobb$boobbbobobbbbbobobbbbbobobbboob$obooboobobbbbbbbbbbbbbobooboobo$bbbobooobobbbbooobbbbobooobobbb$oobboobobbooboboboboobboboobboo$bbobbobobbbbbooooobbbbbobobbobb$oobboobobbooboboboboobboboobboo$bbbobooobobbbbooobbbbobooobobbb$obooboobobbbbbbbbbbbbbobooboobo$boobbbobobbbbbobobbbbbobobbboob$bbobbobbbbobbbobobbbobbbbobbobb$bobbobboobbbbobbbobbbboobbobbob$obbobbobboboobbbbboobobbobbobbo$obobbbbobobbbooooobbbobobbbbobo$bbbobbbbobbooobbbooobbobbbbobbb$bboobbbbbbobooooooobobbbbbboobb$bbbbbbbbbobbbbobobbbbobbbbbbbbb$obboboobobbboobbboobbboboobobbo$boobbobobbooobbobbooobbobobboob$bbobbbbbbobobbobobbobobbbbbbobb$obbobbboobbbobobobobbboobbbobbo!
If you speak, your speech must be better than your silence would have been. — Arabian proverb

Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_

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Apple Bottom

Posts: 952
Joined: July 27th, 2015, 2:06 pm

### Re: Soup search results

On BobShemyakin's database, 15.236 was listed as having as having a 15 glider synthesis, so I made a 7 glider one.

x = 37, y = 46, rule = B3/S235bo$3bobo$4b2o16$34b3o$28bo5bo$27b2o6bo$12bobo12bobo$13b2o$13bo2$14b3o$16bo$15bo3$6b2o$7b2o$6bo11$3o$2bo$bo! However, mniemiec wrote:I haven't yet included Bob Shemyakin's completed list of 15-bit still-lifes (except for a few that improve older ones), but from the others, I have 12 =15 gliders and 72 >15 gliders: Equals: 15.369 15.386 15.405 15.406 15.440 15.447 15.485 15.487 15.598 15.653 15.873 15.1060 Greater: 15.297 15.359 15.370 15.371 15.373 15.376 15.377 15.379 15.381 15.382 15.383 15.385 15.388 15.389 15.390 15.391 15.395 15.402 15.403 15.407 15.410 15.413 15.417 15.418 15.435 15.438 15.441 15.445 15.446 15.451 15.455 15.458 15.470 15.473 15.475 15.476 15.477 15.478 15.480 15.483 15.486 15.489 15.494 15.497 15.501 15.506 15.512 15.544 15.619 15.624 15.731 15.759 15.834 15.835 15.839 15.840 15.845 15.860 15.866 15.868 15.869 15.887 15.918 15.919 15.928 15.929 15.952 15.986 15.1001 15.1013 15.1032 15.1064 15.236 isn't listed there. Does that mean my synthesis was unnecessary, is it just a bookkeeping error between the two databases? EDIT: I noticed as well that 15.297 is listed above, but BobShemyakin's database has this synthesis: x = 146, y = 21, rule = B3/S23129bo$bo47bo68bo8b2o$2bo40bo5bobo25bo41b2o7b2o$3o41b2o3b2o27bo39b2o$43b2o31b3o48bo$35bo24b2o18b2o44b2o$2o34bo2b2o18bo2bo16bo2bo18b2o18b2o3bobo15b2o$b2o8bo22b3obobo19b2obo16b2obo17bobo17bobo19bobo$o8b2o29bo22bo19bo19bo19bo18bo$10b2o11b2o18b2o18b2o18b2o18b2o12b2o4b2o18b2o$24bo10b2o7bo19bo19bo19bo13b2o4bo19bo$23bo12b2o5bo19bo19bo19bo13bo5bo19bo$22bo12bo6bo19bo19bo19bo19bo19bo$21bo19bo19bo19bo19bo19bo19bo$21bobo17bobo17bobo17bobo17bobo17bobo17bobo$22b2o18b2o18b2o18b2o18b2o18b2o18b2o3$7b2o$6b2o$8bo! EDIT2: Here's 15.359 in 11 gliders: x = 33, y = 33, rule = B3/S23obo$b2o$bo3$14bobo$14b2o$15bo$9bobo$10b2o$10bo11bo$17bo3bo$18b2ob3o$8bo8b2o$b3o3bo$3bo3b3o$2bo$5b2o$4bobo8b3o$6bo8bo$11bo4bo$11b2o$10bobo8$30b3o$30bo$31bo!
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 446
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: Soup search results

Goldtiger997 wrote:In BobShemyakin's database, 15.236 was listed as having as having a 15 glider synthesis, so I made a 7 glider one. ...

The shuttle can be made from 3 gliders, reducing this to 6:
x = 30, y = 25, rule = B3/S23o$boo$oo$$12bo12bobobbobo7boobboo3bo21boo25bobo4b3o19bobo4bo23bo5bo21bo26bo6bo19bobo6boo19bobo5bobo20boo67b3o9bo8bo! Goldtiger997 wrote:15.236 isn't listed there. Does that mean my synthesis was unnecessary, is it just a bookkeeping error between the two databases? As I had mentioned earlier, I am attempting to create a complete database, and finally finished all the bookkeeping for the 14-bit still-lifes a few years ago, but only had about half the 15-bit ones synthesized. Bob Shemyakin synthesized all the rest, plus he found many other, cheaper syntheses of some of the smaller ones. I am in the process of assimilating all his data, but there are over 2000 syntheses I need to examine in order to do so, so it will take a while before my list is up to date. Thus, my own list is missing about half of the 15-bit ones, including many of the expensive ones. (I also have the 700 or so difficult 18-bit still-lifes to assimilate, and those are in a more difficult format). Goldtiger997 wrote:I noticed as well that 15.297 is listed above, but BobShemyakin's database has this synthesis: ... This is because the first step, 10.21, had improved, but I had not yet updated all the derived syntheses. Goldtiger997 wrote:Here's 15.359 in 11 gliders: ... Very nice! mniemiec Posts: 929 Joined: June 1st, 2013, 12:00 am ### Re: Soup search results Goldtiger997 wrote:Here's 15.359 in 11 gliders: x = 33, y = 33, rule = B3/S23obob2obo314bobo14b2o15bo9bobo10b2o10bo11bo17bo3bo18b2ob3o8bo8b2ob3o3bo3bo3b3o2bo5b2o4bobo8b3o6bo8bo11bo4bo11b2o10bobo830b3o30bo31bo! There is an impossible glider crossing in that pattern but it can be fixed by making the pond sufficiently early. chris_c Posts: 828 Joined: June 28th, 2014, 7:15 am ### Re: Soup search results chris_c wrote: Goldtiger997 wrote:Here's 15.359 in 11 gliders: x = 33, y = 33, rule = B3/S23obob2obo314bobo14b2o15bo9bobo10b2o10bo11bo17bo3bo18b2ob3o8bo8b2ob3o3bo3bo3b3o2bo5b2o4bobo8b3o6bo8bo11bo4bo11b2o10bobo830b3o30bo31bo! There is an impossible glider crossing in that pattern but it can be fixed by making the pond sufficiently early. 10 gliders: x = 102, y = 41, rule = B3/S2346bobo47b2o47bo9bo2bo97b2o3o94b2o2bo31b2o28b2o33bo2b2o31b2o4b2o13bo8b2o4b2o28bobo7b2o27bo2bo13b2o11bo2bo26b2o2bo2b3ob2o28bo2bo12b2o12bo2bo29b2o4bo3bo28b2o20b2o6b2o3bo51bo3bobo56b2obo55b2o569b3o69bo57bo12bo57b2o56bobo884b3o84bo85bo! Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) : 965808 is period 336 (max = 207085118608). AbhpzTa Posts: 440 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan ### Re: Soup search results Known reaction? x = 10, y = 11, rule = B3/S23b2oo3boo2bob3o47b2o6bo2bo6bobo7bo! LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1753 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: Soup search results mniemiec wrote:As I had mentioned earlier, I am attempting to create a complete database, and finally finished all the bookkeeping for the 14-bit still-lifes a few years ago, but only had about half the 15-bit ones synthesized. Bob Shemyakin synthesized all the rest, plus he found many other, cheaper syntheses of some of the smaller ones. I am in the process of assimilating all his data, but there are over 2000 syntheses I need to examine in order to do so, so it will take a while before my list is up to date. Thus, my own list is missing about half of the 15-bit ones, including many of the expensive ones. (I also have the 700 or so difficult 18-bit still-lifes to assimilate, and those are in a more difficult format). Ah, I see. Well according to BobShemyakin's database, 15.297 takes 15 gliders like this: x = 79, y = 20, rule = B3/S2317bobo40bo17b2o41bobo6bo11bo41b2o7bo5b3o51bo57bobo3bo58b2o2bo62b3o258bobo3bo11bo17b2o18b2o7b2o3b2o4b2o9bobo18bo19bo8bo3bobo4bo6bo10b2o8bo9bob2o16bob2o16bob2o2bobo20bobo8b2obobo14b2obobo14b2obo2bo20b2o13b2o18b2o18b2o17b2o5b2o4b2o3b2o44b2o3o3b2o2bobo5bo39bo2b2o2bo2bo6bo45b2o3bobo55bobo! A different order yields a better synthesis from 11 gliders: x = 50, y = 50, rule = B3/S2347bobo47b2o6bo41bo7bo5b3o1430bobo30b2o31bo333bo31bobo32b2o233b3o33bo34bo916b2o17b2o2b2o16bo3bobo22bo24b2o36b3o8bobo36bo10bo37bo25b3o3o4bo2bo3bobo! I believe that now all 15-bit still-lifes from 15.1 to 15.300 have syntheses in less than 15 gliders. Things to work on: • Work on the snowflakes orthogonoid Goldtiger997 Posts: 446 Joined: June 21st, 2016, 8:00 am Location: 11.329903°N 142.199305°E ### Re: Soup search results Goldtiger997 wrote:... I believe that now all 15-bit still-lifes from 15.1 to 15.300 have syntheses in less than 15 gliders. With the exception of 15.182 (22G): x = 161, y = 29, rule = 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! and 15.252 (16G): x = 118, y = 21, rule = B3/S2353bo37bo7bo43bobo36bo8bo10bo32b2o6bo29b3o6b3o10bobo37bo19b2o38b3o26b3o90bo89bo10bobo22bo19bo11b2o21bobo17bobo17bo19bo14b2o3bo11bo21bobo17bobo3bo13bobo10b2o5bobo13bo3bobo33bo19bo5bobo11bo2bo8bobo5bo2bo13bo2bo2bo31bobo17bobo5b2o10bobo3bo9bo3bobo3bo13bobo3bo11b3o3bobo10bobo17bobo17bobo3b2o12bobo3b2o14bo3b2o13bo3b2o12bo19bo19bo19bo12bo5bo38bo56bo56b3o26b3obo85bob2o51b3o29bo6b2oobo53bo36bobo55bo37bo! Bob Shemyakin BobShemyakin Posts: 208 Joined: June 15th, 2014, 6:24 am ### Re: Soup search results Goldtiger997 wrote:Well according to BobShemyakin's database, 15.297 takes 15 gliders like this: ... A different order yields a better synthesis from 11 gliders: ... This is actually 15.287. In my collection, I try, for multi-part objects, I try, whenever possible, to provide the smallest synthesis, as well as all syntheses beginning with any of the parts. This facilitates future, larger incremental syntheses in which those parts may be already attached to something else. Such techniques would yield both your synthesis and his, with yours being the cheaper path (and, at least at present, there is no "natural" atomic synthesis that is better.) I believe that now all 15-bit still-lifes from 15.1 to 15.300 have syntheses in less than 15 gliders.[/quote] By examining Bob Shemyakin's most recent still15.rar archive, I found the following additional still-lifes that aren't on my lists: Equals: 15.365 15.402 15.410 15.431 15.446 15.487 15.506 15.516 15.751 15.786 15.839 15.855 15.890 15.919 15.931 15.934 15.939 15.942 15.949 15.1024 15.1033 15.1034 15.1036 15.1088 15.1103 15.1207 Greater: 15.182 15.252 15.304 15.416 15.457 15.507 15.508 15.562 15.578 15.620 15.698 15.723 15.791 15.797 15.840 15.848 15.849 15.889 15.923 15.947 15.960 15.983 15.1012 15.1035 15.1065 (15.182 and 15.252 remain unoptimized, from 22 and 16 gliders respectively (EDIT: as Bob just pointed out), and 15.304 from 16 for the next batch.) mniemiec Posts: 929 Joined: June 1st, 2013, 12:00 am ### Re: Soup search results A weird pulsar variant in D4_+1: x = 31, y = 31, rule = 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! I think a synthesis is possible based on this for the [cis x2]-two-quadrant and double-mirrored four-quadrant versions. x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)$$x_1=\eta xV^*_\eta=c^2\sqrt{\Lambda\eta}K=\frac{\Lambda u^2}2P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$http://conwaylife.com/wiki/A_for_all Aidan F. Pierce A for awesome Posts: 1631 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Soup search results From here, for 15.297: x = 8, y = 13, rule = B3/S233b2o3bobo5b2o4b2o34b3o4bo2bo5b3o2b2oo2bob2o! For 15.889: x = 12, y = 18, rule = B3/S2310bo8b2o9b2o6boobo2obo5bobo3b2o4b2o3bo6bo2bo26b2o5bobo7bo! EDIT: 15.182 in 7G: x = 38, y = 22, rule = B3/S2337bo35b2o36b2o10bobo11b2o11bo2obob2obo215bo13b2o14b2o17b3o17bo6bo11bo6b2o5bobo16bo15b2o15bobo! 15.624: x = 27, y = 25, rule = B3/S2325bo24bo11b2o11b3o10b2o11bo514b3o215bo13bobo13b2o7b2o6bob2o6bo3bo7b3o8bo42ob2oo! Everything but the R in 9G: x = 33, y = 31, rule = B3/S2331bo30bo30b3o714bo15bo12bo13b3o10b2o27b2o47bobo8b2o8bo6bo15b2o14bobo25bo4bo9b2o13b2o3b2o8bobo13bobo2bobo10bo42ob2oo! LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1753 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: Soup search results mniemiec wrote:(15.182 and 15.252 remain unoptimized, from 22 and 16 gliders respectively (EDIT: as Bob just pointed out), and 15.304 from 16 for the next batch.) Oh sorry, I must have missed those. BlinkerSpawn wrote:15.182 in 7G: x = 38, y = 22, rule = B3/S2337bo35b2o36b2o10bobo11b2o11bo2obob2obo215bo13b2o14b2o17b3o17bo6bo11bo6b2o5bobo16bo15b2o15bobo! Nice! Here is 15.252 and 15.304 both in 12 gliders. x = 111, y = 121, rule = B3/S23106bo105bo105b3o4073bo73bobo44bo28b2o45b2o44b2o1156bo54bobo55b2o257bo57bobo57b2o1455b3o2b2o57bo2bobo56bo3bo1613b2o14b2o13bo73b3o5bo4bo3b2oobo2bo53o2bobo106b2o108bobo108bo! x = 51, y = 32, rule = B3/S2337bobo37b2o38bo15bo13bobo14b2o319bo20bo18b3o35bo33bobo2bobo34b2o2b2o39bo213b3o15bo8bo6b3o14bo9b2o5bo23bobo6bo317b2o4b2o24b2o16bobo3bobo23b2o18bo5bo25bo53o2bobo! Now all 15-bit still-lifes from 15.1 to 15.300 have syntheses in less than 15 gliders! Things to work on: • Work on the snowflakes orthogonoid Goldtiger997 Posts: 446 Joined: June 21st, 2016, 8:00 am Location: 11.329903°N 142.199305°E ### Re: Soup search results BlinkerSpawn wrote:15.182 in 7G: ... Row 1: The above gives 15.624 from 13. Row 2: 15.465 from 11, giving 15.889 from 17. x = 129, y = 89, rule = B3/S2361bo61bobo61boo$$39boo18boo$39boo18boo5$104bo$98bo5bobo$99boo3boo$98boo$$7bo5bobo119booo5boo24booboboo13booboboo13booboboo13booboboo6bobo14boobobboboo28boboboobo12boboboobo12boboboobo12boboboobo6boo14boboboooo6bobo20bobbo16bobbo16bobbo16bobbo11bo14bobbo8boo22bobo17bobo17bobo17bobo27bobo9bo23bo19bo19bo19bo8bo20bo17boo82boo6bo16boo83bobo4boo18bo89bobo98b3o100bo3boo94bo4boo3bo313boo12boo14bo1625bo25bobo25boo$$bbo109bo$obo17bobo89bobo$boo17boo90boo$21bo88bo$104bo3bobo$105bo3boo$69bobo31b3o$69boo40bo$12bo57bo38boo4bo$11bo98boo3bobo$11b3o57boo42boo$9bo60boo54boo$7bobo36bo19bo5bo13boo18boo19bo$8boo32boobobo14boobobo14boobobo14boobobo14boobo$18bo22boboboo14boboboo14boboboo14boboboo5boo7boboboo$16boo23bobbo16bobbo16bobbo16bobbo7bobo6bobbo$17boo23bobo17bobo17bobo17bobo7bo9bobo$43bo19bo19bo19bo19bo10$16bo$15boo$15bobo3$10bo16boo$10boo14boo$9bobo16bo!
mniemiec

Posts: 929
Joined: June 1st, 2013, 12:00 am

### Re: Soup search results

mniemiec wrote:

Row 1: The above gives 15.624 from 13.
Row 2: 15.465 from 11, giving 15.889 from 17.
x = 129, y = 89, rule = B3/S2361bo$61bobo$61boo$$39boo18boo39boo18boo5104bo98bo5bobo99boo3boo98boo$$7bo$5bobo119boo$o5boo24booboboo13booboboo13booboboo13booboboo6bobo14boobobbo$boo28boboboobo12boboboobo12boboboobo12boboboobo6boo14boboboo$oo6bobo20bobbo16bobbo16bobbo16bobbo11bo14bobbo$8boo22bobo17bobo17bobo17bobo27bobo$9bo23bo19bo19bo19bo8bo20bo$17boo82boo6bo$16boo83bobo4boo$18bo89bobo$98b3o$100bo$3boo94bo$4boo$3bo3$13boo$12boo$14bo16$25bo$25bobo$25boobbo109bo$obo17bobo89bobo$boo17boo90boo$21bo88bo$104bo3bobo$105bo3boo$69bobo31b3o$69boo40bo$12bo57bo38boo4bo$11bo98boo3bobo$11b3o57boo42boo$9bo60boo54boo$7bobo36bo19bo5bo13boo18boo19bo$8boo32boobobo14boobobo14boobobo14boobobo14boobo$18bo22boboboo14boboboo14boboboo14boboboo5boo7boboboo$16boo23bobbo16bobbo16bobbo16bobbo7bobo6bobbo$17boo23bobo17bobo17bobo17bobo7bo9bobo$43bo19bo19bo19bo19bo10$16bo$15boo$15bobo3$10bo16boo$10boo14boo$9bobo16bo! 15.889 in 7G: x = 26, y = 29, rule = B3/S2323bobo$23b2o$24bo3$o$b2o$2o5$14bo$13b2o$13bobo6$4bo15b3o$4bobo13bo$4b2o2b3o10bo$8bo$9bo2$2b2o$b2o\$3bo!
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

Posts: 440
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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