Extrementhusiast wrote:#C Original eater2 in 21 gliders.
While this doesn't improve the original eater2, it DOES improve hat-on-hat by 1,
The cheaper hat-on-hat improves 19.3754 (hat-on-hat with bit) by 1. The extra bit can already be added with 2 gliders instead of 1, so both your synthesis and mine cost the same, but when we combine the best features of both, we save one glider, although this step is no longer necessary (see below).
The cheaper hat-on-hat also improves 21.47034 by 1. The whole side part can be added directly in one step with 3 gliders, saving you 5, for eater2 in 16 gliders.
Code: Select all
#C 19.3754 from hat-on-hat from 2 gliders (saves 1)
#C 21.47034 from hat-on-hat from 3 gliders (saves 5)
#C Corner block to boat from 6 gliders (saves 1; see description below)
x = 77, y = 38, rule = B3/S23
15boobboo$bbo11boboboo12bo19bo19bo$bobo12bo3bo10bobo17bobo17bobo$bobo
27bobo17bobo6bo10bobo$ooboo25booboo15booboo3boo10boob3o$35bo23boo15bo$
ooboo25booboo15booboo15boob3o$bobo27bobo17bobo6bo10bobo$bobo27bobo17bo
bo5boo10bobo$bbo29bo19bo6bobo10bo$$56b3o$58bo$57bo10$57bo$55bobo$56boo
$8bo$9bo3bo18boo13bo4boo4bo$7b3oboo18bobbo13boobobboboo$12boo17bobbo
12boobbobbobboo$32boo9boo7boo$44boo$43bo26bo$10booboo15booboo15booboo
14boboboo$10booboo15booboo15booboo15booboo$$10booboo15booboo15booboo
15booboo$10booboo15booboo15booboo15booboo!
Code: Select all
#C Optimal Eater-2 from 8 gliders, plus improved 16-glider alternate synthesis
x = 151, y = 47, rule = B3/S23
8bo17bo19bo19bo19bo19bo19bo19bo$8bobo14bobo17bobo17bobo17bobo17bobo17b
obo17bobo$8boo15bobo17bobo17bobo17bobo17bobo17bobo17bobo$24booboo15boo
boo15booboo15booboo15booboo15booboo15booboo$$4boo37bo5bo14booboo15boob
oo15boob4o13boob4o13boob4o$bbobobo36boo3boo13bobobobo13bobobobobbo10bo
bobobbo12bobobobbo13boobobbo$obobo37bobo3bobo13bo3bo15bo3bo3bobo9bo19b
o$boo89boo26b3o$122bo$94boo25bo$93bobo$95bo18$6bo19bo19bo19bo19bo19bo
19bo19bo$5bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo$5bobo17bobo
17bobo17bobo17bobo6bo10bobo17bobo17bobo$4booboo15booboo15booboo15boob
oo15booboo3boo10boob3o14boob3o14boob3o$93boo15bo19bo19bo$4booboo15boob
oo8bo6booboo15booboo15booboo15boob3o14boob3o14boob3o$3bobobobo13bobobo
bo8boo3bobobobo15bobo17bobo6bo10bobo17bobo16boobo$4bo3bo15bobbobo7boo
5bobbobo15bobo17bobo5boo10bobo17bobo$27boo18boo17bo19bo6bobo10bo19bo$
40bobo$12bo28boo9boo36b3o31booboo$11boo28bo9boo39bo30bobobobo$11bobo
39bo37bo33bobo$39boo$8b3o29boo$10bo28bo$9bo!
Extrementhusiast wrote:Start on 65p13.1
14.91 (Ram's head w/tub) can be built for 8 gliders instead of 9, saving 1 glider. (Considering the way it forms, it might be possible to find a way of smashing 2 additional gliders into the forming right side to turn it into a tub to directly make the 15.689, saving an additional glider, although I haven't found a way to do so).
Extrementhusiast wrote:Got it!!! with 116 gliders!
Congratulations! I had played with this oscillator several times a bit a few years ago, but could never figure out how to create the final step. There are several ways to reduce this; I've gotten it down to 94 so far.
When turning pi-pairs into pairs of block-on-block, a domino spark can form a boat instead of a block - MUCH cheaper than doing so later. It's easy to do this to the first one, reducing the cost by 5. (Even if this trick couldn't be used, one could still use pond+4 gliders rather than block+5 gliders, so that would reduce it by 1 instead.)
(It's even easy to do it to two opposite sides (ship+8 gliders rather than block+3 gliders), but unfortunately, all the ways I know of making pis either make annoying plumes on one side, or require a glider to pass through another. If this can be solved, and an appropriate domino can be brought in on the remaining side, the cost of this cluster could be reduced even further, although at 14 gliders now, this step would likely cost at least 13, so it probably wouldn't be worth it.)
A slightly different beehive mechanism can convert two blocks to boats without needing the cleanup glider (see first pattern above).
Flipping the eater2s can save one glider, as the 2-glider boat-to-table tool can be used. Unfortunately, the flipped eater2s interfere with one of the final-step activation gliders. However, this reduction CAN be used if one wants to go with "real" eater2s.
Code: Select all
#C 94-glider reduced-cost P13 oscillator synthesis
x = 297, y = 172, rule = B3/S23
43bo$41boo$42boo218bo$123bo21bo117boo$124boo17boo117boo$3bo77bo41boo
19boo$bobo77bobo$bboo77boo98bo45bo23bobo3bobo9bobo3bobo$76bo43bobo23bo
bo30bobo45bobo22boo4boo9boo4boo$3bo19boo18boo32boo42boo23boo28boobboo
45boobboo19bo5bo11bo5bo$3boo17bobbo16bobbo30boo43bo25bo29boo51boo23boo
15boo$bbobo17bobbo16bobbo21bo5boo12bo13bo5bo23bo5bo38bo55bo21bobo15bob
o$23boo18boo16boo3bobo3bobo6boo3bobo11bobo3bobo21bobo3bobo23bo3bo15bo
3bo14boo3bo14boo3bo14boo3boo8bo4boo3boo4bo9booboo$61bobobobo6bo6bobobo
bo13bobobobo23bobobobo23bobobobo13bobobobo12bobbobobo12bobbobobo12bobb
obobbo11bobbobobbo12bobobobo$63bobo17bobo17bobo27bobo25bobobobo8b3obbo
bobobo13bobobobo13bobobobobb3o8bobobobo13bobobobo13bobobobo$63bobo17bo
bo17bobo27bobo24booboboboo9bobooboboboo11booboboboo11booboboboobo9boob
oboboo11booboboboo11booboboboo$64bo19bo19bo29bo28bobo11bo5bobo17bobo
17bobo5bo11bobo17bobo17bobo$163bobo17bobo17bobo17bobo17bobo17bobo17bob
o$117b3o29b3o12bo19bo19bo19bo19bo19bo19bo$119bo4boo17boo4bo$118bo4bobo
17bobo4bo$30bo94bo17bo$29bo18b3o80bobo$29b3o16bo83boo$49bo82bo$30bo$
29boo102boo$29bobo100bobo$134bo3$136boo$136bobo$136bo$46boo$45boo$47bo
13$72bo104bo36b3o$72bobo100bobo38bobbo$64bo7boo102boo37bobbo$65boo113b
o37b3o$64boo5bo106boo$69bobo50bobo54boo59boo18boo28boo$70boo18bo19bo
12boo15bo29bo29bo3bo15bo3bo16bobbo16bobbo26bobbo$89boboboo14boboboo8bo
15boboboo24boboboo24bobobobo13bobobobo15bobobo15bobobo25bobobo$60b3o
27booboo15booboo25booboo3boo20booboo3boo20booboo15booboo15booboo15boob
oo25booboo$62bo59b3o22bobbo26bobbo$61bo11bo16booboo15booboo7bo17booboo
3boo20booboo3boo20booboo15booboo15booboo15booboo25boob4o$73bobo14boob
oo15booboo8bo16booboo25booboo25boobobo14boobobo14boobobo14boobobo6bo
17boobobbo$73boo129bo19bo19bo19bo7bobo19boo$22booboo15booboo15booboo
15booboo15booboo17bo7booboo25booboo12boo11booboo15booboo15booboo15boob
oo15boo8booboo$21bobobobo5bo7bobobobo13bobobobo13bobobobo13bobobobo15b
oo6bobobobo23bobobobo10boo11bobobobo13bobobobo13bobobobo13bobobobo11b
oo10bobobobo$21bobobobo5bobo5bobobobo4boo7bobobobo4boo7bobobobo13bobob
obo15bobo5bobobobo23bobobobo12bo10bobobobo13bobobobo13bobobobo13bobobo
bo10boo11bobobobo$20booboboboo4boo5booboboboo3boo6booboboboo3boo6boobo
boboo11booboboboo21booboboboo21booboboboo7boo12booboboboo11booboboboo
11booboboboo11booboboboo11bo9booboboboo$23bobo10boo5bobo17bobo17bobo
17bobo27bobo27bobo9bobo15bobo17bobo17bobo17bobo27bobo$23bobo10bobo4bob
o17bobo17bobo17bobo27bobo27bobo11bo15bobo17bobo17bobo17bobo27bobo$24bo
11bo7bo19bo19bo19bo29bo29bo29bo19bo19bo19bo29bo7$171bo$51bobo118boo$
52boo117boo$52bo$13bobo150bo9bo$14boo148bobo7boo$14bo6bobo141boo8boo$
17bo3boo$18boobbo144bo$10boo5boo21boo12bobo13boo18boo28boo28boo15bobo
10boo28boo12bobo23boo38boo$11bobbo26bo13boo14bo11boo6bo21boo6bo21boo6b
o15boo4boo6bo16bo12bo12boo12bo12bo26bo12bo$11bobobo25bobo11bo15bobo8bo
bbo5bobo18bobbo5bobo18bobbo5bobo18bobbo5bobo10boobobo11bobo11bo8boobob
o11bobo20boobobo11bobo$10booboo25boob3o24boob3o6bobbo4boob3o16bobbo4b
oob3o16bobbo4boob3o16bobbo4boob3o8booboo11boob3o18booboo11boob3o13boo
3booboo11boob3o$46bo9b3o17bo6boo11bo16boo11bo16boo11bo16boo11bo29bo7b
3o29bo11bobbo24bo$10boob4o23boob3o12bo11boob3o14boob3o24boob3o24boob3o
9bo14boob3o8booboo11boob3o10bo7booboo11boob3o13boo3booboo11boob3o$10b
oobobbo23boobo13bo12boobo16boobo26boobo26boobo9bobo14boobo10booboo11b
oobo11bo8booboo11boobo20booboo11boobo$14boo148boo$bbooboo25booboo25boo
boo15booboo25booboo25booboo25booboo25booboo17bo17booboo35booboo$bobobo
bo11bo11bobobobo23bobobobo13bobobobo17bo5bobobobo23bobobobo23bobobobo
23bobobobo16boo15bobobobo33bobobobo$bobobobo10boo11bobobobo23bobobobo
13bobobobo15bobo5bobobobo17boo4bobobobo17boo4bobobobo23bobobobo15bobo
15bobobobo33bobobobo$ooboboboo9bobo9booboboboo21booboboboo11booboboboo
15boo4booboboboo16boo3booboboboo16boo3booboboboo21booboboboo31boobobob
oo31booboboboo$3bobo27bobo27bobo17bobo15boo10bobo27bobo27bobo27bobo37b
obo37bobo$3bobo27bobo27bobo17bobo14bobo10bobo27bobo27bobo27bobo37bobo
37bobo$4bo29bo29bo19bo17bo11bo29bo29bo29bo39bo39bo11$31bo211bobo$31bob
o209boo$31boo202bobo6bo$28bo207boo3bo$29boo205bobboo$28boo20boo28boo
38boo28boo25boo11boo15boo11boo18boo5boo11boo15boo11boo$38bo12bo12bo3bo
12bo22bo3bo12bo12bo3bo12bo22bobbo13bo12bobbo13bo22bobbo13bo15bo13bo$
34boobobo11bobo9bobobobo11bobo19bobobobo11bobo9bobobobo11bobo19bobobo
13bobo9bobobo13bobo19bobobo13bobo11bobo13bobo$29boo3booboo11boob3o8boo
boo11boob3o18booboo11boob3o8booboo11boob3o18booboo11boob3o8booboo11boo
b3o18booboo11boob3o7b3oboo11boob3o$28bobbo24bo29bo39bo29bo39bo29bo39bo
5bo23bo$29boo3booboo11boob3o8booboo11boob3o18booboo11boob3o6b4oboo11b
oob3o18booboo11boob3o6b4oboo11boob3o16b4oboo11boob3o7b3oboo11boob3o$
34booboo11boobo9boboboo11boobo12bo6boboboo11boobo8bobboboo11boobo12bo
6boboboo11boobo8bobboboo11boobo18bobboboo11boobo11boboo11boobo$64bo29b
obo7bo59bobo7bo28boo38boo$28boo12booboo25booboo18boo15booboo25booboo
18boo15booboo25booboo35booboo25booboo$29boo10bobobobo23bobobobo20boo
11bobobobo23bobobobo20boo11bobobobo23bobobobo21bo11bobobobo23bobobobo$
28bo12bobobobo23bobobobo21boo10bobobobo23bobobobo21boo10bobobobo23bobo
bobo21boo10bobobobo23bobobobo$31boo7booboboboo21booboboboo19bo11boobob
oboo21booboboboo19bo11booboboboo21booboboboo19bobo9booboboboo21boobobo
boo$31bobo9bobo27bobo29b3o5bobo27bobo37bobo27bobo37bobo27bobo$31bo11bo
bo27bobo29bo7bobo27bobo37bobo27bobo37bobo27bobo$44bo29bo31bo7bo29bo39b
o29bo39bo29bo14$148bobo47bobo$149boo47boo$149bo17boo11boo17bo7boo11boo
15boo11boo25boo11boo$167bo13bo25bo13bo15bo13bo25bo13bo$165bobo13bobo
21bobo13bobo11bobo13bobo21bobo13bobo$163b3oboo11boob3o17b3oboo11boob3o
7b3oboo11boob3o17b3oboo11boob3o$155bobo4bo23bo4bobo8bo23bo5bo23bo15bo
23bo$156boo5b3oboo11boob3o5boo10b3oboo11boob3o7b3oboo11boob3o17b3oboo
11boob3o$156bo8boboo11boobo8bo12boboo11boobo11boboo11boobo21boboo11boo
bo$$172booboo36bobo27bobo37bobo$171bobobobo34booboo25booboo35booboo$
171bobobobo32booboboboo21booboboboo31booboboboo$170booboboboo30bobobob
obobo19bobobobobobo29bobobobobobo$173bobo33boobbobobboo19boobbobobboo
29boobbobobboo$173bobo37bobo27bobo37bobo$174bo39bo29bo39bo$$160boo25b
oo29bo5bo23bo5bo$159bobo25bobo28bo5bo23bo5bo$161bo10bo14bo30bo5bo23bo
5bo$171boo$171bobo3bobo40b3o27b3o6boo$165boo10boo80bobo$166boo10bo80bo
$165bo$178boo$179boo4b3o$178bo6bo$186bo!
Code: Select all
#C 113-glider P13 oscillator synthesis with "real" eater2s
x = 296, y = 202, rule = B3/S23
42bo$40boo$41boo218bo$122bo21bo117boo$123boo17boo117boo$bbo77bo41boo
19boo$obo77bobo$boo77boo98bo45bo23bobo3bobo9bobo3bobo$75bo43bobo23bobo
30bobo45bobo22boo4boo9boo4boo$bbo19boo18boo32boo42boo23boo28boobboo45b
oobboo19bo5bo11bo5bo$bboo17bobbo16bobbo30boo43bo25bo29boo51boo23boo15b
oo$bobo17bobbo16bobbo21bo5boo12bo13bo5bo23bo5bo38bo55bo21bobo15bobo$
22boo18boo16boo3bobo3bobo6boo3bobo11bobo3bobo21bobo3bobo23bo3bo15bo3bo
14boo3bo14boo3bo14boo3boo8bo4boo3boo4bo9booboo$60bobobobo6bo6bobobobo
13bobobobo23bobobobo23bobobobo13bobobobo12bobbobobo12bobbobobo12bobbob
obbo11bobbobobbo12bobobobo$62bobo17bobo17bobo27bobo25bobobobo8b3obbobo
bobo13bobobobo13bobobobobb3o8bobobobo13bobobobo13bobobobo$62bobo17bobo
17bobo27bobo24booboboboo9bobooboboboo11booboboboo11booboboboobo9boobob
oboo11booboboboo11booboboboo$63bo19bo19bo29bo28bobo11bo5bobo17bobo17bo
bo5bo11bobo17bobo17bobo$162bobo17bobo17bobo17bobo17bobo17bobo17bobo$
116b3o29b3o12bo19bo19bo19bo19bo19bo19bo$118bo4boo17boo4bo$117bo4bobo
17bobo4bo$29bo94bo17bo$28bo18b3o80bobo$28b3o16bo83boo$48bo82bo$29bo$
28boo102boo$28bobo100bobo$133bo3$135boo$135bobo$135bo$45boo$44boo$46bo
10$258bo$257bo$257b3o$61bo104bo$61bobo100bobo87bobo$53bo7boo102boo88b
oo$54boo113bo85bo$53boo5bo106boo$58bobo50bobo54boo119boo$59boo18bo19bo
12boo15bo29bo29bo3bo15bo3bo25bo3bo15bo3bo24bobobbo$78boboboo14boboboo
8bo15boboboo24boboboo24bobobobo13bobobobo23bobobobo13bobobobo23bobobob
o$49b3o27booboo15booboo25booboo3boo20booboo3boo20booboo15booboo25boob
oo15booboo25booboo$51bo59b3o22bobbo26bobbo$50bo11bo16booboo15booboo7bo
17booboo3boo20booboo3boo20booboo15booboo25boob4o13boob4o23boob4o$62bob
o14booboo15booboo8bo16booboo25booboo25boobobo14boobobobbo21boobobbo13b
oobobbo23boobobbo$62boo129bo19bo3bobo$11booboo15booboo15booboo15booboo
15booboo17bo7booboo25booboo12boo11booboo15booboo11boo12booboo15booboo
25booboo$10bobobobo5bo7bobobobo13bobobobo13bobobobo13bobobobo15boo6bob
obobo23bobobobo10boo11bobobobo13bobobobo23bobobobo13bobobobo23bobobobo
$10bobobobo5bobo5bobobobo4boo7bobobobo4boo7bobobobo13bobobobo15bobo5bo
bobobo23bobobobo12bo10bobobobo13bobobobo12boo9bobobobo13bobobobo23bobo
bobo$9booboboboo4boo5booboboboo3boo6booboboboo3boo6booboboboo11boobobo
boo21booboboboo21booboboboo7boo12booboboboo11booboboboo10bobo8boobobob
oo11booboboboo21booboboboo$12bobo10boo5bobo17bobo17bobo17bobo27bobo27b
obo9bobo15bobo17bobo15bo11bobo17bobo27bobo$12bobo10bobo4bobo17bobo17bo
bo17bobo27bobo27bobo11bo15bobo17bobo27bobo17bobo27bobo$13bo11bo7bo19bo
19bo19bo29bo29bo29bo19bo29bo19bo29bo8$240bobo$28bo212boo$26boo213bo$
27boo178bo$14bo193boo$15boo9bo180boo$14boo9boo$25bobo122bo56bo$19boo
30bo29bo29bo29bo7bo21bo29bo4boo23bo11bobo15bo29bo$18bobobbo5boo19bobo
27bobo27bobo27bobo6b3o18bobo27bobo3bobo21bobo11boo14bobo19boo6bobo$18b
obobobo3boo20bobo27bobo27bobo27bobo27bobo27bobo27bobo11bo15bobo18bobbo
5bobo$19booboo6bo18booboo25booboo25booboo25booboo25boob3o24booboo25boo
boo25booboo17bobbo4booboo$85bo29bo29bo29bo59bo9b3o34boo$19boob4o23boob
4o23boob3obo22boob3obo22boob3obo22boob3o24boob4o23boob3obo10bo11boob4o
23boob4o$19boobobbo23boobobbo23boobo3bo22boobo3bo22boobo3bo3boo17boobo
26boobobbo5bo17boobo3bo9bo12boobobbo23boobobbo$86boo28boo28booboo59boo
24boo$11booboo25booboo25booboo25booboo7bo17booboo7bo7bo9booboo25booboo
14bobo8booboo25booboo25booboo$10bobobobo23bobobobo23bobobobo23bobobobo
6bo16bobobobo6bo16bobobobo23bobobobo23bobobobo23bobobobo23bobobobo$10b
obobobo23bobobobo23bobobobo23bobobobo6bo16bobobobo6bo16bobobobo23bobob
obo23bobobobo23bobobobo23bobobobo$9booboboboo21booboboboo21booboboboo
21booboboboo21booboboboo21booboboboo21booboboboo6boo13booboboboo21boob
oboboo21booboboboo$12bobo27bobo27bobo11boo14bobo27bobo9boo16bobo27bobo
10boo6boo7bobo27bobo27bobo$12bobo27bobo27bobo11bobo13bobo27bobo9bobo
15bobo27bobo9bo7boo8bobo27bobo27bobo$13bo29bo29bo12bo16bo29bo10bo18bo
29bo20bo8bo29bo29bo$82b3o$84bo$83bo4$100bo$101boo$100boo$$95bo9bo134bo
$93bobo7boo135bobo$94boo8boo134boo$237bo$96bo141boo$51bo29bo14bobo12bo
29bo11bobo25bo39bo15boo22bo29bo$42boo6bobo19boo6bobo13boo4boo6bobo14bo
12bobo10boo12bo12bobo24bo12bobo24bo12bobo10bo3bo12bobo$41bobbo5bobo18b
obbo5bobo18bobbo5bobo10boobobo11bobo11bo8boobobo11bobo20boobobo11bobo
20boobobo11bobo9bobobobo11bobo$41bobbo4booboo17bobbo4booboo17bobbo4boo
boo9booboo11booboo19booboo11booboo14boo3booboo11booboo14boo3booboo11b
ooboo9booboo11booboo$42boo28boo28boo49b3o41bobbo36bobbo$49boob4o23boob
4o8bo14boob4o7booboo11boob4o9bo7booboo11boob4o12boo3booboo11boob4o12b
oo3booboo11boob4o7booboo11boob4o$49boobobbo23boobobbo6bobo14boobobbo7b
ooboo11boobobbo8bo8booboo11boobobbo17booboo11boobobbo17booboo11boobobb
o6boboboo11boobobbo$93boo178bo$41booboo25booboo25booboo25booboo17bo17b
ooboo35booboo21boo12booboo25booboo$34bo5bobobobo23bobobobo23bobobobo
23bobobobo16boo15bobobobo33bobobobo21boo10bobobobo23bobobobo$32bobo5bo
bobobo17boo4bobobobo17boo4bobobobo23bobobobo15bobo15bobobobo33bobobobo
20bo12bobobobo23bobobobo$33boo4booboboboo16boo3booboboboo16boo3boobobo
boo21booboboboo31booboboboo31booboboboo22boo7booboboboo21booboboboo$
30boo10bobo27bobo27bobo27bobo37bobo37bobo25bobo9bobo27bobo$29bobo10bob
o27bobo27bobo27bobo37bobo37bobo25bo11bobo27bobo$31bo11bo29bo29bo29bo
39bo39bo39bo29bo8$108bo$109bo58bo$107b3o59boo$168boo69bo$110bobo69bo
54boo$110boo58bo9boo56boo$111bo58boo9boo$169bobo67bo$61bo29bo29bo14boo
13bo24boo13bo13bo15bo17boo4bo15bo13bo15bo$43bo3bo12bobo10bo3bo12bobo
10bo3bo12bobo10bobbobo11bobo13boo5bobbobo11bobo11bobo13bobo15bobo3bobo
13bobo11bobo13bobo$42bobobobo11bobo9bobobobo11bobo9bobobobo11bobo9bobo
bobo11bobo14boo3bobobobo11bobo11bobo13bobo21bobo13bobo11bobo13bobo$43b
ooboo11booboo9booboo11booboo9booboo11booboo9booboo11booboo12bo6booboo
11booboo9booboo11booboo19booboo11boob3o8booboo11boob3o$265bo5bo23bo$
43booboo11boob4o5b4oboo11boob4o5b4oboo11boob4o5b4oboo11boob4o15b4oboo
11boob4o5b4oboo11boob4o15b4oboo11boob3o5bob3oboo11boob3o$39bobboboboo
11boobobbo5bobboboo11boobobbo5bobboboo11boobobbo5bobboboo11boobobbo15b
obboboo11boobobbo5bobboboo11boobobbo9bo5bobboboo11boobo7bo3boboo11boob
o$37bobo3bo191boo32boo$38boo11booboo25booboo25booboo25booboo35booboo
25booboo18bobo14booboo25booboo$50bobobobo23bobobobo23bobobobo23bobobob
o33bobobobo23bobobobo33bobobobo23bobobobo$36boo12bobobobo23bobobobo23b
obobobo23bobobobo33bobobobo23bobobobo33bobobobo23bobobobo$36bobo10boob
oboboo21booboboboo21booboboboo21booboboboo31booboboboo21booboboboo23b
oo6booboboboo21booboboboo$36bo15bobo27bobo27bobo27bobo37bobo27bobo17b
oo6boo10bobo27bobo$52bobo27bobo27bobo27bobo37bobo27bobo18boo7bo9bobo
27bobo$53bo29bo29bo29bo39bo29bo18bo20bo29bo14$147bobo47bobo$86bo61boo
47boo$25bo15bo13bo15bo15bo7bo15bo13bo15bo6bo16bo15bo16bo6bo15bo13bo15b
o23bo15bo$24bobo13bobo11bobo13bobo12b3o6bobo13bobo11bobo13bobo21bobo
13bobo21bobo13bobo11bobo13bobo21bobo13bobo$24bobo13bobo11bobo13bobo21b
obo13bobo11bobo13bobo21bobo13bobo21bobo13bobo11bobo13bobo21bobo13bobo$
23booboo11boob3o8booboo11boob3o18booboo11boob3o7b3oboo11boob3o17b3oboo
11boob3o17b3oboo11boob3o7b3oboo11boob3o17b3oboo11boob3o$21bo23bo5bo23b
o15bo23bo5bo23bo8bobo4bo23bo4bobo8bo23bo5bo23bo15bo23bo$20bob3oboo11b
oob3o5bob3oboo11boob3o15bob3oboo11boob3o7b3oboo11boob3o10boo5b3oboo11b
oob3o5boo10b3oboo11boob3o7b3oboo11boob3o17b3oboo11boob3o$20bo3boboo11b
oobo7bo3boboo11boobo12boo3bo3boboo11boobo11boboo11boobo12bo8boboo11boo
bo8bo12boboo11boobo11boboo11boobo21boboo11boobo$19boo28boo35booboo$31b
ooboo17bo7booboo19bo7bo7booboo25booboo35booboo36bobo27bobo37bobo$30bob
obobo16bo6bobobobo26bo6bobobobo23bobobobo33bobobobo34booboo25booboo35b
ooboo$30bobobobo16bo6bobobobo26bo6bobobobo23bobobobo33bobobobo32boobob
oboo21booboboboo31booboboboo$29booboboboo21booboboboo31booboboboo21boo
boboboo31booboboboo30bobobobobobo19bobobobobobo29bobobobobobo$19boo11b
obo27bobo26boo9bobo27bobo37bobo33boobbobobboo19boobbobobboo29boobbobo
bboo$18bobo11bobo27bobo25bobo9bobo27bobo37bobo37bobo27bobo37bobo$20bo
12bo29bo28bo10bo29bo39bo39bo29bo39bo$22b3o$22bo136boo25boo29bo5bo23bo
5bo$23bo134bobo25bobo28bo5bo23bo5bo$160bo10bo14bo30bo5bo23bo5bo$170boo
$170bobo3bobo40b3o27b3o6boo$164boo10boo80bobo$165boo10bo80bo$164bo$
177boo$178boo4b3o$177bo6bo$185bo!
Sokwe wrote:Off topic: I always found this to be one of the most amazing "early" oscillators. Mark, do you known how David Buckingham found it?
On the contrary - I think that the "why" is often very much on topic in trying to understand the "what".
I really have no idea. Many of the things he came up with (such as many of the billiard table oscillators, some other oscillators like this one, and many of the synthesis mechanisms, especially ones where complex objects spontaneously erupt from soup) have seemed like voodoo to me. Since I've been working with the synthesis materials for several decades now, much of that has become more clear (an sometimes even obvious), but there is still much that still appears to be black magic.
He originally studied chemistry, and I think that strongly influenced the way that he thinks about things. I am firmly convinced that only a chemist (or someone who thought like one) could have created such a huge corpus of synthesis methods as we have, since object synthesis has so many things in common with synthesis of complex organic molecules.
I also think that much of the expertise in such topics came from the fact that back in the 1970s and 1980s, computer resources were fairly limited (compared to what we have available today), so much Life was done manually, on graph paper, or on a Go board (or similar), or later, on small computers with limited limited CPU and limited display resources. Under such circumstances, it was common to run small collisions of gliders or other patterns, and observe the effects generation by generation. After doing much of this, one eventually develops a sense of what kinds of reactions work and under what circumstances. One had to focus on the small things, because it wasn't possible to run large things. (At one point, he constructed the Adder, a large construction that added two binary numbers together, encoded as streams of glieders. Doing this required us to develop several specialized tools, as the ones we were used to using at the time were totally inadequate for creating patterns several hundred cells on a side.)
To put this in perspective, I recall one phone conversation I had with Dave sometime in the 1990s, when I mentioned one 15-bit still-life that looked like it would be very difficult to synthesize (15.355 - a super-pond - a large pond with a pre-block inside). After thinking about it for only a minute or two, he dictated a successful synthesis to me, over the phone - for an object that did not previously have a synthesis, and which didn't look like it could be synthesized at all. The final step involved the intuitive leap. Once that had been done, all the previous steps were just standard existing boiler-plate.
Code: Select all
#C Synthesis of 15.355 from 24 gliders
#C by David Buckingham, 1997 or earlier
x = 135, y = 68, rule = B3/S23
35bo$34bo$34b3o36bobo$69bo3boo$31bo38boobbo$29bobo37boo$30boo$67bo$65b
obo34bo$30bo22boo11boo5boo15bobboo8bo6bobboo15bobboo$30boo6boo11bobbo
16bobbo14bobobbo6b3o5bobobbo14bobobbo$29bobo6bobo10boo18boo12boobboboo
12boobboboo16boboo$38bo46boo3bo14boo3bo19bo$51boo18boo18boo18boo18boo$
52bo10b3o6bo19bo19bo19bo$31boo19bobo10bo6bobo17bobo17bobo17bobo$32boo
19boo9bo8boo18boo18boo18boo$31bo3boo$35bobo$35bo16$106bo$107bo$105b3o
$$11bo$10bo10bo87bo3bo5bo$10b3o8bobo83boboboo4boo$8bo12boo85boobboo4b
oo$6bobo$7boo3$58bo$oo29boo18boo5bobo10boo28boo28boo$boo7bobboo15bobbo
16bobbo4boo10bobbo26bobbo26bobbo$o8bobobbo14bobobo15bobobo15bobobo25bo
bobo25bobobbo$9boboo16boboo16boboo5bo10boboo4boo20boboo4boo20boboobo$
10bo19bo19bo6boo11bo5bobbo20bo5bobbo20bobbo$11boo18boo18boo4bobo11boo
3bobbo21boo3bobbo21boo$12bo19bo19bo19bo4boo23bo4boo$12bobo17bobo17bobo
17bobo27bobo15bo$13boo18boo18boo18boo28boo14boo$119bobo8$86b3o16boo$
88bo15boo$87bo18bo!
The key voodoo here is to be able to look at an object, and intuitively see a predecessor - much the way a sculptor can look into a piece of granite and "see" the finished sculpture lurking inside. One that can be done successfully, the rest is mostly justa matter of engineering and elbow grease. This is a kind of intuition that mainly come with experience, and isn't easy to teach.
Unfortunatley, with the resources we have available today, like Golly, that can run patterns a billion cells on a side at millions of generations per second, it's very easy to focus on the macroscopic, and develop breeders and constructors and other grandiose and spectacular patterns. This means it's much less likely that many people will spend time focusing on the microscopic - it involves a lot of work, and the rewards dont look nearly as spectacular.
Sokwe wrote:Back on topic: Mark, what are the two 15-cell still lifes without known syntheses? I have heard them referenced (back when there were 3), but I do not know which they are.
These are the objects that have been on my "to-do" list for over a decade. In particular, the few remaining objects from lists where all other objects had known syntheses. In particular, 15-bit still-lifes, pseudo-still-lifes up to 17 bits, and (nontrivial) P2 pseudo-oscillators up to 21 bits. (There are, of course, many other unsolved items, but the the few remaining ones these lists that are 99.9% solved are particularly irksome).
Back in 2002, I wrote a simple expert system that applies known synthesis recipes to list of objects to identify ways to synthesize them from simpler ones (which, by induction, one can find simple proofs of which objects have known syntheses). This was mostly to eliminate the "obviously easy" objects, to allow me to concentrate my efforts on the few remaining difficult ones. From this, all but 13 15-bit still-lifes, all but 5 pseudo-still-lifes up to 17 bits, and but 5 period-2 pseudo-oscillators up to 21 bits can be trivially synthesized. Of these few remaining objects, I have explicit syntheses for most of them, except the few mentioned previously.
This is a very crude pseudo-code approximation to how this program works (there's no cleverness; just sheer brute force):
Code: Select all
for (p in all patterns in input list) { // e.g. "all 16-bit still-lifes"
for (t in list of all templates) { // currently around 864 templates
for (r in list of all 8 transformations) {
for (y in 0...t.height-p.height) {
for (x in 0...t.width-p.width) {
final = apply transformation (r,x,y) to p;
current = init = combine (final, t);
if (viable) { // no contradictory cells
for(g=0...time limit) { // arbitrary; currently 700
if (g%p.period == 0 && current == final) {
output 'pattern',p,'via template',t,'from predecessor',init;
break;
}
current = automate (current);
if (!viable) break;
}
}
}
}
}
}
}
This has actually proven to be a useful tool in other ways. Sometimes, when a large object is needed (like some of the large still-lifes that have come up recently, like the Snark, Bellman One, etc.), this can suggest immediate predecessors that may not necessarily be obvious.
I've recently set my sights on the 16-bit still-lifes. Of 3268, all but around 100 can be synthesized via recipe. About a dozen of these rely on as-yet-unsynthesized predessors, but about a dozen of the remaining ones have have explicit unique syntheses, so there are still around 100 that have no known syntheses. In the past few weeks I have been toying with some of these as the mood hits me, and I've whittled around a dozen off the list.
Code: Select all
#C 15.389 and 2 pseudo-P2s (solved in 2010, 2011, 2013)
#C 15.387, 15.390, down hook w/tail below hook w/tail (unsolved)
#C 4 pseudo-P2s (unsolved)
x = 55, y = 28, rule = B3/S23
bboo12booboo10booboo$bobobbo10bobo10bobobo$o3b3o9bo5bo7bo6bo$b3o11bo5b
oo8bo4boo$4bo10boo13boo$3boo16boo13boo$18bobobo10bobobo$18boo13boo3$bb
oo13boo11bo$bobo11bobbo11b3o$o3boo9boobboo12boboo$oboobbo10boobbo10bo
3bo$bobobo11bobbo11boobo$4bo13boo16b3o$38bo4$booboo10booboo9bobooboo
10booboo$bbobo12bobobo8boobobo10bobobobo$bo5bo7bo22bo6bo$o5boo7boo4bob
o13boo7boo4bobo$b3o13bo4boo9boo12bo5boo$3bobboo9b3o14bobboo7bo$3bobobo
12bo13bobobo8b3o$4bo14boo14bo13bo!
The two 15s are also prerequisites for many derived trivial 19-21-bit pseudo-P2s. Also, 15.587 is the needed for one 16-bit still-life, the one remaining unsolved P4 oscillator up to 20 bits, and two P3s at 21 bits (hosting mold and 2 jams, respectively).
Sokwe wrote:Also, my name is Matthias Merzenich.
I'm pleased to finally make your acquaintenace. I have heard much about you by reputation recently (mostly from many new oscillators, and oscillator syntheses).
Sokwe wrote:There was an old glider synthesis topic here. The most interesting things to come out of it were probably these large oscillator syntheses:
Thanks. I had come across all of these fairly recently. I had seen all of them at some point in recent months - most likely from that very same topic when I first joined this site and read all topics that might be even remotely interesting, or possibly from some other related places, like the wiki, or Jason Summer's collection. (I haven't been spending huge amounts of time in recent years on Life, and when I started to get back into it again this year, I've been inundated by huge quantities of new discoveries from the web that I hadn't seen before, so it's hard to remember where I've first read about what!).
Here are a few obligatory new syntheses for a few oscillators that I had found out about recently but didn't know how to synthesize. I had seen some larger P3s in H. Koenig's collections, where Jam was growing on something that wasn't quite a loaf. In fact, it can grow on a mango with an appropriate bushing. 21 bits is the first time that these occur. It's fortunate that one of these provides a bases for the other two.
Code: Select all
#C 3 21-bit mango jams w/loaf,tail,bun for 18,21,25 gliders
#C Mark D. Niemiec 20130821
x = 143, y = 60, rule = B3/S23
118bo$119bo$117b3o$123bo$122bo$122b3o$bbo$obo110bobo$boo111boo11bo$22b
oo18boo18boo18boo18boo10bo7boo3bobo$bbo18bobo17bobo17bobo17bobo17bobo
17bobo3boo11boo$bboo3bo12bobo17bobo17bobo17bobo17bobo9boo6bobo16bobbo$
bobo3bobo9bobo17bobo18boo18boo18boo11boo5boo16bobobo$7boo11bo19bo17boo
18boo18boo12bo5boo10boo5bobobo$57bobo17bobo17bobo17bobo10bobo3bobbo$
58bo19bo17bobo17bobo11bo5bobobbo$40boo31bo23bo19bo19bo3bo$36bobboo33b
oo44boo4b3o12bo$36boo3bo31boobboo40bobo4bo11bo$35bobo38bobo42bo5bo11b
oo$78bo$116boo$117boo$116bo$$119boo$119bobo$119bo$115boo$114bobo$116bo
10$120bo$120bobo$78bo41boo$78bobo$78boo18boo18boo$38bo45bo13boo18boo$
39bo38bo3boo$37b3o39bo3boo$77b3o$45bo$40boo3bobo14boo18boo16boo18boo
18boo$39bobbobboobboo8bobbo16bobbo17bobo17bobo17bobo$38bobobo5boo8bobo
bo15bobobo15bobobo15bobobo15bobobo$37bobobo8bo6bobobo15bobobo15bobobo
15bobobo15bobobo$36bobbo16bobbo16bobbo16bobbo16bobbo16bobbo$36bobobbo
14bobobbo14bobobbo14bobobbo14bobobbo14bobobbo$37bo3bo15bo3bo15bo3bo15b
o3bo15bo3bo15bo3bo$41bo19bo19bo19bo19bo19bo$38bo19bo19bo19bo19bo19bo$
39boo18boo18boo18boo18boo18boo!
Extrementhusiast wrote:Three candidates, from easiest to hardest:
The first is easy. I whipped that one up a few months ago. It uses 100% existing technology. I think I subsequently saw a synthesis of it somewhere else (that worked in much the same way), so I think somebody else synthesized it first.
Code: Select all
#C 46p22 from 15 gliders
#C Mark D. Niemiec 2013-06-02
x = 109, y = 71, rule = B3/S23
79bo$79bobo$75bo3b2o$76b2o29b2o$75b2o29bobo$106bo$14bo90b2o$13bo$13b3o
25b2o28b2o28b2o$40bo2bo26bo2bo26bo2bo$12bo28b2o28b2o28b2o$11b2o$11bobo
27b2o28b2o28b2o$40bo2bo26bo2bo26bo2bo$5b3o33b2o28b2o28b2o$7bo$6bo98b2o
$106bo$75b2o29bobo$76b2o29b2o$75bo3b2o$79bobo$79bo10$76bo$75bo$75b3o$
63bo$61bobo$62b2o3$2bo$obo$b2o3bo$4b2o11b2o14b2o12b2o14b2o12b2o14b2o
12b2o$5b2o9bobo14bobo10bobo14bobo10bobo14bobo5bo4bobo$16bo18bo10bo18bo
10bo18bo5bo4bo$15b2o18b2o8b2o18b2o8b2o18b2o4bo3b2o2$11b2o28b2o28b2o28b
2o$10bo2bo26bo2bo26bo2bo26bo2bo$11b2o28b2o28b2o28b2o2$11b2o28b2o28b2o
28b2o$10bo2bo26bo2bo26bo2bo26bo2bo$11b2o28b2o28b2o28b2o2$15b2o18b2o8b
2o18b2o8b2o18b2o4bo3b2o$16bo18bo10bo18bo10bo18bo5bo4bo$5b2o9bobo14bobo
10bobo14bobo10bobo14bobo5bo4bobo$4b2o11b2o14b2o12b2o14b2o12b2o14b2o12b
2o$b2o3bo$obo$2bo3$62b2o$61bobo$63bo$75b3o$75bo$76bo!
The second one looks like it could be done with a little bit of work, but it could get a bit tight. The third one also looks like it might be possible, given the central core, but I can't think of a way to make that. (I remember once seeing a still-life based on four connected tables surrounding a block, and I have no idea how to make that either, but it could provide a good starting point). This looks like it might require some billiard-table-construction voodoo.
