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Synthesising Oscillators

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

Re: Synthesising Oscillators

Postby Extrementhusiast » January 19th, 2014, 8:09 pm

And only NOW do I realize that the rle zip is sorted by size.

EDIT: To make this post not entirely useless, this is an improved version of the key component used in 15.390:
x = 21, y = 22, rule = B3/S23
4bobo$5b2o$5bo5$14b2obo2bo$15bob4o$15bo$2o14b3o$b2o15bo$o3$4b2o$5b2o$
4bo$16b2o$3o13bobo$2bo13bo$bo!
I Like My Heisenburps! (and others)
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Re: Synthesising Oscillators

Postby mniemiec » January 25th, 2014, 10:58 pm

Here are some 18-bit P2 oscillators with inducting toads. These should all have been listed with the "unknown 18-bit P2" list, because although they are all buildable from 18-bit still-lifes, those still-lifes themselves did not yet have syntheses. All of these could be easily solved from similar 16-bit still-lifes, with a working tail-to-snake converter, but such a converter has not been completed yet.

This is a 47-glider synthesis of Z w/tub and snake, leading to 54-glider synthesis of a Z w/tub and toad:
x = 152, y = 135, rule = B3/S23
43bo$41bobo$42boo4bo$47bo$21bo21bo3b3o$21bobo19boo$21boo19bobo37bo$80b
obo$10bo70boo$8bobo56boo18boo18boo18boo18boo$9booboo12boo18boo17bobbo
16bobbo19bo19bo5bo13bo$12bobo11boboboo14boboboo13booboboo6bobo4boobob
oo16boboo16boboobo14boboo$12bo15bobo17bobo17bobo8boo7bobo14boobobo14b
oobobobb3o9boobobo$5b3o20bobo8boo7bobo17bobo8bo8bobo14boobobo14boobobo
14boobobbo$7bo21bo8bobo8bo19bo13bo5bo19bo19bo19boo$6bo33bobb3o30boo5b
oo50bo$43bo33boo3bobo48boo$44bo31bo53boobboo$130bobo$84b3o43bo$80boobb
o$81boobbo$75boo3bo$76boo$75bo10$40bo$41boo$bbobo35boo76bo$bboo115bo$
3bo74bo38b3o$bo5boo18boo18boo18boo10bo7boo18boo18boo18boo$bbo5bo19bo
11bo7bo19bo8b3o8bo19bo11boo6bo19bo$3o5boboo16boboo8boo6boboo9booboobbo
boo9booboobboboo12boobboboo9booboobboboo13bobboboo$5boobobo14boobobo8b
obo3boobobo10boobobobobo10boobobobobo13bobobobo9bo3bobobobo13bobobobo$
5boobobbo12bobobobbo12bobobobbo13bobbobo14bobbobo14bobbobo14bobbobo14b
obbobo$bo7boo14bo3boo14bo3boo17boo18boo18boo18boo18boo$boo$obo$$51boo$
50bobo$52bobboo$55bobo$47boo6bo$46bobo$48bo12$17bobo$16bo$16bo$16bobbo
$16b3o$$11bo49bo$11bobo46bo$11boo47b3o$15bo22bo19bo41bobo$15bobo19bobo
17bobo41boo4bo$15boo6boo12boo18boo42bo4bo$22b4o80b3o$7boo12booboo11boo
4boo12boo4boo12boo4boo12boo4boo6boo14boo$8bo13boo14bo4bo14bo4bo14bo4bo
14bo4bo6boo16bo$5bobboboo23bobboboobo11bobboboobo11bobboboobo11bobbob
oobobboo4bo12bobboboobo$4bobobobo23bobobobobo11bobobobobo11bobobobobo
11bobobobobo3bobo15boboboboboo$5bobbobo24bobbo16bobbo16bobbo16bobbo7bo
18bobbo$8boo8bo19boo18boo18boo18boo28boo$17boo$13boobbobo$14boo$13bo$
22b3o$22bo$8b3o12bo$10bo$9bo9$64bo$64bobo$14boo48boo$10bo3bobo$11bobbo
27boo18boo$9b3o30boo18boo$23bobo$23boo$24bo8$25bo$7boo15bo12boo18boo
18boo$8bo15b3o11bobbo16bobbo16bobbo$5bobboboobo21bobbobobbo11bobbobobb
o11bobbobobbo$4boboboboboo20bobobobobbo10bobobobobbo10bobobobobbo$5bo
bbo26bobbo3bo12bobbo3bo12bobbo3bo$8boo28boo18boo18boo6$18b3o$18bo$10b
oo7bo$9bobo$11bo!


This is a 53-glider synthesis of Z w/tail and snake, leading to a 60-glider synthesis of Z w/tail and toad. It can likely be improved, especially the 12-glider Rube-Goldberg procedure to restore one single deleted bit. Its cousin (bottom right corner) remains unsythesized:
x = 175, y = 126, rule = B3/S23
85bo5bo$86bo5bo41bo$84b3o3b3o11bo30bo$105bo27b3o$103b3o11b2o18b2o$4bo
102bo8bo2bo16bo2bo$5b2o46bo53bobo7b2o18b2o$4b2o48bo52b2o$14bo37b3o2bo$
12b2o13b2o18b2o8bobo7b2o28b2o19b2o18b2o18b2o$13b2o11bo2bo16bo2bo7b2o7b
o2bo18bo7bo2bo17bobo17bobo17bobo$6b2o8b2o9bobo17bobo17bobo18b2o7bobo
17bobob2o14bobob2o14bobob2o$7b2o7bobo7b2obobo14b2obobo14b2obob2o14bobo
6b2obob2o13b2obobo14b2obobo14b2obobo$6bo9bo13b2o18b2o17bo2bo26bo2bo16b
obo17bobo17bobo$69b2o28b2o18b2o18b2o18b2o2$2b3o119b2o18b2o$4bo48bobo
68b2o18b2o$3bo49b2o56b2o$9bo38b3o3bo56bobo32b3o$8b2o40bo60bo34bo$8bobo
38bo4b2o91bo$54bobo40b3o$54bo44bo$98bo12$98bobo$97bo$97bo$97bo2bo$97b
3o$81bo$79bobo$80b2o$45bo$45bobo17b2o18b2o9bo44bobo$41b3ob2o17bo2bo16b
o2bo8bobo43b2o4bo$43bo20bobo17bobo9b2o6b2o36bo4bo$42bo22bo19bo17b4o40b
3o$8b2o18b2o18b2o18b2o18b2o12b2ob2o11b2o4b2o12b2o4b2o6b2o14b2o$7bobo
17bobo17bobo17bobo17bobo13b2o14bo4bo14bo4bo6b2o16bo$7bobob2o14bobob2o
14bobob2o14bobob2o14bobob2o24bobob2obo12bobob2obo2b2o4bo13bobob2obo$2b
o3b2obobo13b3obobo13b3obobo13b3obobo13b3obobo23b3obobobo11b3obobobo3bo
bo15b3obobob2o$obo6bobo12bo4bobo12bo4bobo12bo4bobo12bo4bobo22bo4bo14bo
4bo7bo16bo4bo$b2o6b2o13b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o8bo14b2o3b2o
13b2o3b2o23b2o3b2o$98b2o$3bo90b2o2bobo$3b2o90b2o$2bobo89bo$103b3o$103b
o$89b3o12bo$91bo$90bo9$65bo$65bobo$15b2o48b2o$11bo3bobo$12bo2bo27b2o
18b2o$10b3o30b2o18b2o68bo$24bobo107b2o$24b2o107b2o$25bo$135bo$135b2o6b
obo$134bobo6b2o$144bo15b2o$96bobo19bo12b2o5bo20bobo$97b2o18bobo12b2o3b
obo7b2o10bo$97bo20b2o11bo6b2o7bobo8b2o$26bo120bo$8b2o15bo12b2o18b2o18b
2o18b2o18b2o18b2o18b2o$9bo15b3o11bo2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo
2bo16bo2bo$7bobob2obo22bobobo2bo12bobobo2bo12bobobo2bo12bobobo2bo12bob
obo2bo12bobobo2bo12bobobo2bo$5b3obobob2o20b3obobo2bo10b3obobo2bo10b3ob
obo2bo10b3obobo2bo10b3obobo2bo10b3obobo2bo10b3obobo2bo$4bo4bo24bo4bo3b
o10bo4bo3bo10bo4bo3bo10bo4bo3bo10bo4bo3bo10bo4bo3bo10bo4bo3bo$4b2o3b2o
23b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o6$19b3o
$19bo$11b2o7bo$10bobo$12bo6$62bo$62bobo$55bo6b2o$56bo$10b2o18b2o17bobo
2b3o3b2o$4bo4bobo17bobo18b2o7bobo$5bo3bo19bo20bo8bo$3b3o2b2o14b2o2b2o
24b2o2b2o$24bo20b2o7bo$3o5b2o15b5o16b2o7b5o18b2o18b2o18b2o18b3o17b2o$
2bo6bo2bo16bo2bo12bo13bo2bo14bobo2bo8bo5bobo2bo14bobo2bo14bo3bo15bobo
2bo$bo5bobobo2bo12bobobo2bo22bobobo2bo12bobobo2bo7bo4bobobo2bo12bobobo
2bo16bo14bo2bobo2bo$5b3obobo2bo10b3obobo2bo20b3obobo2bo10b3obobo2bo5b
3o2b3obobo2bo11b2obobo2bo14b2o15b2obobo2bo$4bo4bo3bo10bo4bo3bo20bo4bo
3bo10bo4bo3bo10bo4bo3bo15bo3bo15bo19bo3bo$4b2o3b2o13b2o3b2o23b2o3b2o
13b2o3b2o13b2o3b2o18b2o38b2o$139bo!


Extrementhusiast wrote:And only NOW do I realize that the rle zip is sorted by size.

Which zip file are you referring to, and What tools are you using to unzip it? Ones I create are usually in quasi-alphabetical order, with numbers being sorted as units (e.g. 15.3 < 15.21 < 15.123), but GUI-based unzippers like winzip tend to re-order them according to whatever column heading is selected.

Extrementhusiast wrote:To make this post not entirely useless, this is an improved version of the key component used in 15.390:


This component looks very familiar. Unfortunately, when new improved converters are found, it's hard to remember every single synthesis that could use them, so many still contain outmoded ones until they get actively re-examined.
mniemiec
 
Posts: 793
Joined: June 1st, 2013, 12:00 am

Re: Synthesising Oscillators

Postby Extrementhusiast » January 26th, 2014, 2:22 pm

mniemiec wrote:
Extrementhusiast wrote:And only NOW do I realize that the rle zip is sorted by size.

Which zip file are you referring to, and What tools are you using to unzip it? Ones I create are usually in quasi-alphabetical order, with numbers being sorted as units (e.g. 15.3 < 15.21 < 15.123), but GUI-based unzippers like winzip tend to re-order them according to whatever column heading is selected.

I meant in terms of the way you numbered them.

mniemiec wrote:
Extrementhusiast wrote:To make this post not entirely useless, this is an improved version of the key component used in 15.390:


This component looks very familiar. Unfortunately, when new improved converters are found, it's hard to remember every single synthesis that could use them, so many still contain outmoded ones until they get actively re-examined.

The majority of cases occur with a mango+bit, as in 15.390. Scrutinize those.

mniemiec wrote:Here are some 18-bit P2 oscillators with inducting toads. These should all have been listed with the "unknown 18-bit P2" list, because although they are all buildable from 18-bit still-lifes, those still-lifes themselves did not yet have syntheses. All of these could be easily solved from similar 16-bit still-lifes, with a working tail-to-snake converter, but such a converter has not been completed yet.

This is a 47-glider synthesis of Z w/tub and snake, leading to 54-glider synthesis of a Z w/tub and toad:
x = 152, y = 135, rule = B3/S23
43bo$41bobo$42boo4bo$47bo$21bo21bo3b3o$21bobo19boo$21boo19bobo37bo$80b
obo$10bo70boo$8bobo56boo18boo18boo18boo18boo$9booboo12boo18boo17bobbo
16bobbo19bo19bo5bo13bo$12bobo11boboboo14boboboo13booboboo6bobo4boobob
oo16boboo16boboobo14boboo$12bo15bobo17bobo17bobo8boo7bobo14boobobo14b
oobobobb3o9boobobo$5b3o20bobo8boo7bobo17bobo8bo8bobo14boobobo14boobobo
14boobobbo$7bo21bo8bobo8bo19bo13bo5bo19bo19bo19boo$6bo33bobb3o30boo5b
oo50bo$43bo33boo3bobo48boo$44bo31bo53boobboo$130bobo$84b3o43bo$80boobb
o$81boobbo$75boo3bo$76boo$75bo10$40bo$41boo$bbobo35boo76bo$bboo115bo$
3bo74bo38b3o$bo5boo18boo18boo18boo10bo7boo18boo18boo18boo$bbo5bo19bo
11bo7bo19bo8b3o8bo19bo11boo6bo19bo$3o5boboo16boboo8boo6boboo9booboobbo
boo9booboobboboo12boobboboo9booboobboboo13bobboboo$5boobobo14boobobo8b
obo3boobobo10boobobobobo10boobobobobo13bobobobo9bo3bobobobo13bobobobo$
5boobobbo12bobobobbo12bobobobbo13bobbobo14bobbobo14bobbobo14bobbobo14b
obbobo$bo7boo14bo3boo14bo3boo17boo18boo18boo18boo18boo$boo$obo$$51boo$
50bobo$52bobboo$55bobo$47boo6bo$46bobo$48bo12$17bobo$16bo$16bo$16bobbo
$16b3o$$11bo49bo$11bobo46bo$11boo47b3o$15bo22bo19bo41bobo$15bobo19bobo
17bobo41boo4bo$15boo6boo12boo18boo42bo4bo$22b4o80b3o$7boo12booboo11boo
4boo12boo4boo12boo4boo12boo4boo6boo14boo$8bo13boo14bo4bo14bo4bo14bo4bo
14bo4bo6boo16bo$5bobboboo23bobboboobo11bobboboobo11bobboboobo11bobbob
oobobboo4bo12bobboboobo$4bobobobo23bobobobobo11bobobobobo11bobobobobo
11bobobobobo3bobo15boboboboboo$5bobbobo24bobbo16bobbo16bobbo16bobbo7bo
18bobbo$8boo8bo19boo18boo18boo18boo28boo$17boo$13boobbobo$14boo$13bo$
22b3o$22bo$8b3o12bo$10bo$9bo9$64bo$64bobo$14boo48boo$10bo3bobo$11bobbo
27boo18boo$9b3o30boo18boo$23bobo$23boo$24bo8$25bo$7boo15bo12boo18boo
18boo$8bo15b3o11bobbo16bobbo16bobbo$5bobboboobo21bobbobobbo11bobbobobb
o11bobbobobbo$4boboboboboo20bobobobobbo10bobobobobbo10bobobobobbo$5bo
bbo26bobbo3bo12bobbo3bo12bobbo3bo$8boo28boo18boo18boo6$18b3o$18bo$10b
oo7bo$9bobo$11bo!


This is a 53-glider synthesis of Z w/tail and snake, leading to a 60-glider synthesis of Z w/tail and toad. It can likely be improved, especially the 12-glider Rube-Goldberg procedure to restore one single deleted bit. Its cousin (bottom right corner) remains unsythesized:
x = 175, y = 126, rule = B3/S23
85bo5bo$86bo5bo41bo$84b3o3b3o11bo30bo$105bo27b3o$103b3o11b2o18b2o$4bo
102bo8bo2bo16bo2bo$5b2o46bo53bobo7b2o18b2o$4b2o48bo52b2o$14bo37b3o2bo$
12b2o13b2o18b2o8bobo7b2o28b2o19b2o18b2o18b2o$13b2o11bo2bo16bo2bo7b2o7b
o2bo18bo7bo2bo17bobo17bobo17bobo$6b2o8b2o9bobo17bobo17bobo18b2o7bobo
17bobob2o14bobob2o14bobob2o$7b2o7bobo7b2obobo14b2obobo14b2obob2o14bobo
6b2obob2o13b2obobo14b2obobo14b2obobo$6bo9bo13b2o18b2o17bo2bo26bo2bo16b
obo17bobo17bobo$69b2o28b2o18b2o18b2o18b2o2$2b3o119b2o18b2o$4bo48bobo
68b2o18b2o$3bo49b2o56b2o$9bo38b3o3bo56bobo32b3o$8b2o40bo60bo34bo$8bobo
38bo4b2o91bo$54bobo40b3o$54bo44bo$98bo12$98bobo$97bo$97bo$97bo2bo$97b
3o$81bo$79bobo$80b2o$45bo$45bobo17b2o18b2o9bo44bobo$41b3ob2o17bo2bo16b
o2bo8bobo43b2o4bo$43bo20bobo17bobo9b2o6b2o36bo4bo$42bo22bo19bo17b4o40b
3o$8b2o18b2o18b2o18b2o18b2o12b2ob2o11b2o4b2o12b2o4b2o6b2o14b2o$7bobo
17bobo17bobo17bobo17bobo13b2o14bo4bo14bo4bo6b2o16bo$7bobob2o14bobob2o
14bobob2o14bobob2o14bobob2o24bobob2obo12bobob2obo2b2o4bo13bobob2obo$2b
o3b2obobo13b3obobo13b3obobo13b3obobo13b3obobo23b3obobobo11b3obobobo3bo
bo15b3obobob2o$obo6bobo12bo4bobo12bo4bobo12bo4bobo12bo4bobo22bo4bo14bo
4bo7bo16bo4bo$b2o6b2o13b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o8bo14b2o3b2o
13b2o3b2o23b2o3b2o$98b2o$3bo90b2o2bobo$3b2o90b2o$2bobo89bo$103b3o$103b
o$89b3o12bo$91bo$90bo9$65bo$65bobo$15b2o48b2o$11bo3bobo$12bo2bo27b2o
18b2o$10b3o30b2o18b2o68bo$24bobo107b2o$24b2o107b2o$25bo$135bo$135b2o6b
obo$134bobo6b2o$144bo15b2o$96bobo19bo12b2o5bo20bobo$97b2o18bobo12b2o3b
obo7b2o10bo$97bo20b2o11bo6b2o7bobo8b2o$26bo120bo$8b2o15bo12b2o18b2o18b
2o18b2o18b2o18b2o18b2o$9bo15b3o11bo2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo
2bo16bo2bo$7bobob2obo22bobobo2bo12bobobo2bo12bobobo2bo12bobobo2bo12bob
obo2bo12bobobo2bo12bobobo2bo$5b3obobob2o20b3obobo2bo10b3obobo2bo10b3ob
obo2bo10b3obobo2bo10b3obobo2bo10b3obobo2bo10b3obobo2bo$4bo4bo24bo4bo3b
o10bo4bo3bo10bo4bo3bo10bo4bo3bo10bo4bo3bo10bo4bo3bo10bo4bo3bo$4b2o3b2o
23b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o6$19b3o
$19bo$11b2o7bo$10bobo$12bo6$62bo$62bobo$55bo6b2o$56bo$10b2o18b2o17bobo
2b3o3b2o$4bo4bobo17bobo18b2o7bobo$5bo3bo19bo20bo8bo$3b3o2b2o14b2o2b2o
24b2o2b2o$24bo20b2o7bo$3o5b2o15b5o16b2o7b5o18b2o18b2o18b2o18b3o17b2o$
2bo6bo2bo16bo2bo12bo13bo2bo14bobo2bo8bo5bobo2bo14bobo2bo14bo3bo15bobo
2bo$bo5bobobo2bo12bobobo2bo22bobobo2bo12bobobo2bo7bo4bobobo2bo12bobobo
2bo16bo14bo2bobo2bo$5b3obobo2bo10b3obobo2bo20b3obobo2bo10b3obobo2bo5b
3o2b3obobo2bo11b2obobo2bo14b2o15b2obobo2bo$4bo4bo3bo10bo4bo3bo20bo4bo
3bo10bo4bo3bo10bo4bo3bo15bo3bo15bo19bo3bo$4b2o3b2o13b2o3b2o23b2o3b2o
13b2o3b2o13b2o3b2o18b2o38b2o$139bo!

I seem to remember cheaper methods of doing such. Let me see if I can find them.

EDIT: Sure enough, here they are:
x = 292, y = 149, rule = B3/S23
186bo$184b2o$185b2o2$182bo$180b2o$127bo53b2o$128b2o56bo$127b2o55b2o$
131bo53b2o$130bo$130b3o3$135bo51bo$135bobo47b2o16bobo$127bo7b2o49b2o
15b2o47bobo$128b2o41b2o31bo4b2o17b2o23b2o6b2o22b2o$127b2o43bo37bo14bo
3bo23bo4bo3bo23bo$168b2o2bob2o25b3o2b2o2bob2o10bobo2bob2o24bobo2bob2o
15b3o2bob2o$116b3o6b2o30bobo8bobobo2bo27bo2bobobo2bo10bo2bobo2bo24bo2b
obo2bo16b3obo2bo$118bo5bobo30b2o10b2ob2o28bo4bo2bobo12b2o2bobo26b2o2bo
bo21bobo$117bo8bo31bo51b2o17b2o23bo7b2o22b2o$151b3o101b2o$153bo100b2o
3bo$124bo27bo2b3o101bo$123b2o30bo97bo5bo$116b3o4bobo30bo96b2o$118bo
103b2o28bobo$117bo103bobo$223bo$225b3o$225bo$226bo$185bo$184b2o$184bob
o4$12bo$10bobo$11b2o3$o181bo$b2o178bo$2o179b3o$179bo$124bobo53bo$125b
2o51b3o$125bo$40b3o$42bo2bo20bobo111bobo$41bo2bo22b2o111b2o$27b2o15b3o
20bo99bobo11bo$23b2o2bobo137b2o83bobo$22bobo2bo37b2o8b2o27b2o29b2o31bo
4b2o28b2o23b2o23b2o6b2o22b2o$24bo21bo17bobo9bo19bobo6bo30bo37bo25bo3bo
2b2o3bo12bo3bo2bo20bo4bo3bo2bo20bo2bo$45bobob2obo13bo9bob2obo15b2o6bob
2obo25bob2obo23b3o2b2o2bob2obo19bobo2bobobob2o12bobo2bobobo23bobo2bobo
bo14b3o2bobobo$46b2obob2o22b2obob2o15bo4b2obobob2o22b2obobob2o25bo2bob
obobob2o19bo2bobo2bo3b2o11bo2bobo2bo24bo2bobo2bo16b3obo2bo$68bo23b3o7b
2ob2o25bobob2o28bo4bo2bo25b2o2bo20b2o2bo28b2o2bo23bo$68b2o24bo29b2o7bo
40b2o28b2o7b3o13b2o23bo7b2o22b2o$15b2o50bobo23bo31b2o86bo41b2o$16b2o
79b2o25bo57b3o29bo39b2o3bo$15bo82b2o82bo76bo$97bo41bobo41bo69bo5bo$80b
3o36b2o18b2o112b2o$80bo37bobo19bo81b2o28bobo$81bo38bo21b2o77bobo$137b
2o3bobo78bo$74b2o60bobo3bo82b3o$75b2o49bo11bo86bo$74bo51b2o98bo$82b2o
41bobo$81b2o$83bo3$153b2o$153bobo$153bo11$192bobo$192b2o58bobo$193bo4b
2o28b2o23b2o6b2o22b2o$199bo25bo3bo23bo4bo3bo23bo$190b3o2b2o2bob2obo19b
obo2bob2obo22bobo2bob2obo13b3o2bob2obo$192bo2bobobobob2o19bo2bobobob2o
22bo2bobobob2o14b3obobob2o$191bo4bo2bo25b2o2bo28b2o2bo23bo$199b2o28b2o
23bo7b2o22b2o$255b2o$254b2o3bo$259bo$253bo5bo$253b2o$222b2o28bobo$221b
obo$223bo$225b3o$225bo$226bo2$35bo$33bobo$34b2o3$23bo$24b2o$23b2o2$
147bobo$148b2o$148bo$63b3o$65bo2bo20bobo$64bo2bo22b2o$50b2o15b3o20bo
101bobo$46b2o2bobo139b2o58bobo$45bobo2bo23b2o12b2o8b2o3b2o22b2o3b2o24b
2o3b2o28bo4b2o3b2o23b2o23b2o6b2o22b2o$47bo21bo5bo11bobo9bo4bo14bobo6bo
4bo25bo4bo34bo4bo20bo3bo23bo4bo3bo23bo$68bobob3o14bo9bob3o16b2o6bob3o
26bob3o26b3o2b2o2bob3o2b3o15bobo2bob2o24bobo2bob2o15b3o2bob2o$69b2obo
25b2obo18bo4b2obobo25b2obobo30bo2bobobobo4bo17bo2bobobo25bo2bobobo17b
3obobo$91bo23b3o7b2ob2o25bobob2o30bo4bo2bobo5bo17b2o2bobo26b2o2bobo21b
obo$91b2o24bo29b2o7bo42b2o28b2o23bo7b2o22b2o$38b2o50bobo23bo31b2o105b
2o$39b2o79b2o25bo106b2o3bo$38bo82b2o136bo$120bo132bo5bo$103b3o36b2o
109b2o$103bo37bobo25b2o51b2o28bobo$104bo38bo25bobo49bobo$156b3o10bo53b
o$97b2o59bo66b3o$98b2o57bo67bo$97bo128bo$105b2o$104b2o$106bo!
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Re: Synthesising Oscillators

Postby mniemiec » January 28th, 2014, 7:55 pm

Extrementhusiast wrote:I meant in terms of the way you numbered them.

My still-life numbering is based on the canonical representation used by my still-life enumerator. Each object is put in a shallow bounding box; these are sorted by increasing height, then width, then comparison order, defined as follows. Within boxes of the same size, treat each pattern as a number defined by a big-endian string of bits (i.e. comparison order is like string comparison bit-by-bit). Each pattern is oriented to have the largest possible representation among its reflections (and rotations, if square). Patterns are then sorted in ascending comparison order. This is purely arbitrary and not always obvious to the eye, but it is consistent and repeatable.
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Re: Synthesising Oscillators

Postby Extrementhusiast » February 2nd, 2014, 5:34 pm

A completely different way to make 11.44:
x = 25, y = 21, rule = B3/S23
19bobo$19b2o$20bo7$15bobo$16b2o4b3o$9b2o5bo5bo$9bobo11bo$10b2o$2bo$obo
$b2o$11b2o$3b3o4bobo$5bo6bo$4bo!
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Re: Synthesising Oscillators

Postby mniemiec » February 5th, 2014, 3:27 pm

Extrementhusiast wrote:I seem to remember cheaper methods of doing such. Let me see if I can find them.

Extrementhusiast wrote:Sure enough, here they are:

Very nice! I had syntheses for the second and fourth, but not the other two. I don't think I was aware of the loaf-to-toad converter; it means such objects can be built from predecessors with a 1-bit induction site, which may be easier in some cases than from the 2-bit induction site provided by a snake.

BTW, there is a typo in the last one: the first step creates down-boat-on-snake, but the next step relies down-boat-above-eater (also trivial, and for the same cost). You can also save 2 gliders by starting directly with 13-201 (down-table-above-eater) from 5 gliders instead; a similar consolidation is also possible with the snake-based ones, but it saves no gliders, so there is no advantage in using it:
x = 30, y = 16, rule = B3/S23
6bobo$7boo$7bo$$9bobo$9boo$boo7bo15bobbo$obo23b4o$bbo$26boo$27bo$6boo
19bobo$7boo19boo$6bo3boo$10bobo$10bo!
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Re: Synthesising Oscillators

Postby mniemiec » February 14th, 2014, 8:16 pm

Some of Lewis's soup results can dramatically reduce some of the exotic naturally-occuring P2 oscillators found in Achim Flammenkamp's soup experiments.

New 11-glider synthesis of a 20-bit P2. (The northwest glider just cleans up debris. There are several orientations that produce a single still-life. There might be others that leave nothing; if so, this would take 10 gliders.) Much better than the brute-force synthesis from 24 gliders I created last May:
x = 192, y = 80, rule = B3/S23
41bo$39bobo$40boo23$5bo4bo7bo$6boboo7bo$4b3obboo6b3o5boobboo44boobboo$
25boobboo44boobboo$147bo$145bobo$146boo$$118boo28boo$118boo28boo$85bo$
83boo50boobo26boobo16boobo$84boo48bobob3o23bobob3o13bobob3o$80boo52bo
6bo22bo6bo12bo6bo$79boo54b5obo23b5obo13b5obo$81bo58bo29bo19bo$137bo29b
o19bo$137boo28boo18boo10$21boo48boo39b3o$3o18boo48boo39bo$bbo110bo$bo$
3b3o$3bo$4bo19$107boo$107bobo$107bo!


New 9-glider synthesis of a related 20-bit P2. I had also synthesized this last May from 41 gliders by brute force:
x = 141, y = 36, rule = B3/S23
bo$bbo85bo19bo$3o84bobo17bobo$4bo83bo19bo$3bo$3b3o27boo28boo$33boo28b
oo38bo$104boo$87boo14boobboo$87boo18boo3$61bo$62bo$60b3o$64boo$65boo$
64bo$94booboo15booboo15booboo$93bobobobo13bobobobo13bobobobo$93bo6bo
12bo6bo12bo6bo$36b3o27b3o25b5obo13b5obo13b5obo$7bo91bo19bo19bo$5bobo
26bo5bo23bo5bo25bo19bo19bo$bboobboo26bo5bo23bo5bo25boo18boo18boo$bobo
30bo5bo23bo5bo$3bo$36b3o27b3o3$12bo$12bobo26boo28boo$12boo27boobboo24b
oobboo$15b3o27boo28boo$15bo$16bo!
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Re: Synthesising Oscillators

Postby Extrementhusiast » February 16th, 2014, 4:02 pm

This shortens a piston with length >=3, which gives all odd pistons other than 1:
x = 260, y = 27, rule = B3/S23
11bo37bo$12b2o33b2o$11b2o35b2o$45bo$17bo28bo$15b2o27b3o174bobo7bo$12bo
3b2o198bo4b2o6b2o$13b2o38bo33bo124bo3bobo3bo7b2o$12b2o37b2o33bo123bobo
3b2o$52b2o32b3o66bo55b2o$83b2o69bo33bo37bo3bo$2o16b2o9b2o10b2o4b2o16b
2o10b2o3bo2bo10b2o10b2o3b2o17b2o10b2o3b2o3b3o9b2o10b2o3b2o2bobo14b2o
10b2o3b2o2bobobo13b2o13b2o$obo2bo2bo2bo2bo2bobo9bobo2bo2bo2bo2bo2bobo
16bobo2bo2bo2bo2bobob2o11bobo2bo2bo2bo2bobobo17bobo2bo2bo2bo2bobobo15b
obo2bo2bo2bo2bobobo2b2o15bobo2bo2bo2bo2bobobo2b2o2b3o11bobo2bo2bo2bo2b
obo$2b4o2b4o2b4o13b4o2b4o2b4o20b4o2b4o2bobo16b4o2b4o2bobo5bo15b4o2b4o
2bobo19b4o2b4o2bobo23b4o2b4o2bobo24b4o2b4o2bo$obo2bo2bo2bo2bo2bobo9bob
o2bo2bo2bo2bo2bobo16bobo2bo2bo2bo2bobob2o11bobo2bo2bo2bo2bobobo3bobo
11bobo2bo2bo2bo2bobobo2b2o11bobo2bo2bo2bo2bobobo2b2o15bobo2bo2bo2bo2bo
bobo2b2o2b3o11bobo2bo2bo2bo2bobo$2o16b2o9b2o10b2o4b2o16b2o10b2o3bo2bo
10b2o10b2o3b2o3b2o12b2o10b2o3b2o2b2o11b2o10b2o3b2o2b2o15b2o10b2o3b2o2b
obobo13b2o13b2o$83b2o36b2o103bo3bo$52b2o32b3o32bobo31b3o53b2o$12b2o37b
2o33bo34bo33bo36bo17bobo3b2o$13b2o38bo33bo68bo28b2o4b2o19bo3bobo3bo7b
2o$12bo3b2o168b2o3bobo22bo4b2o6b2o$15b2o27b3o138bo35bobo7bo$17bo28bo$
45bo142b2o$11b2o35b2o138bobo$12b2o33b2o139bo$11bo37bo!


EDIT: A modified version of the above gives the length-1 piston:
x = 146, y = 33, rule = B3/S23
113bobo$116bo$106bo9bo$5bo29bo71b2o4bo2bo$6b2o25b2o71b2o6b3o$5b2o27b2o
$31bo83bo$11bo20bo75bo5bo$9b2o19b3o68b2o6bo4b3o$6bo3b2o87b2ob2o3b3o$7b
2o30bo25bo23bobo7b4o$6b2o29b2o25bo24b2o9b2o21bo$38b2o24b3o23bo32bobo$
61b2o60b2o$2o10b2o7b2o4b2o4b2o14b2o4b2o3bo2bo12b2o4b2o3b2o2b2o13b2o4b
2o21b2o7b2o$obo2bo2bo2bobo7bobo2bo2bo2bobo14bobo2bo2bobob2o13bobo2bo2b
obobob2o14bobo2bo2bob2o17bobo2bo2bobo$2b4o2b4o11b4o2b4o18b4o2bobo18b4o
2bobo5bo15b4o2bobobo18b4o2bo$obo2bo2bo2bobo7bobo2bo2bo2bobo14bobo2bo2b
obob2o13bobo2bo2bobobo17bobo2bo2bobo2bo15bobo2bo2bobo$2o10b2o7b2o4b2o
4b2o14b2o4b2o3bo2bo12b2o4b2o3b2o17b2o4b2o3bobo15b2o7b2o$61b2o55bo$38b
2o24b3o$6b2o29b2o25bo35b2o$7b2o30bo25bo33b4o$6bo3b2o87b2ob2o3b3o12b3o$
9b2o19b3o68b2o6bo4b3o5bo$11bo20bo75bo5bo8bo$31bo83bo$5b2o27b2o$6b2o25b
2o71b2o6b3o$5bo29bo71b2o4bo2bo$106bo9bo$116bo$113bobo!


EDIT 2: This reaction comes heartbreakingly close to constructing an inducting eater from a tail:
x = 101, y = 52, rule = B3/S23
o12bobo$b2o10b2o$2o12bo4bobo40bo$19b2o34bo5bo$20bo32bo7b3o4bo$54bo2bo
6bo2bo$5b2o54b2ob2ob3o$5b2o49b2o3bo2bo$11bo46bo$5b2o3b3o23bobo17b3ob2o
$b2obobo5bo20bo2bobo13b2obob2obo$2bobo27b3obobo14bobo$2bobo28bo2bobo
14bobo$3bo32bobo15bo2b2o$3o48b3o3bobo3b2o$o50bo11bobo$9b2o44bo7bo$8b2o
5b2o37bo$10bo3b2o40b2o$b2o13bo$2b2o$bo14$62bo$43bo11bo5bo35bo$42bo10bo
7b3o4bo29bo$41bo12bo2bo6bo2bo31bo$41bo19b2ob2ob3o29bo$40bo15b2o3bo2bo
35bo$40bo48b2o9bo$40bo15b3ob2o28bo9bo$40bo11b2obob2obo23b2ob3o10bo$40b
o12bobo29bobo12bo$40bo12bobo29bo14bo$40bo13bo2b2o27bo13bo$41bo9b3o3bob
o3b2o18b3o13bo$41bo9bo11bobo17bo15bo$42bo12bo7bo34bo$43bo10bo42bo$56b
2o!

Something that amplifies this heartbreak is that part of the early stage of the two-glider mess would work, if it didn't produce an obtrusive spark that can't be removed without getting rid of the point of the mess. Here are two possible alternate predecessors that are, unfortunately, much more complicated to synthesize:
x = 14, y = 40, rule = B3/S23
7bobo$7b2o$6b3o$5b2o$5b2o2$5b2o2bo$b2obobobob2o$2bobo6bo$2bobo$3bo3bo$
3o3b2o$o5bobo$4b3o$4b3o$3bobo9$7bobo$7b2o$6b3o$5b2o$5b2o2$5b2o2b2o$b2o
bobobo2bo$2bobo7bo$2bobo7b2o$3bo3bo$3o3b2o$o5bobo$4b3o$4b3o$3bobo!


EDIT 3: To relieve some of the heartbreak, have an original eater 3 from 73 gliders:
x = 463, y = 62, rule = B3/S23
22bo$23bo$21b3o6$276bobo$277b2o$13bo263bo19bobo$11bobo283b2o$12b2o266b
obo15bo$281b2o105bo$281bo107b2o$71bo138bo123bo53b2o$69b2o140b2o9bo100b
o3bo6bobo$32bo37b2o50bo87b2o8b2o102b2obobo4b2o58bo$33bo89bo97b2o100b2o
2b2o63b2o$31b3o31bo55b3o93bo171bo3b2o4bobo$66b2o147b2o56bobo114b2o7b2o
$34bo30b2o3bo16bo22bo59bo45b2o56b2o113b2o9bo$33bo34b2o17bobo18bobo60b
2o101bo$33b3o33b2o16b2o20b2o10b2o47b2o$44bo67b2o6b2o128b2o21b3o9b2o38b
2o93b2o25b2o$43b2o40b3o23bo2bo7bo17b2o31b2o3bobo69bo2bo21bo9bo2bo36bo
3bo22bo2bo33bo2bo26bo2bo23bo2bo$32b2o9bobo12bobo26bo4b2o17bobo3b2o21bo
32bo4b2o39bobo29b3o15b2o3bo11b3o37b4o22b4o33b4o3b3o21b3o24b3o$33b2o24b
2o7bo2bo14bo4bo2bo17bo3bo2bo21bo32bo4bo39b2o47bobo125bo$32bo26bo8b4o
19b4o21b4o20b2o4bo16bobo7b2o35b2o8bo28b3o18bo13b3o37b4o22b4o33b4o6bo
20b5o22b5o$obo58bo4b2o21b2o23b2o23bo6bobo15b2o6bo5b2o29bo2bo35bo3bo30b
o3bo22bobo10bo4bo20bo4bo31bo4bo25bo4bo21bo4bo$b2o39bo12bo5b2o4bo2b2o
16bobo2b2o18bobo2b2o18bob2o4b2o16bo6bob2o3b2o28bob2obo8bo12bo11bob2obo
29bob2obo23b2o9bob3obo19bob3obo30bob3obo24bo2bo23bo2bo$bo39bobo11b2o3b
obo4bobo2bo15bobobo2bo17bobobo2bo13b2obobo2bo6b2o16b2obobo2bo18bobo10b
obo2bo9bobo8bobo10bobo2bo29bobo2bo24bo6b2o2bobo2bo20bobo2bo16bobo12bob
o2bo22bo2bob2o20bo2bob2o$36b2o4b2o10bobo9b2obobo17b2obobo19b2obobo14bo
b2obobo7bobo15bob2obobo20b2o10bobobo10b2o10b2o6b2o2bobobo26b2o2bobobo
32bobobobobo18b2obobobo18b2o3bobo3b2obobobo22bobobo6bo15bobobo5bo$b3o
31b2o33bo22bo17bo6bo21bo8bo23bo21bo12bobo26b2o3bobobo2bo23b2o2bobobo2b
o25b3o7bobo2bo20bobo2bo4bo14bo5b2o4bobo2bo3bo19bobobo5bo16bobobo4bobo$
bo35bo68bo3b2o97bo11bo14bobo5bo2b2o24b2o4bo2b2o28bo7bo2b2o21bo2b2o4bo
21bo5bo2b2o3bobo19b2ob2o4b3o15b2ob2o2bo2bo$2bo101bobo3bobo107b2o16bo4b
2o33b2o31bo7b2o24b2o8b3o17bo6b2o6bo2bo54b2o$105b2o60b2o2b2o26bo20bobo
152b2o14b2o28b2o$137b3o28b2ob2o26b2o153b2o18bobo43bobo$139bo27bo30bobo
152bobo38b3o25bo$138bo216bo27b2o9bo$140b3o62b2o102b3o71bobo9bo$140bo
55bo9b2o6b2o95bo71bo$141bo54b2o7bo7b2o95bo65b2o$195bobo11b3o3bo161b2o$
211bo70bo93bo$210bo70b2o$281bobo$263b2o168bo13b2o10bo$262bobo167bo13bo
2bo10bo$264bo166bo15b3o11bo$431bo29bo$430bo14b5o12bo$430bo13bo4bo12bo$
430bo12bo2bo15bo$430bo9bo2bob2o15bo$430bo8bobobo5bo12bo$430bo8bobobo4b
obo11bo$430bo9b2ob2o2bo2bo11bo$431bo16b2o11bo$431bo19b2o8bo$432bo18b2o
7bo$433bo25bo!
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Re: Synthesising Oscillators

Postby mniemiec » February 24th, 2014, 7:54 pm

Extrementhusiast wrote:This shortens a piston with length >=3, which gives all odd pistons other than 1:

Very nice! I hadn't thought about shortening them. The first steps, that move the house forward one (silencing a spark coil) appears especially useful. The nearby boat-on-boat can be made via a beacon, saving 1 glider:
x = 194, y = 14, rule = B3/S23
93bo$92bo29bo29bo39bo$oo10boo3boo12bo8boo10boo3boo11boo10boo3boo3b3o5b
oo10boo3boobbobo6boo10boo3boobbobo16boo10boo3boobbobo$obobbobbobbobbob
obo10boo9bobobbobbobbobbobobo11bobobbobbobbobbobobo11bobobbobbobbobbob
obobboo7bobobbobbobbobbobobobboo17bobobbobbobbobbobobobboo$bb4obb4obbo
bo13boo10b4obb4obbobo15b4obb4obbobo15b4obb4obbobo15b4obb4obbobo25b4obb
4obbobo$obobbobbobbobbobobo15boo4bobobbobbobbobbobobobboo7bobobbobbobb
obbobobobboo7bobobbobbobbobbobobobboo7bobobbobbobbobbobobobboo5bo11bob
obbobbobbobbobobobboo$oo10boo3boo7bo6boo5boo10boo3boobbo8boo10boo3boo
bbo8boo10boo3boobbo8boo10boo3boobbo6bobo9boo10boo3boobbobo$25boo8bo28b
o29bo29bo29bo3boo32bo$25bobo35boo28boo28boo28boo3$153b3o$155bo$154bo!


Extremethusiast wrote:To relieve some of the heartbreak, have an original eater 3 from 73 gliders:

Also very nice! This version will allow syntheses of the glider-pair shuttles, which the alternate eater-3 didn't.
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Re: Synthesising Oscillators

Postby Extrementhusiast » March 3rd, 2014, 9:16 pm

This, while not synthesizing an oscillator per se, does synthesize the missing Schick ship behind MWSS on MWSS #3 (or at least I think that's the one):
x = 77, y = 39, rule = B3/S23
17bo$15bo3bo$20bo$15bo4bo$5b2o9b5o$4b2o5b3o$3o6b2ob2o$4b2o5b3o$5b2o9b
5o$15bo4bo13bo26b2o2b3o$20bo14b2o12bobo9bobobo$15bo3bo14b2o13b2o11bo3b
o$17bo32bo9$75b2o$74b2o$76bo3$34b2o$33bobo$35bo8$63b2o$62b2o$64bo!

EDIT: Looks like I misunderstood what I was going for.

EDIT 2: Remember that one p9 oscillator that looked like two tied cuphooks?
x = 592, y = 40, rule = B3/S23
387bo$386bo$139bo246b3o155bo$140bo404bo$138b3o238bobo161b3o3bo$114bo
265b2o157bo7b2o$88bo26b2o58bo204bo159b2o6b2o$87bo26b2o34bobo21bo215bo
148b2o$87b3o60b2o22b3o53bo30bo127bo$85bo28bo36bo4bo74bo25bo4b2o125b3o$
86bo27b2o38b2o15bobo55b3o23bobo3b2o$65bo18b3o26bobo26b3o10b2o15b2o82b
2o8b2o81bo68bo25bo62bo$66bo22bo17bo28bobo33bo54b2o36b2o28bo54b2o30bo
35bobo23bobo61b2o$64b3o21bo16bobo29b2o41b2o19bo8b2o14bobo4b2o3b2o17bo
3b2o4bo15b2o9bo21b2o23b2o6b2o2bo19b2o6bobo21b2o11b2o14b2o8b2o15b2o31b
2o11b2o22b2o11b2o34b2o$o12bo26bobo4bo20bo19b3o15b2o29bo41bo2bo19b2o2b
2obo2bo15bo4bobobo2bo15bobobo2bo18bobo2b2o5b3o18bobo2b2o18bobo2b2o6bob
o16bobo2b2o2b2o21bobo2b2ob2ob2o16bobo2b2ob2o17bobo2b2o26bobo2b2o29b2ob
2o9bobo2b2o31bo2b2o$b2o3bo7b2o25b2o3bo20bo14bo34b2o26b2o11bo17bo2bobob
o17b2o2bobobobobo21bobobobo14bobobobobo17bobobobo26bobobobo18bobobobo
6b2o17bobobobo25bobobobob2ob2o16bobobobob2o17bobobobo26bobobobo7bo21b
4o10bobobobo31bobobo$2o2bobo6b2o21bo4bo4b3o18b3o13b2o7b2o13bo10bo3b2o
11b2o9bo3b2o5b2o16bobobo2bo22bobobo2bo21b2obo2bo16b2obo2bo17b2obo2bo9b
2o15b2obo2bo18b2obo2bo25b2obo2bo12bo12b2obo2bo22b2obo2bo20b2obo2bo26b
2obo2bo7b2o22b2o10b2obo2bo29b2obo2bo$5b2o27bobo45b2o8b2o13b2o8bo4b2o
10bo2bo7bo4b2o5bobo16bo2bo21bo4bo2bo27bo22bo23bo12bobo17bo5b3o16bo5b2o
24bo5b2o6b2o16bo28bo26bo32bo10bobo36bo32b2obo$16bo18b2o7b2o60bobo8b2o
15bo2bo7b2o32b2o20b2o6b2o26b2o21b2o22b2o11bo19b2o8b2o13b2o4b2o24b2o4b
2o7b2o15b2o27b2o25b2o31b2o48b2o34b2o$4bo10bo16b2o11bo15bob2o21bob2o29b
o15b2o10bo33bo18bobo8bo27bo22bo23bo32bo6b2o16bo10b2o19bo31bo5bo22bo5bo
20bo5bo26bo5bo43bo5b2o7bobo16bo7b2o$4b2o6bo2b3o2b2o9bobo4b2o4bo16b2obo
21b2obo29bo27bo33bo29bo27bo22bo23bo32bo8bo15bo9b2o20bo31bo4bobo21bo4bo
bo19bo4bobo25bo4bobo42bo4bobo7b2o18b2o4bobo$3bobo4b2o7b2o12bo3bobo4b2o
19b2o16b2o5b2o28b2o26b2o32b2o28b2o26b2o21b2o22b2o31b2o23b2o9bo20b2o30b
2o3bobo21b2o3bobo19b2o3bobo25b2o3bobo27b4o11b2o3bo9bo20bo4bo$11b2o8bo
17bo6bob2o17bob2o11bobo7bob2o26bob2o24bob2o30bob2o26bob2o24bob2o19bob
2o20bob2o29bob2o21bob2o28bob2o28bo4bo23bo4bo21bo4bo27bo4bo3b3o20bo3bo
13bo33bobo$16bo29b2obo17b2obo13bo7b2obo26b2obo24b2obo30b2obo26b2obo24b
2obo19b2obo20b2obo29b2obo21b2obo28b2obo28b5o24b5o22b5o28b5o4bo26bo13b
6o8b2o19b7o$3b2o10b2o284bo27bo24bo31bo123bo21bo2bo19bo8bobo24bo$2bobo
10bobo278b2o2b2o27bo24bo31bo26bo28b3o24b3o30b3o47b3o9bo22b2o$4bo292b2o
bobo26bo24bo31bo25bobo6bo19bo2bo24bo2bo29bo2bo46bo34b2o$296bo116bo7bob
o18b2o27b2o30b2o4b2o51bo$393b2o26b2o85b2o51b2o$393bobo22b2o24bo30b2o
33bo50bobo$384b2o7bo23b2o20b2o2b2o30bobo$322b2o23b2o30b2o2b2o34bo20b2o
bobo29bo$289b2o30bo2bo21bo2bo28bo2bo3bo53bo31b3o71b3o$290b2ob3o25bo2bo
21bo2bo28bo2bo91bo70bo2bo$289bo3bo28b2o23b2o30b2o91bo74bo$294bo252bo6b
o$544bobo6b3o$552b2obo$552b3o$553b2o!


EDIT 3: Finally finished the component to convert a tail to an inducting eater, and boy, is it messy:
x = 81, y = 29, rule = B3/S23
obo$b2o$bo17bo$9b2o8bobo30bo$9bo9b2o29bobo3bo$10b3o38b2o3bobo$12bo10bo
32b2o$7b2o8bo3b2o30b2o$7b2o8bobo2b2o28bo2bo$17b2o34bobo23b2o$7b2o45bo
25bo$3b2obobo5bo33b2ob3o20b2ob3o$4bobo7bo34bobo23bobo$4bobo7bo34bo25bo
$5bo44bo25bo$2b3o42b3o23b3o$2bo23bo20bo25bo$20b3o2b2o$13bo6bo4bobo$12b
2o7bo$12bobo$2bo$2b2o$bobo3$20b3o8b2o$20bo10bobo$21bo9bo!


EDIT 4: This significantly cleans up that first step, although it still takes a lot of setup:
x = 25, y = 27, rule = B3/S23
obo$b2o$bo17bo$9b2o8bobo$9bo9b2o$10b3o$12bo9bo$7b2o8bo4bobo$7b2o8bobo
2b2o$17b2o$7b2o$3b2obobo5bo$4bobo7bo$4bobo7bo$5bo$2b3o$2bo2$13bo$12b2o
$12bobo$2bo$2b2o$bobo$20bo$19b2o$19bobo!


EDIT 5: Full synthesis of minimal 1-2-3-4:
x = 493, y = 59, rule = B3/S23
252bobo$253b2o5bo$253bo4b2o$259b2o2$251bo$252bo$250b3o$254bo$253bobo5b
obo3bo$237bo15bobo5b2o4bobo$171bobo61bobo16bo7bo4b2o$172b2o62b2o8bo$
172bo74b2o$10bobo162bo70b2o$11b2o163b2o$11bo163b2o2bobo3bo54bo25bo$
179b2o4bobo50bobo23b2o202bo$16b2o162bo4b2o52b2o16b2o6b2o182bo11bobo4bo
bo$15b2o150bo88bobo191bo10b2o5b2o$17bo150bo87b2o10bo179b3o11bo9bo$67bo
bo96b3o98bo87bobo114bobo$68b2o106bo90b3o86b2o114b2o$68bo105b3o5b2o6bo
165bo76bobo17bobo$o63bo14bo93bo8b2o5b2o12bo50bo178b2o19b2o$b2o62bo11b
2o25b2o29b2o25b3o8b2o3b2o9bobo10bobo48bobo38bob2o51bob2o13bobo9bob2o
34bob2o14bo19bo5bob2o$2o61b3o4bo2bo4b2o23bo2bo27bo2bo26bo12bo2bo21bo2b
o47bo2bo37b2obo51b2obo13b2o10b2obo34b2obo40b2obo$69bob2obo29b2obo27b2o
bo24bo14b2obo21b2obo47b2obo40b2o53b2o12bo14b2o36b2o13b2o15b2o10b2o$70b
o2bo20bobo9bobo28bobo9bobobo13b3o10bobo22bobo11bobobo32bobo41bo54bo28b
o37bo12bobo13bobo12bo$5bo64bo2bo21b2o9bobo28bobo29bo10bobo22bobo48bobo
41bo54bo28bo37bo12bo17bo12bo20bo$4b2o63bob2obo20bo8b2obo27b2obo29bo9b
2obo21b2obo47b2obo40b2ob2o17bobobo28b2ob2o24b2ob2o13bobobo15b2ob2o39b
2ob2o16b5o$4bobo56b3o4bo2bo29bo2bo27bo2bo39bo2bo21bo2bo30b2o15bo2bo3bo
36bo2bo2bo48bo2bo2bo22bo2bo2bo31bo2bo2bo7bo21bo7bo2bo2bobo10bobo5bobo$
65bo28b3o7b2o27bobo40bobo22bobo31bobo4b2o8bobo4bobo34bobo3b2o47bobo3b
2o21bobo3bobo29bobo3bobo5b2o21b2o5bobo2b2ob2o10b2obobobob2o$64bo31bo
37bo42bo24bo34bo3bobo9bo5bobo35bo54bo9b2o17bo5bo31bo5bo6bobo19bobo6bo
4bo16bo3bo$75bo14b2o3bo147bo16bo100bo2bo57bo43bobo16bobobo$74b2o13bobo
270bobo56bobo41bobo18bobo$74bobo14bo179b2o79b2o2b2o5bo58bo43bo20bo$
270b2o72bo6bobo2b2o$272bo3b2o64bobo6b2o72b2o35b2o$275b2ob3o62b2o79bobo
35bobo$276b5o145bo5bo23bo5bo$43b2o232b3o151b2o23b2o$42b2o223bo89b2o9b
2o61bobo21bobo$44bo54b3o164b2o90b2o7b2o$101bo164bobo79b2o7bo11bo52b3o
39b3o$100bo15b3o230b2o73bo39bo$116bo231bo74bo41bo$95b3o19bo151bo$97bo
170b2o$96bo171bobo3$258b3o$257bo2bo$260bo$256bo3bo$28bo231bo$27b2o228b
obo$27bobo!


EDIT 6: A less restrictive (but more expensive) partially-synthesized block-to-snake converter:
x = 16, y = 15, rule = B3/S23
4bo$5bo$3b3o4$15bo$13b2o$14b2o$2o6bo$2o2b3obo$8bo$14b2o$13b2o$15bo!

Getting the thunderbird there will be tricky.

EDIT 7: Found a completely different (and much easier) way to do it:
x = 48, y = 27, rule = B3/S23
47bo$2bo42b2o$obo43b2o$b2o13$33bo$32bo$32b3o2$10b2o8b2o$10b2o7bo2bob3o
$20b2o2$36b3o$36bo$37bo!

This could be improved by another two gliders if a suitable theta spark synthesis is found.

EDIT 8: Reduced by one glider:
x = 40, y = 23, rule = B3/S23
2bo$obo$b2o11$26bo$24bobo5bo$25b2o4bo$7b2o8b2o12b3o$7b2o7bo2bo$17b2o7b
2o$25bobo$27bo9b2o$37bobo$37bo!

This still leaves room for reduction by one more glider, although this comes quite close:
x = 28, y = 9, rule = B3/S23
bo$2bo10bo$3o10bobo$13b2o$26b2o$26b2o$12b2o$12bobo$12bo!

One or two additional gliders will beat the method with the beehive, and three additional gliders ties it. (Ironically, the theta spark in the beehive method needs a bit of additional debris in order for the whole reaction to be completely clean.)

EDIT 9: Syntheses of an 18-bitter, and a 36-bit pseudo made of two copies of that 18-bitter:
x = 60, y = 85, rule = B3/S23
13bo$14bo$12b3o3$16bo3bo$2bo11bobob2o$obo12b2o2b2o$b2o3$12bo$10bobo16b
o$11b2o15bo24b2obo$28b3o22b2ob3o$23bo35bo$24b2o27b5obo$23b2o28bo2bobo
3$29b3o$29bo$30bo$7b2o$6bobo$8bo2$3o$2bo$bo3$29b2o$28b2o$30bo14$13bo$
14bo$12b3o3$16bo3bo$2bo11bobob2o$obo12b2o2b2o$b2o3$12bo$10bobo16bo$11b
2o15bo24b2obo$28b3o22b2ob3o$23bo35bo$24b2o27b5obo$23b2o28bo2bobo2$53bo
2bobo$29b3o21b5obo$29bo29bo$30bo22b2ob3o$7b2o44b2obo$6bobo$8bo2$3o$2bo
$bo13b2o2b2o$14bobob2o$16bo3bo3$12b3o$14bo$13bo!

I'm pretty sure that constructing the 36-bit pseudo via pretty much any other method would be extremely expensive, if not impossible.

EDIT 10:
mniemiec wrote:New 11-glider synthesis of a 20-bit P2. (The northwest glider just cleans up debris. There are several orientations that produce a single still-life. There might be others that leave nothing; if so, this would take 10 gliders.) Much better than the brute-force synthesis from 24 gliders I created last May:
x = 192, y = 80, rule = B3/S23
41bo$39bobo$40boo23$5bo4bo7bo$6boboo7bo$4b3obboo6b3o5boobboo44boobboo$
25boobboo44boobboo$147bo$145bobo$146boo$$118boo28boo$118boo28boo$85bo$
83boo50boobo26boobo16boobo$84boo48bobob3o23bobob3o13bobob3o$80boo52bo
6bo22bo6bo12bo6bo$79boo54b5obo23b5obo13b5obo$81bo58bo29bo19bo$137bo29b
o19bo$137boo28boo18boo10$21boo48boo39b3o$3o18boo48boo39bo$bbo110bo$bo$
3b3o$3bo$4bo19$107boo$107bobo$107bo!


This includes one such cleanup glider that leaves nothing:
x = 75, y = 53, rule = B3/S23
35b2o2b2o$35b2o2b2o7$45bo$43b2o$44b2o$40b2o$39b2o$41bo12$31b2o39b3o$
31b2o39bo$73bo18$3o$2bo$bo3$67b2o$67bobo$67bo!
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Re: Synthesising Oscillators

Postby mniemiec » March 20th, 2014, 9:18 pm

Extrementhusiast wrote:A less restrictive (but more expensive) partially-synthesized block-to-snake converter:

Here is my list of variants of that tool. (If you DO find a way to do this with 3 gliders, it will improve hundreds of syntheses - but I don't look forward to having to edit all of them!)
x = 166, y = 83, rule = B3/S23
4boo18boo18boo18boo18boo18boo$4boo18boo18boo9bobo6boo18boo9bo8boo$55b
oo37bo$4boo7bo10boo12bo5boo10bo7boo18boo8b3o7boo$4boo6bo12bo13boo3boo
19bo18boo19bo$12b3o9bo13boo24bo39bo$bbo21boo38boo14boo22boo$obo72bobob
oo$boo73boo3bo3bobo$45boo29bo8boo$3bobo40boobobo34bo$3boo40bo3boo$4bo
45bo$$7boo$7bobo$7bo81boo$50boo37bobo$49boo38bo$51bo11$156bobo$156boo$
45bo49bo61bo$43boo48boo$44boo48boo6$24boo28boo18boo28boo28boo28boo$24b
oo28boo18boo28boo28boo28boo$$24boo28boo18boo28boo28boo28boo$24boo29bo
18boo29bo28boo29bo$54bo49bo59bo$10bo43boo32bo15boo58boo$8bobo77bobo$9b
oo77boo$$21boo53boo$20bobbo51bobbo$21boo53boo55b3o$$19boo57boo$18bobo
57bobo$20bo57bo4$6boo83boo$7boo81boo$6bo85bo$$131boo$130bobo$132bo$$
133b3o$133bo$134bo$$132bo$116bo14boo$116boo13bobo$115bobo5$33b3o27b3o$
33bo31bo$34bo29bo!


Extrementhusiast wrote:Syntheses of an 18-bitter, and a 36-bit pseudo made of two copies of that 18-bitter: ... I'm pretty sure that constructing the 36-bit pseudo via pretty much any other method would be extremely expensive, if not impossible.

It's probably possible, but based on the related hook-with-tail pseudo syntheses, it's likely to be extremely difficult, not to mention extremely unpleasant.
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Re: Synthesising Oscillators

Postby Extrementhusiast » March 21st, 2014, 6:41 pm

Key step for two copies of the Gray code (with a different stator):
x = 75, y = 43, rule = B3/S23
2bo$3b2o$2b2o6$2bo11bo$3bo8b2o$b3o5b2o2b2o15bo$8bobo18bo$9bo19b3o5$6bo
$7b2o13b2o$obo3b2o14b2o8bobo$b2o29b2o$bo20b2o9bo$22b2o$59b2ob2o3b2ob2o
$15b2o43bobobobobobo$16bo2bo37bo2bo3bobo3bo2bo$2b2o12bobobo10b2o23bobo
b2ob2ob2ob2obobo$bo2bo12bobo10bo2bo23bo2bo3bobo3bo2bo$bo2bo13bo11bo2bo
26bobobobobobo$2b2o27b2o26b2ob2o3b2ob2o$11b2o9b2o$11b2o9b2o2$11b2o9b2o
$11b2o9b2o6$3b3o23b3o$5bo23bo$4bo25bo!

However, I don't yet know how to do the singular case.
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Re: Synthesising Oscillators

Postby mniemiec » March 27th, 2014, 9:15 pm

Extrementhusiast wrote:Syntheses of an 18-bitter, and a 36-bit pseudo made of two copies of that 18-bitter:

This gives the corresponding loop-on-loop for four more gliders. (In fact, this was the first of around 100 as-yet-unsynthesizable 20-bit pseudo-still-lifes).
x = 37, y = 21, rule = B3/S23
4bobo$5boo$5bo3$10boobo19bo$10boob3o17b3o$4bo11bo19bo$5boo3b5obo16boob
o$4boo4bobbobo17bobo$boo$obo7bobbobo17bobo$bbo7b5obo16boobo$16bo19bo$
10boob3o17b3o$10boobo19bo3$5bo$5boo$4bobo!


There are two versions of Pressure Cooker, a P3 billiard table. The left version, for which Dave Buckingham devised a synthesis, is apparently called "Mini Pressure Cooker", while "Pressure Cooker" is actually the one on the right (and also several similar related forms, stabilized by a bookend, house, etc.) That version does not yet have a synthesis, since the only known mini pressure cooker synthesis starts from the hat-end, while the synthesis of the cauldron (that has a stabilized end like a true pressure cooker) starts from the stabilizer end. This is a project for inventive synthesis:
x = 31, y = 12, rule = B3/S23
5bo19bo$4bobo17bobo$4bobo17bobo$3booboo15booboo$obo5bobo9bobo5bobo$oob
oboboboo9booboboboboo$3bo3bo15bo3bo$3bobobo15bo3bo$4bobo17b3o$5bo$23bo
boo$23boobo!
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Re: Synthesising Oscillators

Postby Extrementhusiast » March 29th, 2014, 5:19 pm

mniemiec wrote:There are two versions of Pressure Cooker, a P3 billiard table. The left version, for which Dave Buckingham devised a synthesis, is apparently called "Mini Pressure Cooker", while "Pressure Cooker" is actually the one on the right (and also several similar related forms, stabilized by a bookend, house, etc.) That version does not yet have a synthesis, since the only known mini pressure cooker synthesis starts from the hat-end, while the synthesis of the cauldron (that has a stabilized end like a true pressure cooker) starts from the stabilizer end. This is a project for inventive synthesis:
x = 31, y = 12, rule = B3/S23
5bo19bo$4bobo17bobo$4bobo17bobo$3booboo15booboo$obo5bobo9bobo5bobo$oob
oboboboo9booboboboboo$3bo3bo15bo3bo$3bobobo15bo3bo$4bobo17b3o$5bo$23bo
boo$23boobo!

This variation could possibly end up being a waypoint:
x = 11, y = 9, rule = B3/S23
5bo$4bobo$4bobo$3b2ob2o$obo5bobo$2obobobob2o$3bo3bo$3bobobo$4b2ob2o!


Also, a synthesis of an interesting symmetrical still life:
x = 43, y = 42, rule = B3/S23
10bo$11b2o$obo7b2o$b2o$bo$11bo$12bo8bo$10b3o7bobo$20bobo$21bo4$21bo$
21b3o$24bo$23bobo14bo$6b2o8bo6bobo13bo$7b2o8bo4b2ob3o11b3o$6bo8b3o10bo
$22b2ob3obo$22b2obo3bo$29b2o$14bo$14b2o$13bobo6$22b2o$21bobo$23bo$40b
3o$4b2o28bo5bo$3bobo27b2o6bo$5bo27bobo2$37bo$36b2o$36bobo!
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Re: Synthesising Oscillators

Postby mniemiec » April 1st, 2014, 7:12 pm

Extrementhusiast wrote:Key step for two copies of the Gray code (with a different stator): However, I don't yet know how to do the singular case.

I found this oscillator sometime between 1972-1974, and called it the Gray Counter, as the rotor appears to count from 0-3 in Gray code. I am not sure if anyone else had previously discovered it. The Wiki doesn't say, but uses the name I gave it. (Shortly after that, Peter Raynham found a longer P8 variant whose name I don't remember; someone else also subsequently re-discovered this with a different stator (like yours) and named that version R2-D2, based on the stator). This is Dave Buckingham's synthesis of the minimal Gray Counter, with several different still-life inductors on the left. (It should be obvious how to add different inductors on the right).
x = 144, y = 150, rule = B3/S23
31bo$29bobo$30boo74bobo$37bobo67boo$37boo68bo$38bo$$72bo$35bo21bo12bob
o4bo14boo3bo14boo3bo19bo$o3bo31bo19bobo12boo3bobo13boobbobo13boobbobo
17bobo$boobobo27b3o20bobo8boo7bobo17bobo17bobo17bobo$oobboo16bo7b3o9bo
16bobbo4bobo9bobbo16bobbo16bobbo16bobbo$21bobo8bo8bobo15bobobo5bo9bobo
bo15bobobo15bobobo14boobobo$6b3o13bo8bo10bo13boobobbo13boobobbo13boobo
bbo13boobobbo16bobbo$6bo49bobbo16bobbo16bobbo9bo6bobbo17bobo$7bo49boo
18boo18boo10boo6boo17bobo$108bobo26bo$$39b3o$39bo$32bo7bo$32boo78bo$
31bobo78boo$111bobo$$115bobo$115boo$116bo$$116boo$116bobo$116bo7$60bob
o$59bo$59bo$59bobbo$59b3o5$3bo7bo$4boo6bo4bo19bo29bo19bo29bo19bo$3boo
5b3o3bobo17bobo27bobo17bobo27bobo17bobo$17bobo15bobobo25bobobo15bobobo
25bobobo15bobobo$19bobbo12bo3bobbo22bo3bobbo9bobbo3bobbo19bobbo3bobbo
9bobbo3bobbo$10b3o5boobobo10boobboobobo20boobboobobo7bobobo3bobobo13bo
3bobobo3bobobo7bobobo3bobobo$12bo6bobbo16bobbo26bobbo8boobbo3bobbo15b
ooboobbo3bobbo9bobbo3bobbo$11bo5bobo17bobo27bobo15bobobo17boo6bobobo
15bobobo$16bobo17bobo27bobo17bobo27bobo17bobo$17bo19bo29bo19bo16b3o10b
o19bo$11boo39boo52bo$10bobo38bobo51bo$12bo40bo3b3o$59bo$13bo44bo$12boo
$12bobo48bo$9bo52boo$9boo51bobo$8bobo$60bo$54bo5boo$54boo3bobo$53bobo
11$66bo$65bo$65b3o42bo$111bo$109b3o$$82boo28boo$67bo14boo3bo24boo3bo
19bo$49b4o13bobo17bobo27bobo17bobo$48bo3bo12bobobo15bobobo25bobobo15bo
bobo$52bo12bo3bobbo9bobbo3bobbo19bobbo3bobbo9bobbo3bobbo$48bobbo12boo
bboobobo7bobobo3bobobo17bobobo3bobobo7bobobo3bobobo$69bobbo8boobbo3bo
bbo18boobbo3bobbo8boobbo3bobbo$67bobo15bobobo25bobobo15bobobo$66bobo
17bobo27bobo17bobo$67bo19bo29bo19bo3$57b3o$59bo$58bo$$63bo$62boo$62bob
o$$60bo$54bo5boo$54boo3bobo$53bobo8$60bobo$59bo$59bo$59bobbo$59b3o6$
67bo19bo29bo19bo$66bobo17bobo27bobo17bobo$65bobobo15bobobo25bobobo15bo
bobo$65bo3bobbo8boobbo3bobbo18boobbo3bobbo8boobbo3bobbo$64boobboobobo
6bobbobo3bobobo16bobbobo3bobobo6bobbobo3bobobo$69bobbo8boobbo3bobbo18b
oobbo3bobbo8boobbo3bobbo$67bobo15bobobo25bobobo15bobobo$51boo13bobo17b
obo27bobo17bobo$50bobo14bo19bo29bo19bo$52bo$$57b3o$59bo$53boo3bo26boo
28boo$52bobo29bobbo26bobbo$54bo8bo21boo28boo$62boo47b3o$62bobo48bo$
112bo$60bo$60boo$59bobo!


Extrementhusiast wrote:Also, a synthesis of an interesting symmetrical still life:

While instantiating the full synthesis, I noticed that Eater-2 (i.e. the form you used in this synthesis, without the two tails) is 19.11763, while you found the synthesis for 20.11763:
OO..OO....
O..O.O....
.OO...OO..
...OOO..O.
...O...O.O
........OO

With only 72 out of 45759 19-bit still-lifes and 77 out of 112243 20-bit still-lifes having instantiated syntheses, the odds that the same index number would occur in both lists is less than one in a million!
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Re: Synthesising Oscillators

Postby Extrementhusiast » April 8th, 2014, 1:48 pm

Again, when looking back through the archives, I found a way to attach an integral with tub to another tub (or similar surface). Here it is, improved:
x = 27, y = 24, rule = B3/S23
23bo$21b2o$22b2o6$12bobo$13b2o$13bo8bo$22bo$22bo$11b3o11bo$13bo10bobo$
12bo12bo3$3o$2bo$bo$18b3o$18bo$19bo!


EDIT: And here's another from the archives: the thirteenth 16-bitter can be reduced by three gliders:
x = 69, y = 21, rule = B3/S23
23bo$21bobo$22b2o2$24bo$24bobo$24b2o$3bo14bo24b2o$2bo14bobo16bo2bobo2b
o17bo2bob2o$2b3o12b2o17b4ob3o18b5obo$51bobobo$bo15b2o17b4ob3o20bob2o$
2o15bobo16bo2bobo2bo19b2obo$obo4bo10bo24b2o$6b2o16b2o$6bobo15bobo$24bo
2$22b2o$21bobo$23bo!

The intermediate steps were already posted by Sokwe.

EDIT 2: Synthesis of an 18-bitter:
x = 20, y = 20, rule = B3/S23
6bo$7b2o$6b2o$2bo9bobo$bobo8b2o$bobo9bo$2ob2o2b2o$o2bo3b2o$bobo$2bo$5b
2o3bobo$4bo2bo2b2o$4bo2bo3bo$5b2o4$17b3o$17bo$18bo!


EDIT 3: This fully solves the "two related oscillators" on page ten:
x = 344, y = 75, rule = B3/S23
259bo$260bo$258b3o2$263bo11bobo5bo$257bo6bo10b2o5bo$258b2o2b3o11bo5b3o
$250bo6b2o$248bobo63bo$249b2o63bobo$279b3o32b2o$279bo32bo$280bo31bo$
256bo11bo2bo36bo3bo$254bobo7b2o2b4o30b2o2b3o27b2o2bo$255b2o6bobo6b2o
28bo2bo3b2o25bo2bobo$264bo3b2o2bobo8b3o17bob2o2bobo25bob2obo$267bo2bob
obo8bo20bo2bobobo26bo2bobo$124bo25bobo115b3obob2o8bo20b3obob2o26b3obo$
125bo25b2o5bo112bo36bo33bo$123b3o25bo7b2o90b2o17bo36bo33bo$158b2o90bob
o17b2o35b2o32b2o$7bo129bo11b2o101bo$6bo121bo6b2o11bobo20bo87b2o$6b3o
117bobo7b2o12bo20bobo22bobo59bobo$102bo24b2o42b2o24b2o61bo59b2o$bo40bo
46b2o11bobo47bo44bo122bobo$2bo39bobo42bobobo10b2o48b2o5b2o20b2o73b2o
13b2o47bo$3o3bo35b2o41bobobo61bobo5b2o19b4o71bobo12b2o$5bo9bo55bo14b2o
16b2o73b2ob2o73bo14bo$5b3o6bo56bobo7b2o20bobo3bo49b4o17b2o22b2o$14b3o
54b2o9b2o21bo2bobo18bo2bo25bo4bo33bobo4bo2bo2bo17bo2bo$81bo27b2o18b4o
26b4o35b2o5b6o17b4o$10b2o5b3o13b2obo26b2o24b2o22b2o20b2o28b2o31bo12b2o
19b2o$9bobo5bo11b2o2bob2o22b2o2bobobo17b2o2bobo17b2o2bobo15b2o2bobo23b
2o2bobo39b2o2bobo14b2o2bobo$5bo3bo8bo9bo2bobo24bo2bobo2b2o16bo2bobobo
16bo2bobobo14bo2bobobo22bo2bobobo28bo9bo2bobobo13bo2bobobo$5b3obo19b3o
bo12bo12b3obo8bobo10b3obob2o16b3obob2o14b3obob2o22b3obob2o25bobo10b3ob
ob2o13b3obob2o$8bo23bo11b2o16bo9b2o14bo23bo21bo29bo30b2o13bo20bo$7bo
23bo13b2o14bo11bo13bo23bo21bo29bo45bo20bo28bo$7b2o22b2o28b2o3b2o19b2o
22b2o20b2o28b2o32bo11b2o19b2o25bobo$38b2o27b2o128b2o59b2o$39b2ob3o21bo
3b2o124bobo$38bo3bo27bobo191bobo$43bo26bo194b2o$265bo2$258bobo13bo$
259b2o11b2o$259bo6bo6b2o$267bo$265b3o$314bo$257bo56bobo$255bobo56b2o$
256b2o54bo$312bo$268bo2bo36bo3bo$268b4o34b3o31bo$272b2o31bo3b2o28bobo$
263b2o3b2o2bobo30b2o2bobo27b2obo$262bo2bobo2bobobo28b2o2bobobo25b2o2bo
bo$263b2o3b3obob2o26bo2b3obob2o23bo2b3obo$271bo30b2o4bo27b2o4bo$270bo
36bo33bo$270b2o35b2o32b2o2$255b2o$254bobo$256bo10b3o50b2o$267bo52bobo$
268bo51bo2$257b3o$259bo$258bo!
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Re: Synthesising Oscillators

Postby mniemiec » April 19th, 2014, 1:55 am

Extrementhusiast wrote:Synthesis of an 18-bitter:

This solves 3 18s (this one, a similar one with the base still-life turned upside down, and one where the base still-life is two siamese hats), 1 19, 1 20, 3 21s, 10 22s, 9 23s, 34 24s.
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Re: Synthesising Oscillators

Postby Extrementhusiast » April 24th, 2014, 10:13 pm

Solved the tail-to-snake problem without the boat-bit kludge:
x = 36, y = 58, rule = B3/S23
33bo$33bobo$33b2o$2bo$obo$b2o2$18bo$16b2o$17b2o$26bo$25bo$25b3o4$27bob
o$27b2o$22bo5bo$20bobo$21b2o2$12bo$11bobo$10bo2bo$6b2obob2o$7bobo$7bob
o$8bo$5b3o$5bo3$29b2o$11b2o16bobo$12b2o15bo$11bo21b2o$33bobo$33bo2$15b
2o$14bobo$15bo2$15b2o$14bobo$16bo9$3b2o$2bobo$4bo!
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Re: Synthesising Oscillators

Postby mniemiec » April 26th, 2014, 1:16 am

Extrementhusiast wrote:Solved the tail-to-snake problem without the boat-bit kludge:

Very nice! I'm going to have to go through my lists to see which syntheses this can be applied to. Considering the number of times I've beaten my head against this particular wall, I'm pretty sure there are quite a fair number of them!
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Re: Synthesising Oscillators

Postby Extrementhusiast » April 26th, 2014, 1:30 pm

Converts one type of pressure cooker into the other, but with a nonstandard inductor:
x = 65, y = 43, rule = B3/S23
9bo45bo$7bobo45bobo$8b2o45b2o5$14bobo31bobo$15b2o15bo15b2o$15bo15bobo
15bo$31bobo$30b2ob2o$27bobo5bobo$27b2obobobob2o$30bo3bo$2b2o9bo16bobob
o16bo9b2o$2ob2o6bobo17bobo17bobo6b2ob2o$4o8b2o18bo18b2o8b4o$b2o59b2o2$
29b3ob3o$25b2o11b2o$25b2o11b2o10$28bo$29bo$27b3o2bo$31bobo$13b3o15bo2b
o14b3o$15bo16b2o15bo$14bo35bo2$29bo$29bo$29bo!

Converting that into a snake won't be easy, because the hook gets in the way. Barring an easier way to get rid of it, you'd probably have to convert it into a tail, then convert it back into a hook.

EDIT: Finished that, using a very roundabout method:
x = 697, y = 50, rule = B3/S23
38bo$39bo$37b3o$41bo$41bobo$31bobo7b2o$32b2o56bobo$32bo57b2o65bo45bo
223bo52bobo$91bo63bobo45bobo220bo42bo10b2o$156b2o45b2o221b3o38bobo11bo
$51bo416b2o43bo163bo$51bobo31bobo426bo160b2o$51b2o32b2o425b3o161b2o$
17bo68bo485bobo$11bo3b2o145bobo31bobo312b3o58b2o$5bo6b2o2b2o16bo16bobo
19bo37bo51b2o15bo15b2o41bo31bo23bo38bo29bo41bo57bo33bo6b2o4bo17bo6b2ob
2o16bo6b2ob2o4bo16bo6b2ob2o21bo6b2ob2o24bo6b2ob2o20bo$4bobo4b2o20bobo
15b2o19bobo4b2o29bobo50bo15bobo15bo40bobo29bobo21bobo36bobo27bobo39bob
o55bobo31bobo4bobo5bo15bobo4bobobobo14bobo4bobobobo19bobo4bobobo21bobo
4bobobo24bobo4bobobo20bobo$4bobo26bobo16bo19bobo3bobo5bo23bobo3b2o61bo
bo3b2o51bobo3b2o24bobo3b2o16bobo3b2o31bobo3b2o22bobo3b2o34bobo3b2o50bo
bo3b2o26bobo3bobo22bobo3bobo3bo15bobo3bobo2bobo2b2o15bobo3bobo2bo21bob
o3bobo2bo24bobo3bobo2bo20bobo$3b2ob2o24b2ob2o3b2o29b2ob2o2bo5b2o23b2ob
2o2bo61b2ob2o2bo51b2ob2o2bo24b2ob2o2bo16b2ob2o2bo31b2ob2o2bo22b2ob2o2b
o34b2ob2o2bo50b2ob2o2bo26b2ob2o2bo5bo17b2ob2o2bo20b2ob2o2bo4b2o2b2o15b
2ob2o2bo4bobo6bo11b2ob2o2bo4bobo21b2ob2o2bo4bobo17b2ob2o$obo5bobo2bobo
13bobo5bo2bo27bobo5bob2o5b2o19bobo5bobo58bobo5bobo48bobo5bobo21bobo5bo
bo13bobo5bobo28bobo5bobo19bobo5bobo31bobo5bobo13bo33bobo5bobo23bobo5bo
bo5b2o13bobo5bobo17bobo5bobo10bo11bobo5bobo5b2o6bobo6bobo5bobo5bobo17b
obo5bobo5bobo13bobo5bobo$2obobobob2o2b2o14b2obobobobobo27b2obobobobo2b
o25b2obobobobo15bobobo39b2obobobobo49b2obobobobo22b2obobobobo14b2obobo
bobo29b2obobobobo20b2obobobobo32b2obobobobo13bo8bo25b2obobobobo5bo18b
2obobobobo5bobo13b2obobobobo10bo7b2obobobobo23b2obobobobo14b2o7b2obobo
bobo7bo18b2obobobobo7bobo12b2obobobob2o$3bo3bo6bo17bo3bo2bo31bo3bo2b2o
29bo3bo64bo3bo54bo3bo27bo3bo4bo14bo3bo34bo3bo25bo3bo37bo3bo15b3o6bobo
26bo3bo6bo22bo3bo26bo3bo11b2o10bo3bo28bo3bo13b2o13bo3bo14bo16bo3bo10bo
16bo3bo$3bobobo24bobobo34bobobo33bobobo36b2o9bo16bobobo16bo9b2o26bo3bo
27bo3bo4bobo12bo3bo3b2o29bo3bo3b2o20bo3bo3b2o32bo3bo3b2o19b2o27bo3bo6b
3o20bo3bo26bo3bo3bo7bobo9bo3bo3bo24bo3bo3bo8b2o14bo3bo12b2o17bo3bo27bo
3bo$4bobo4b3o19bobo36bobo13b3o19bobo35b2ob2o6bobo17bobo17bobo6b2ob2o
25b3o29b3o5b2o14b3o4b2o5bobo22b3o4b2o21b3o4b2o33b3o4b2o49b3o31b3o28b3o
4bo20b3o4bo25b3o4bo10bo14b3o4b2o4b2o2b2o17b3o4b2o23b3o$5bo7bo20bo38bo
14bo22bo36b4o8b2o18bo18b2o8b4o68b2o25b2o162b2o3b2o56bo4b3o20bo32bo4b2o
25bo2bo3bobo26bo2bo$12bo76bo59b2o59b2o24b3ob3o25b3ob3o6bobo8b3ob3o10bo
21b3ob3o23b3ob3o36bob4o52bob2o5bobo3bobo16bob2o27bob2o11bo12bob2o29bob
2o8bobo18bob2o3bo2bo3bo21bob2o3bo2bo6b2o13bob2o$235bo2bobo2bo23bo2bobo
2bo5bo9bo2bobo2bo30bo2bobo2bob2o18bo2bobo2bob2o32b2obo2bob2o48b2obo7bo
3bo18b2obo7b2o18b2obo10bo13b2obo29b2obo10bo18b2obo4b2o26b2obo4b2o7bobo
12b2obo$82bobo92b3ob3o51b2o5b2o23b2o4bobo15b2o4bobo30b2o4bobobobo17b2o
2bo2b2obobo36b2obobo92bobo164bo$78b2o2b2o89b2o11b2o86bo23bo38bo3bo29bo
41bo93bo87b2o71b2o$79b2o2bo89b2o11b2o67bo99b3o145b3o90b2o69bobo$78bo
176bobo47b2o50bo3b2o142bo89bo66bo6bo$251bo3b2o48bobo24b2o3bo18bo3bobo
3b2o24b3o2b2o105bo157b2o$47b3o200bo49bo4bo25bobo2b2o24bo3bobo25bob2o
31b2o230bobo$47bo187b2o13b3o47bobo30bo2bobo27bo26bo4bo29b2o$48bo187b2o
62b2o128bo$235bo15bo39b2o370b3o$250b2o40b2o3b3o363bo$242b3o5bobo38bo5b
o366bo$229b2o11bo55bo106b2o253b3o$176bo51bobo12bo140b3o19b2o254bo$177b
o52bo155bo18bo255bo$175b3o2bo204bo$179bobo239b3o$161b3o15bo2bo14b3o
211b2o8bo$163bo16b2o15bo212b2o10bo$162bo35bo213bo2$177bo$177bo$177bo!


EDIT 2: Found the missing step for trice tongs siamese loaf siamese tub:
x = 332, y = 52, rule = B3/S23
248bo$247bo$247b3o7$246bo$245bo$245b3o6$228bo10bo$221bo7bo8bo$222bo4b
3o8b3o$220b3o$195bo$196bo$123bo70b3o18bo8bobo$123bobo34bo7bo21bo25bo8b
2o$123b2o30bo5bo5bo20bobo6bobo14b3o8bo$121bo34bo2b3o5b3o19b2o6b2o19b3o
$20bo60bobo38bo31b3o41bo21bo$21bo60b2o36b3o96bo89bo$19b3o60bo110b2o
113bo$23bo99bobo30b3o34bo42b2o70b3o$22bo32b2o23b2o41b2o32b3o34bo41bo$
22b3o9bobo3b2o12bo2bo2b2o17bo2bo2b2o19b2o16bo9b2o27b2o30bo2b2o37bo2b2o
21b2o2b2o28b2o2b2o22b2o$35b2o3b2o12bo2bo2b2o13bo3bo2bo2b2o17bo2bo24bo
2bo10bobo12bo2bo31bo2bo38bo2bo20bo2bo2bo27bo2bo2bo21bo2bo$2bo32bo19b2o
19b2o2b2o22b3o25b3o12b2o3bobo6b3o30bob3o37bob3o20bobob3o27bobob3o4b2o
15bobob3o$obo72b2o25b2o26b2o15bo5b2o4b2o32bobo39bobo24bobo31bobo6b2o
17bobo3bo$b2o8bo9b2o11b2o3b2o18b2o23b2o17bob2o24bob2o18bo6bob2o29bobob
2o36bobob2o23bob2o30bob2o5bo18bo2bo$11bobo7bobobo7bobo3bobobo15bobobo
16b2o2bobobo12bobobobobo21bobobobo22bobobobo3b3o21b2ob2o21b3o13b2ob2o
22b2ob2o3bo25b2obo25bob2o$11b2o11b2o9bo6b2o10b3o5b2o16b2o5b2o12b2o5b2o
22bo3b2o23bo3b2o3bo5b3o43bo48bobo20bo8bo23bo2b2o$8b2o46bo94bo19bo4bo
44bo49b2o19bobo7b2o26b2o$2b2o3b2o46bo47bo47b2o24bo78b2o4b2o29b2o$bobo
5bo47b3o42b2o46bobo104b2o2bo2bo32b2o$3bo53bo44bobo51b2o98bo4bo2bo2b3o
27bobo$58bo40b2o56b2o4b2o60b2o35b2o3bo29bo$98bobo55bo6bobo2b2o54bobo
41bo$100bo62bo3b2o57bo$169bo69b2o25b2o$155b3o80b2o27b2o$157bo82bo25bo$
156bo14b3o51b2o43b3o$171bo52bobo43bo$172bo53bo44bo!


EDIT 3: Minimal form of 28P7.1 from a 17-bitter:
x = 368, y = 36, rule = B3/S23
312bo$312bobo$312b2o$287bo$282bo3bo23b2o$283b2ob3o20bo2bo$63bo218b2o
25bo2bo$62bo247b2o$62b3o$218bo82bobo$173bo43bo84b2o$111bo8bobo49bo40bo
3b3o82bo$9bo45bo54bo9b2o39bo10b3o39b2o7bo6bo27bo$7b2o46bobo52b3o8bo37b
obo51b2o6b2o5b2o28bobo74bo$o7b2o17bo20bobo4b2o51bo51b2o7bo52b2o5b2o18b
o8b2o75bobo4bo24bo$b2o12bo9bobo10bo10b2o55bobo54bobo2bo80bobo78bo4b2o
3b3o22b3o$2o3bo7b2o11b2o9bo11bo4bo4bo47b2o54b2o3b3o78b2o80bo7bo24bo$3b
2o9b2o21b3o15b2obobo103bo76bobo85b3o7b2o23b2o$4b2o21bo21b2o3b2o2bobo2b
2o137bobo37b2o$27b2o11b3o5bo2bo7bo3bobo14b2o23b2o24b2o29b2o3b2o24bo8b
2o19bo18bo8b2o23b2o26b2o29b2o24b2o$16bo9bobo11bo7bo2bo11bo16bobo22bobo
23bobob2o25bobobobo23bobo8bo18bobo27bo23bo27bo30bo$15b2o24bo7b2o31bo7b
o16bo2b2o21bobo8bo19bobo4b2o19bobo6bo20bobo14b3o10bobo23bobo25bobo17bo
10bobo22bobo$6b2o7bobo14b2ob2o17b2ob2o22b2ob2o2b2o16b2obobo20b2obo7bo
19b2ob2o2b2o19b2ob2o4b2o5bo13b2ob3o14bo9b2ob3o20b2ob3o22b2ob3o15b2o8b
2ob3o20bob3o$5bo2bob2o18bo2bobobo14bo2bobobo19bo2bobobo2b2o13bo2bobo
20bo2bob2o6b3o15bo2bo7bo16bo2bo3bo3bobo3b2o11bo2bo4bo12bo8bo2bo4bo17bo
2bo4bo19bo2bo4bo13bobo6bo2bo4bo16bo2bo4bo$5b2obobobo17b2obobobo14b2obo
bobo19b2obobobo17b2obobobo18b2obobo25b2obob2o21b2obob2o10bobo10b2obob
3o22b2obob3o18b2obob3o20b2obob3o23b2obob3o17b2obob3o$6bobo2bo19bobo2bo
16bobo2bo21bobo2bo6b2o11bobo2b2o19bobobo15b2o9bobobo23bobobo27bobo27bo
bo23bobo25bobo28bobo22bobo$6bobo22bobo19bobo24bobo8b2o12bobo23bobob2o
7b3o4bobo8bobobobo21bobobobo25b2o28b2o24b2o26b2o29b2o23b2o$7bo24bo21bo
26bo11bo12bo25bo11bo6bo11bo3b2o22bo3b2o$145bo55bo$181b2o3b2o12b2o$107b
2o73b2o2bobo11bobo$106bobo72bo4bo$108bo88b2o$110b3o8bo75bobo$110bo9b2o
75bo$111bo8bobo!


EDIT 4: One of the toad-on-toad pseudo-oscillators can be made with just five gliders:
x = 20, y = 12, rule = B3/S23
12bo$10b2o$11b2o2$5b2o$2bo2bobo$obo2bo12b2o$b2o14b2o$19bo$9b2o$10b2o$
9bo!


EDIT 5: Finally solved that one p10 from six pages back:
x = 1187, y = 55, rule = B3/S23
528bo$527bo$527b3o9$309bo$310b2o$309b2o743bo$1055bo$232bobo70bobo745b
3o$226bo5b2o47bo24b2o75bobo124bo$2bo221b2o7bo48b2o22bo17bo58b2o44bobo
79bo4bo$obo186bobo33b2o54b2o41bobo53bo3bo9bo34b2o78b3o5b2o$b2o186b2o
43b2o73bobo12b2o52bobo12bo16bo19bo85b2o159bo23bo72bo287bo$190bo22bo20b
obo50bo22b2o67b2o12b3o12bobo68bo43bo154bo21bo72bo286bobo$106bo75bo28bo
bo20bo27bobo20b2o23bo98b2o7bo59bo43bo153b3o3bo13bo3b3o10bo59b3o285b2o
4bobo$6bo97bobo60bo15bo3bo24b2o48b2o18bo3b2o50bo41bo33bob2o37bo18bo3b
3o41b3o147bo7b2o15b2o7bo4b2o190bobo91bo31bo37b2o$4bobo16bo81b2o4bo24b
2o27bobo13b3ob2o45bo30bo19b2o53bobo39b2o30bobo2b2o37bo18b2o30bo165b2o
6b2o13b2o6b2o6b2o190b2o2bo88bobo30bo27bo4bo4bo$5b2o16bobo84bo5bobo16bo
bobo26b2o18b2o14b2o20b2o5b2o49b2o50bo3b2o39bobo31b2o39b3o17b2o32bo5b2o
156b2o31b2o60bo3bo132bo3bobo86b2o29b3o13bo12bobob2o$23b2o64bo16bo3b3o
3b2o19bobobo59b4o19b2o5bobo75bo23bo88b2o82b3o5bobo26bo69b3o152b2obobo
77bo38bo17b2o4bo124bo3bo9b2o2bobo2b2o3b2o31bo$17bo9bo40bo20bobo14b2o9b
o21b2o23b2o35b2ob2o104bo22b3o28b2o21b2o33bo26bo7bobo20bo35bo24bobo66bo
2bo32bo120b2o2b2o78bobo34b2o22b2o23b2o29b2o55b3o12b2ob3o6bobo3bo7bo2bo
21b2o7bobo14b2o32b2o24b2o$15b2o9bo22bo18bobo18b2o2b2o10bobo36b2o14bo3b
obo36b2o17b4o29b2o51b3o14b2o28bobo6bo22bo35bo25b3o5b2o21b3o33b3o23b2o
67bo2bo29b2o205b2o36b2o22b2o23bo30bo7bo49bo11b2o13bo11bo2bo20bobo7b2o
14bobo31bobo23bobo$13bo2b2o8b3o20bobo16b2o2b2o18b2o49b2o14bobo2bo19bo
2bo33bo4bo23bo2bo2bo4bobo17bo2bo39bo2bo6bo16bo3b2o8bo22bo35bo27bo5bo
24bo2b2o31bo2b2o21bo32bobo28b3o33b2o269b2o20bobo28bobo5bobo46bo40b2o
21bo25bo33bo5bo19bo$11bobo35b2o2b2o16b2o21bo22bo5bo21bo13b2o23b4o34b4o
24b6o5b2o18b4o39b4o5b2o17b2o2bo5b4o19b4o32b4o24b4o27b4o2bo29b4o2bo16b
3o2bobob2o18b2ob2o6b2o17b2ob2o22b2ob2o28b2ob2o6bo9bobo13b2ob2o6b2o14b
2ob2o12bobo16b2ob2o39b2ob2o25b2ob2o31b2ob2o28b2ob2o10bobo10b2ob2o5b2o
19b2ob2o5b2o5b2o26b2ob2o21b2ob2o23b2ob2o23b2ob2o8bo12b2ob2o7b2o4bo15b
2ob2o4bobo14b2obo$12b2o38b2o19bo15bo26bobo2b2o13b2o17b2o23b2o36b2o28b
2o12bo16b2o24bobo14b2o9bobo15b2o8bo22bo35bo27bo11bo18bo7b3o25bo7b3o15b
o3b2obo19b2obo7bo18b2obo23b2obo6b2o3bobo15b2obo6bobob2o5b2o14b2obo6bob
o14b2obo13b2o17b2obo40b2obo26b2obo32b2obo29b2obo11bo12b2obo27b2obo41b
2obo22b2obo24b2obo24b2obo8b2o12b2obo7bo2bob2o16b2obo5b2o15b2obob2o$44b
2o8bo7b2o4bo13b2o4bobo18b2o4bobo4b2o11bobo2b2o12bobo2b2o18bobo2b2o31bo
bo2b2o23bobo2b2o24bobo2b2o21b2o13bobo2b2o33bo2b2o18bo2b2o31bo2b2o23bo
2b2o6bo19bo2b2o5bo25bo2b2o5bo14bo7bo2b2o18bo2b2o25bo2b2o3bo18bo2b2o2bo
4b2o19bo2b2o2bobob2o6bo17bo2b2o2bo19bo2b2o10bo20bo2b2o39bo2b2o25bo2b2o
31bo2b2o28bo2b2o23bo2b2o26bo2b2o40bo2b2o21bo2b2o23bo2b2o23bo2b2o4bobo
14bo2b2o3bo2bo2b2o18bo2b2o21bob2o$44bobo2bo12bobo2bobo12bobo2bobo19bob
o2bobo18bobobo2bo11bobobo2bo17bobobo2bo30bobobo2bo22bobobo2bo9bo13bobo
bo2bo20bo14bobobo2bo29b2obobo2bo14b2obobo2bo27b2obobo2bo19b2obobo2bo5b
3o14b2obobo2bo27b2obobo2bo24b2obobo2bo14b2obobo2bo5bo15b2obobo2bobobo
14b2obobo2bobo5bo16b2obobo2bobobo24b2obobo2bob2o15b2obobo2bob2o4bo19b
2obobo2bob2o32b2obobo2bob2obo16b2obobo2bob2obo22b2obobo2bob2o21b2obobo
2bob2o16b2obobo2bob2o19b2obobo2bob2o33b2obobo2bo17b2obobo2bo19b2obobo
2bo19b2obobo2bo17b2obobo2bo3b2o20b2obobo2bo17b2obobo$7bo37bo2bobo12bo
2bobo14bo2bobo21bo2bobo20bo2bo2bo12bo2bo2bo18bo2bo2bo31bo2bo2bo23bo2bo
2bo9bobo12bo2bo2bo36bo2bo2bo29bobo2bo2bo13bo2bo2bo2bo26bo2bo2bo2bo18bo
2bo2bo2bo21bo2bo2bo2bo20bo5bo2bo2bo2bo24bobo2bo2bo14bobo2bo2bo4bo16bob
o2bo2bob2o15bobo2bo2bob2o21bobo2bo2bobobo24bobo2bo2bobo16bobo2bo2bobo
4b2o5bo13bobo2bo2bobobo8bo22bobo2bo2bobob2o16bobo2bo2bobob2o22bobo2bo
2bobobobo18bobo2bo2bobobo15bobo2bo2bobobo18bobo2bo2bobobo8bo23bobo2bo
2bo17bobo2bo2bo19bobo2bo2bo19bobo2bo2bo17bobo2bo2bo25bobo2bo2bo17bobo
2bo2b2o$7b2o14bobo20b2obo14b2obo16b2obo23b2obo22b2ob2o14b2ob2o20b2ob2o
33b2ob2o25b2ob2o10b2o14b2ob2o38b2ob2o33b2ob2o14b2o2b2ob2o27b2o2b2ob2o
19b2o2b2ob2o22b2o2b2ob2o22bo4b2o2b2ob2o28b2ob2o18b2ob2o5b3o17b2ob2o22b
2ob2o8b2o18b2ob2o3bo28b2ob2o2bo19b2ob2o2bo4bobo3b2o16b2ob2o2bobo7bo26b
2ob2o2bo22b2ob2o2bo28b2ob2o2bo2b2o21b2ob2o2bobo18b2ob2o2bobo21b2ob2o2b
obo7b2o26b2ob2o21b2ob2o23b2ob2o23b2ob2o21b2ob2o29b2ob2o4b2o15b2ob4o2b
2o$6bobo14b2o23bo17bo19bo26bo8bo16bo18bo24bo37bo29bo30bo42bo30bo6bo22b
o35bo27bo10b2o18bo22b3o10bo32bo22bo29bo26bo10bobo19bo36bo4b2o20bo4b2o
9bobo17bo4b2o8b3o26bo4bo24bo4bo12bo17bo4bo27bo4bob2o19bo4bob2o3bo18bo
4bob3o5bobo27bo4bo20bo4bo22bo4bo22bo4bo20bo4bo3bobo22bo4bo2bo17bo7bo$
24bo23bobo15bobo17bobo24bobo6bobo14bob3o14bob3o20bob3o33bob3o25bob3o7b
o18bob3o38bob3o21bo3b2o6bob3o18bob3o31bob3o23bob3o5b2o19bob3o31bob3o
28bob3o18bob3o4b3o18bob3o22bob3o6bo21bob3o32bob3o22bob3o31bob3o39bob3o
25bob3o11b2o18bob3o28bob3o23bob3o7bobo16bob3o5bo34bob4o20bob4o22bob4o
22bob4o20bob4o3b2o2b3o18bob6o18bob6o$49bobo15bobo17bobo24bobo5b2o16bo
2bo15bo2bo21bo2bo34bo2bo26bo2bo6b2o19bo2bo39bo2bo19bobo3bobo6bo2bo19bo
2bo32bo2bo24bo2bo7bo19bo2bo32bo2bo29bo2bo19bo2bo6bo19bo2bo23bo2bo29bo
2bo33bo2bo23bo2bo32bo2bo40bo29bo15b2o18bo32bo27bo10b2o18bo7b2o35bo25bo
27bo27bo25bo8bo2bo21bo25bo$21b3o26b2o16b2o18b2o25b2o24b2o17b2o23b2o36b
2o28b2o7bobo19b2o41b2o21b2o13b2o21b2o34b2o26b2o29b2o22b2o10b2o31b2o21b
2o6bo21b2o25b2o31b2o35b2o25b2o34b2o42bo29bo35bo8bobo21bo27bo30bo44bob
2o22bob2o24bob2o24bob2o22bob2o8bo21bob2o22bob2o$21bo484bobo299b2o27bob
o7b2o24bobo8b2o20bobo25bobo8bo19bobo43b2obobo20b2ob2o23b2ob2o23b2ob2o
21b2ob2o3b2o24b2ob2o21b2ob2o$22bo97b2o386bo295bo9bo22b2o9b2ob3o19b2o
10bo20b2o26b2o8b2o19b2o14b2o32bo86b2o22bo2bo$121b2ob3o678b2o5b2o33bo3b
o92bobo34bobo33b3o82bobo22b2o$120bo3bo550b3o126b2o7b2o37bo30b3o95bo35b
o84bo$16b2o107bo549bo207bo75b3o12b2o38b2o2bo80b2o36b2o$17b2o657bo135bo
71bo76bo12bobo36bobo82bobo24b3o9bobo$16bo10b3o277b3o501b2o147bo3b2o8bo
40bo84bo26bo9bo$27bo281bo493b3o5bobo72b3o75bobo159bo$28bo279bo494bo82b
o77bo$777b2o6bo18bo82bo$32b3o735b2o4b2o6b2o$32bo638bo79b2o17bobo5bo5bo
bo$33bo636b3o77bobo17bo$670bob2o78bo13b2o13b2o$671b3o91b2o13b2o$671b2o
94bo14bo!

The "missing step" mentioned on page seven actually turned out to be twenty-eight missing steps. And with 165 gliders, this is now the most expensive oscillator.

EDIT 6: Synthesis of one particularly hard 3-MWSS combination:
x = 64, y = 30, rule = B3/S23
19bo$19bobo$8bo10b2o$9bo$2bo4b3o$obo$b2o3$16bo$15bobo$14bobo$9bo5bo$7b
obo$8b2o$11bo$11bo$11bo$15bo$14bobo$14b2o$22b3o24b3o3b3o$22bo2bo22bo2b
o3bo2bo$22bo28bo3bo$22bo5bo18bo3bo3bo5bo$8b2o12bo4b3o21bo3bo4b3o$9b2o
12bo3bob2o17bobo5bo3bob2o$8bo19b3o30b3o$28b3o30b3o$28b2o31b2o!

Unfortunately, the exact method that I used won't help in pushing the back MWSS on, as the spark gets in the way. However, perhaps we could use that spark to our advantage....

EDIT 7: Predecessor to putting the other MWSS on:
x = 12, y = 12, rule = B3/S23
b2o$3o$2o$10bo$3b2o4b3o$2bo2bo2b2obo$4bo3b3o$3ob2o2b3o$9b2o$4bo$3b3o$
6bo!


EDIT 8: This improves 19.4199 by one glider:
x = 25, y = 27, rule = B3/S23
12bo$11bo$2bo8b3o$obo$b2o4$24bo$8bo13b2o$6bobo14b2o$7b2o7bo$10bo4bobo$
10b2o3bo2bo$9bobo4b2o8$b2o$obo$2bo8b3o$11bo$12bo!


EDIT 9: The heads can be turned into tubs for just one more glider each:
x = 20, y = 45, rule = B3/S23
19bo$17b2o$18b2o3$5bo$3b2o$4b2o3$obo$b2o$bo5$19bo$3bo13b2o$bobo14b2o$
2b2o7bo$5bo4bobo$5b2o3bo2bo$4bobo4b2o9$bo$b2o$obo3$4b2o$3b2o$5bo3$18b
2o$17b2o$19bo!
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Re: Synthesising Oscillators

Postby mniemiec » June 7th, 2014, 6:22 pm

Extrementhusiast wrote:Synthesis of one particularly hard 3-MWSS combination:

This is a very nice sideways MWSS inserter - probably the least obtrusive one I've seen. I can see it being very useful in some situations (and I think it may eventually prove useful in some of the more intractible OWSS flotillae), However, it's not necessary here. The traditional 2-glider+boat synthesis works just fine:
x = 53, y = 13, rule = B3/S23
4bo$5boo$4boo$$11b3o24b3o3b3o$5boo4bobbo22bobbo3bobbo$5bobo3bo28bo3bo$
boo3bo4bo5bo18bo3bo3bo5bo$obo8bo4b3o21bo3bo4b3o$bbo9bo3boboo17bobo5bo
3boboo$17b3o30b3o$17b3o30b3o$17boo31boo!
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Re: Synthesising Oscillators

Postby Extrementhusiast » June 7th, 2014, 11:07 pm

A really messy way to put the back MWSS on:
x = 35, y = 45, rule = B3/S23
10bobo$13bo$3bo9bo$bobo6bo2bo13bo4bo$2b2o7b3o13bobo2bobo$27b2o3b2o$18b
o$19bo$17b3o10bo$8bo21bobo$9bo20b2o$7b3o$17bo$16bobo$3bobo10b2o$4b2o
15b2o$4bo15bo2bo$20bobo$2bo18bo$obo$b2o15b2o10b2o$10b2o7bo10bobo$3bo5b
obo6bo11bo$3b2o6bo6b2o$2bobo3$8b3o$10bo$9bo2$12b2o9b3o$11bobo8bo2bo$
13bo11bo$21bo3bo$25bo$6b2o14bobo$7b2o$6bo2$15b3o$14bo2bo$17bo$17bo$14b
obo!
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Re: Synthesising Oscillators

Postby mniemiec » June 8th, 2014, 7:45 pm

Extrementhusiast wrote:A really messy way to put the back MWSS on:


Astounding! This now means that all spaceship flotillae of any number of instances of any of the three primary spaceships, in any phase and position, can now be synthesized.
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Re: Synthesising Oscillators

Postby Extrementhusiast » June 13th, 2014, 2:28 pm

Missing step for one of the 21-bit P2 pseudos:
x = 243, y = 36, rule = B3/S23
34bo$35bo$33b3o$37bo150bo$37bobo146b2o$27bobo7b2o148b2o$28b2o153bo$28b
o47bobo75bo29b2o$76b2o76bobo26b2o$77bo76b2o$47bo138bo$47bobo22bobo78bo
4bo16bobo7bo18bobo5bo$47b2o23b2o80b2obo18b2o7b3o17b2o5bobo$16bo56bo79b
2o2b3o16bo28bo6b2o$10bo3b2o117bobo73b2o6bo$11b2o2b2o30bobo84b2o3bo40b
2o27b2o4b2o$4b2o4b2o18b2o15b2o11b2o4b2o22b2o32b2o8bo2b2o16b2o23bobo24b
2o7b2o19b2o$4b2o24b2o16bo11b2o3bobo5bo16b2o3b2o27b2o3b2o7b2o15b2o3b2o
19b2o3b2o19b2o3b2o6b2o15b2o$36b2o27bo5b2o22bo33bo30bo25bo25bo7bobo$4b
4obo2bobo15b4o2bo23b4ob2o5b2o16b4obo11bo16b4obo25b4obo20b4obo20b4obo3b
o3bo16b4obo$2obo2bob2o2b2o12b2obo2bobobo19b2obo2bobo2bo18b2obo2bobo12b
obo10b2obo2bobo3b2o17b2obo2bobo17b2obo2bobo17b2obo2bobo3b2o16b2obo2bob
2o$2obo9bo12b2obo5bo20b2obo5b2o19b2obo17b2o11b2obo8bobo5bo10b2obo22b2o
bo22b2obo8bobo15b2obo$3b2o24b2o28b2o28b2o32b2o8bo4b2o14b2o6bobo15b2o
24b2o28b2o$3bo6b3o16bo29bo15b3o11bo33bo15b2o13bo3b2o2b2o2b3o11bo3b2o
20bo3b2o24bo3b2o$4bo7bo17bo29bo14bo14bo33bo30bo2b2o3bo2bo14bo2bobo20bo
2bobo24bo2bobo$3b2o6bo17b2o28b2o15bo12b2o32b2o6bo4b2o16b2o11bo12b2o3bo
20b2o3bo24b2o3bo$106b2o22b2o3b2o25b2o$69bobo34bobo21bobo4bo23b2o$65b2o
2b2o35bo56bo$66b2o2bo$65bo38b2o$103bobo$43b3o59bo$43bo82bo$44bo81b2o$
125bobo!

Presumably, a similar strategy will work for the 23-bit variant.

EDIT: It does (with additional trivial operations):
x = 190, y = 37, rule = B3/S23
146bo$147b2o$146b2o2$152bo$145bo4b2o$145b2o4b2o$95bo48bobo$95bobo53bo$
95b2o28bo24b2o$117bo5b2o25bobo$94bo22bobo4b2o35bo$95b2obobo16b2o42bobo
$16bo77b2o2b2o61b2o$10bo3b2o83bo15bo29b2o34b2o$11b2o2b2o57bobo39bo5bo
22bobo33bobo$4b2o4b2o18b2o32b2o9b2o3bo14b2o17b3o4bobo23bo35bo$4b2o24b
2o32b2o9bo2b2o15b2o24b2o24b2o34b2o$36b2o32b2o7b2o20b2o24b2o24b2o$4b4ob
o2bobo15b4o2bo27b4o2bo24b4o2bo11b3o5b4o2bo19b4o2bo29b4o$3bo2bob2o2b2o
15bo2bobobo11bo14bo2bobobo23bo2bobobo13bo4bo2bobobo18bo2bobobo28bo2bob
obo$3bo9bo15bo5bo12bobo12bo5bo3b2o19bo5bo13bo5bo5bo19bo5bo29bo5b2o$2ob
2o21b2ob2o17b2o10b2ob2o8bobo5bo9b2ob2o21b2ob2o21b2ob2o18bo12b2ob2o$2ob
o6b3o13b2obo30b2obo10bo4b2o10b2obo8bobo11b2obo22b2obo18b2o12b2obo$4bo
7bo17bo33bo15b2o13bo3b2o2b2o2b3o11bo3b2o20bo3b2o12bobo15bo3b2o$5bo5bo
19bo33bo30bo2b2o3bo2bo14bo2bobo20bo2bobo6b3o21bo2bobo$4b2o24b2o32b2o6b
o4b2o16b2o11bo12b2o3bo20b2o3bo7bo22b2o3bo$47b2o22b2o3b2o25b2o56bo$47bo
bo21bobo4bo23b2o$47bo56bo2$45b2o$44bobo$46bo$67bo$67b2o$66bobo!

The only part that changed, aside from the obvious, was the mechanism to turn the hook with tail back into a snake again.

EDIT 2: Albeit very late, this finally finishes my original method for one of the 16-bitters:
x = 56, y = 51, rule = B3/S23
7bo$5bobo$6b2o3$15bo7b2o$16bo5bobo6b2o$14b3o7bo6bobo$31bo2$11bo$9bobo$
10b2o$6bo$7b2o$6b2o3$6bo$4bobo$5b2o$27b2o$27bo2b2o$28b2obo$21b2o9b2o
12bobo$21bo11bo12b2o2b3o$22b3o2b2o3bo14bo2bo$24bo2bobo2bobo16bo$28b2o
3b2o$b2o$4o$2ob2o23b2o18b3o$2b2o24b2o20bo$49bo6$48b2o$48bobo$48bo4$6b
3o$8bo24b3o$7bo25bo$34bo18b3o$53bo$54bo!

However, this does end up solving all longer variants of that, with an extra kickback needed if it gets long enough. (But by then, progress could probably be made via snake-joining mechanisms.)
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Re: Synthesising Oscillators

Postby mniemiec » June 22nd, 2014, 12:15 am

Extrementhusiast wrote:Missing step for one of the 21-bit P2 pseudos:

Nice! This now comes in at 178 gliders.

Extrementhusiast wrote:Presumably, a similar strategy will work for the 23-bit variant.

Extrementhusiast wrote:It does (with additional trivial operations):

With some re-tooling of the original attempt, this now comes in at 137 gliders.

Extrementhusiast wrote:Albeit very late, this finally finishes my original method for one of the 16-bitters:

At 35 gliders, this is almost as cheap as my original (33) for this object. While neither compares to the direct 12-glider one that works for this one specific object, that trick won't work for any of the larger ones, so yours may well be the cheapest for some of the larger variations.

I was looking at some of the larger variants of Elkies's P5, that can usually be made by activating an appropriately-shaped still-life with populations 2 less than the corresponding oscillator. Up to 25 bits, there are only 12 remaining unsolved oscillators, that can be reduced to just 4 base oscillators, one each of sizes 22-25. Here are the missing corresponding still-lifes (plus a few for additional unsolved ones for 26, 27, 27, and 28 bits respectively)
x = 115, y = 9, rule = B3/S23
bboo13boo13boo13boo13boo13boo13boo13boo$bobbo11bobbo11bobbo11bobbo11bo
bbo11bobbo11bobbo11bobbo$bbobobbo9bobobbo9bobobbo9bobobbo9bobobbo9bobo
bbo9bobobbo9bobobbo$boob4o8boob4o8boob4o8boob4o8boob4o8boob4o8boob4o8b
oob4o$obbo11bobbo14bo11bobbo11bobbo14bo4boo5bobbo11bobbo$oo3bo8bobo3bo
12boboobo6boobboo9boobboo12bobobbo7bobobo10bobboboo$4boo9bo3boo13boob
oo11bo14bo13bobobo8bobobo10boo3bo$49bo15bobo12bobo10bobbo15bobo$49boo
15boo13bo12boo17boo!
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