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### Re: Synthesising Oscillators

Posted: December 6th, 2013, 5:26 pm
I would like to see a synthesis "for beginners". I need to practice to reach your level!

### Re: Synthesising Oscillators

Posted: December 6th, 2013, 10:08 pm
Although this is actually one of the syntheses with the most steps, don't be intimidated, as most of the steps are simple:

Code: Select all

``````x = 303, y = 232, rule = B3/S23
15bo95bo\$13b2o53bobo40bobo\$14b2o55bo39b2o165bo\$71bo207bo\$8bo46bobo10bo
2bo17b2o18b2o166b3o\$9b2o45b2o11b3o17b2o18b2o170bo\$8b2o46bo224bobo\$bo
67bo211b2o\$2bo65bo5b2o\$3o21bo15b2ob2o15b2ob2o3b3o2b2o12b2o18b2o18b2o
28b2o18b2o18b2o18b2o18b2o18b2o18b2o17b2o\$24bobo13bo3bo15bo3bo10bo9bo2b
o16bo2bo16bo2bo26bo2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo2b
o\$24b2o15b3o17b3o21b3o17b3o17b3o27b3o17b3o17b3o17b3o17b3o17b3o17b3o17b
3o\$13bo132bo\$14b2o27b3o17b3o17b3o17b3o17b3o19bo7b3o17b3o17b3o17b3o17b
3o17b3o17b3o17b3o\$13b2o27bo3bob2o12bo3bob2o12bo3bob2o12bo3bob2o12bo3bo
b2o15b3o4bo3bob2o12bo3bob2o12bo3bob2o12bo3bob2o12bo3bob2o12bo3bob2o12b
o3bob2o12bo3bob2o\$17b2o23bo3bob2o12bo3bob2o12bo3bob2o12bo3bob2o12bo3bo
b2o12b2o8bo3bob2o12bo3bob2o12bo3bob2o12bo3bob2o12bo3bob2o12bo3bob2o12b
o3bob2o12bo3bob2o\$16bobo20b2obo3bo12b2obo3bo12b2obo3bo12b2obo3bo12b2ob
o3bo14b2o6b2obo3bo10b2obobo3bo10b2obobo3bo10b2obobo3bo10b2obobo3bo10b
2obobo3bo10b2obobo3bo10b2obobo3bo\$18bo20b2obobobo12b2obobobo12b2obobob
o12b2obobobo12b2obobobo16bo5b2obobobo10bob2obobobo10bob2obobobo10bob2o
bobobo10bob2obobobo10bob2obobobo10bob2obobobo10bob2obobobo\$28b2o13b3o
17b3o17b3o17b3o17b3o27b3o17b3o17b3o17b3o17b3o17b3o17b3o17b3o\$28bobo
106b3o\$3b3o22bo16b3o17b3o17b3o17b3o17b3o11bo15b3o17b3o17b3o13b3o17b3o
17b3o17b3o17b3o\$5bo3b3o5b3o24bo3bo15bo3bo15bo3bo15bo3bo15bo3bo9bo15bo
3bo15bo3bo4bo10bo3bo11bo2bo16bo2bo16bo2bo16bo2bo16bo2bo\$4bo6bo7bo24b2o
b2o15b2ob2o15b2ob2o15b2ob2o15b2ob2o25b2ob2o15b2ob2o5b2o2b3o3b2ob2o11b
2o18b2o18b2o18b2o19b2o\$10bo7bo164b2o5bo\$148b2o39bo76b2o\$148bobo51bo62b
obo\$20b2o126bo38b3o11b2o5b2o18b2o37bo\$19b2o166bo2bo10bobo4b2o18b2o39b
3o\$21bo165bo37b2o42bo\$187bo36bobo43bo\$12b2o174bobo35bo\$13b2o\$12bo\$171b
obo\$171b2o\$172bo3\$146bo\$147bo\$103bo36bo4b3o\$104bo36b2o120bo\$16bo85b3o
35b2o121bobo\$17b2o52bo34bo156b2o\$16b2o45bobo4bo34bo42bo112bo\$59bo3b2o
5b3o32b3o17b2o21b2o5b2o102bobo\$60b2o2bo60b2o20bobo5b2o51bo51b2o\$59b2o
146bo\$25bo6bobo172b3o73b2o\$16b2o8b2o4b2o12b2o18b2o16b2o18b2o18b2o28b2o
27b2o28b2o10bo17b2o18b2o19bo\$15bo2bo6b2o6bo11bo2bo16bo2bo15bo2bo16bo2b
o16bo2bo26bo2bo25bo3bo16bobo6bo3bo7bobo15bo3bo15bo3bo15bo3bo\$15b3o27b
3o17b3o5b3o9b3o17b3o17b3o27b3o26b4o17b2o7b4o7b2o17b4o8b2o6b4o16b4o\$25b
o47bo131bo51b2o\$13b3o8b2o17b3o17b3o8bo8b3o17b3o17b3o27b3o26b4o26b4o26b
4o10bo5b4o16b4o\$12bo3bob2o4bobo15bo3bob2obo10bo3bob2obo10bo3bob2obo10b
o3bob2obo10bo3bob2obo7bo12bobobob2obo19bo4bob2obo19bo4bob2obo19bo4bob
2o11bo4bob2o11bo4bob2o\$12bo3bob2o22bo3bobob2o10bo3bobob2o10bo3bobob2o
10bo3bobob2o10bo3bobob2o8bo11bo3bobob2o6b3o11bo3bobob2o20bo3bobob2o18b
obo3bobo11bobo3bobo11bobo3bobo\$7b2obobo3bo20b2obobo3bo10b2obobo3bo10b
2obobo3bo10b2obobo3bo10b2obobo3bo11b3o6b2obobo3bo11bo8b2obobo3bo20b2ob
obo3bo23bobo3bobo11bobo3bobo11bobo3bobo\$7bob2obobobo20bob2obobobo10bob
2obobobo10bob2obobobo10bob2obobobo10bob2obobobo20bob2obo3bo12bo7bob2ob
o4bo19bob2obo4bo21b2obo4bo11b2obo4bo11b2obo4bo\$13b3o27b3o8bo8b3o17b3o
17b3o17b3o27b3o27b4o26b4o26b4o16b4o16b4o\$19bo35bo167bo\$11b3o5b2o20b3o
9b3o5b3o17b3o17b3o17b3o27b3o27b4o17b2o7b4o7b2o17b4o16b4o16b4o\$10bo2bo
4bobo19bo2bo16bo2bo17bo2bo16bo2bo16bo2bo26bo2bo26bo3bo15bobo7bo3bo6bob
o16bo3bo15bo3bo15bo3bo\$11b2o28b2o18b2o20b2o18b2o18b2o28b2o29b2o17bo10b
2o28b2o18b2o18b2o\$219b3o\$68b2o151bo\$64bo2b2o53b2o28b2o5bobo58bo\$56b3o
5b2o3bo31b3o18b2o28b2o5b2o\$58bo4bobo37bo56bo\$57bo44bo\$104b3o60b2o\$104b
o61b2o\$105bo55b3o4bo\$161bo\$162bo3\$136bo\$136b2o\$135bobo4\$91bo\$92bo\$90b
3o38bo89bo\$16bo34bo4bo42bo30bo88bobo\$16bobo30bobo2b2o41b2o27bo3b3o87b
2o\$10bo5b2o28b2o2b2o3b2o41b2o27b2o\$8bobo2b2o32b2o52b2o23b2o22b2o28b2o
18b2o28b2o18b2o18b2o18b2o\$5b2o2b2o3bo31bo26bo19bo7bobo46bobo27bobo17bo
bo27bobo17bobo17bobo17bobo\$6b2o5bo3bo14b2o18b2o18bobo17bobo6bo10bo2bo
16bo2bo16bo2bo26bo2bo16bo2bo19bo6bo2bo16bo2bo16bo2bo16bo2bo\$5bo8b4o14b
2o18b2o18b2o18b2o18b4o16b4o16b4o26b4o16b4o20b2o4b4o16b4o16b4o16b4o\$
169bo55b2o\$12b4o16b4o16b4o16b4o16b4o16b4o16b4o16b4o14bo11b4o16b4o10bob
o2b3o8b4o16b4o16b4o16b4o\$11bo4bob2o11bo4bob2o11bo4bob2o11bo4bob2o11bo
4bob2o11bo4bob2o11bo4bob2o11bo4bob2o8b3o10bo4bob2o11bo4bob2o7b2o4bo7bo
4bob2o9bobo4bob2o9bobo4bob2o9bobo4bob2o\$10bobo3bobo11bobo3bobo11bobo3b
obo11bobo3bobo11bobo3bobo11bobo3bobo11bobo3bobo11bobo3bobo21bobo3bobo
11bobo3bobo8bo4bo7bobo3bobo10b2obo3bobo10b2obo3bobo10b2obo3bobo\$10bobo
3bobo11bobo3bobo11bobo3bobo11bobo3bobo11bobo3bobo11bobo3bobo11bobo3bob
o11bobo3bobo12bo8bobo3bobo11bobo3bobo21bobo3bobo13bo3bobo13bo3bobo13bo
3bobo\$9b2obo4bo11b2obo4bo11b2obo4bo11b2obo4bo11b2obo4bo11b2obo4bo11b2o
bo4bo11b2obo4bo13b2o6b2obo4bo11b2obo4bo21b2obo4bo14bo4bo14bo4bo14bo4bo
\$13b4o16b4o16b4o16b4o16b4o16b4o16b4o16b4o13bobo10b4o9bo6b4o19bo6b4o16b
4o16b4o16b4o3b2o\$195bobo27bobo53b2o16bo2bo\$11b4o16b4o16b4o16b4o16b4o
16b4o16b4o16b4o26b4o11b2o3b4o21b2o3b4o18b2o18b2o6bobo9b2o5b2o\$11bo3bo
15bo3bo15bo3bo15bo3bo15bo3bo15bo3bo15bo3bo15bo3bo17b3o5bo3bo15bo3bo25b
o3bo17b2o18b2o6bo11b2o\$14b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o19bo8b
2o18b2o28b2o42b2o\$174bo102bobo\$279bo2\$214bo4bo\$214b2o3b2o\$213bobo2bobo
\$225b3o15bo\$227bo14b2o\$226bo15bobo6\$11bobo\$12b2o\$12bo5bo123bo\$18bobo
119bobo88bo\$18b2o121b2o34bo9bobo41bobo\$144bo33b2o7b2o42b2o\$144bobo16b
2o12b2o4b2o3bo19b2o18b2o\$28bo115b2o16bo2bo16bo2bo22b2o18b2o32bo\$26b2o
135b2o18b2o77bobo\$27b2o159bo73b2o\$188bobo\$10b2o28b2o18b2o18b2o18b2o9bo
bo6b2o18b2o18b2o18b2o6b2o5bo4b2o18b2o18b2o18b2o\$10bobo8b2o17bobo17bobo
17bobo17bobo8b2o7bobo17bobo17bobo17bobo10b2o5bobo17bobo17bobo17bobo\$
12bo2bo4b2o20bo19bo19bo19bo9bo9bo19bo19bo19bo11b2o6bo19bo19bo19bo19bo\$
12b4o6bo19b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b3o17b3o17b3o17b3o
17b3o\$45b2o18b2o18b2o18b2o6b2o10b2o3b2o13b2o3b2o13b2o3b2o13b2o3b2o13bo
19bo19bo19bo19bo\$12b4o14bo11b3obo15b3obo15b3obo15b3obo6bobo6b3obo4bo
10b3obo4bo10b3obo4bo10b3obo4bo10b3obo15b3obo15b3obo15b3obo15b3obo\$9bob
o4bob2o10bobo6bobo2bobob2o9bobo2bobob2o9bobo2bobob2o9bobo2bobob2o3bo5b
obo2bobob3o8bobo2bobob3o8bobo2bobob3o8bobo2bobob3o8bobo2bobo12bobo2bob
o12bobo2bobo12bobo2bobo12bobo2bobo\$9b2obo3bobo11b2o7b2obobobobo10b2obo
bobobo4bo5b2obobobobo10b2obobobobo10b2obobobobo10b2obobobobo10b2obobob
obo10b2obobobobo10b2obobobob2o9b2obobobob2o9b2obobobob2o9b2obobobob2o
9b2obobobob2o\$12bo3bobo23bo3bobo13bo3bobo4bobo6bo3bobo13bo3bobo13bo3bo
bo13bo3bobo13bo3bobo13bo3bobo3bo9bo3bo2bo12bo3bo2bo12bo3bo2bo12bo3bo2b
o12bo3bo2bo\$12bo4bo24bo4bo14bo4bo5b2o7bo4bo14bo4bo14bo4bo14bo4bo14bo4b
o14bo4bo4bobo7bo4bo14bo4bo14bo4bo14bo4bo14bo4bo\$13b4o3b2o21b4o4bo11b4o
4bo11b4o16b4o16b4o16b4o16b4o16b4o5b2o9b4o16b4o16b4o16b4o16b4o\$19bo2bo
27bobo17bobo\$13b2o5b2o21b2o4bo2bo10b2o4bo2bo10b2o18b2o18b2o18b2o18b2o
18b2o18b2o18b2o18b2o18b2o18b2o\$13b2o28b2o5b2o11b2o5b2o11b2o18b2o18b2o
18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o3\$191b3o\$191bo\$192bo2\$12b2o\$
11bobo\$13bo7\$81bobo\$82b2o\$82bo5bo83bo\$88bobo79bobo98bo\$88b2o81b2o34bo
9bobo51bobo\$174bo33b2o7b2o52b2o\$174bobo16b2o12b2o4b2o3bo29b2o18b2o\$98b
o75b2o16bo2bo16bo2bo32b2o18b2o\$96b2o95b2o18b2o\$97b2o119bo\$218bobo\$10b
2o38b2o28b2o19bo8b2o18b2o9bobo6b2o18b2o18b2o18b2o6b2o5bo14b2o18b2o18b
2o\$10bobo37bobo27bobo8b2o6b2o9bobo17bobo8b2o7bobo17bobo17bobo17bobo10b
2o15bobo17bobo17bobo\$12bo2bo36bo2bo26bo2bo4b2o8b2o10bo19bo9bo9bo19bo
19bo19bo11b2o16bo19bo19bo\$12b4o36b4o26b4o6bo12bo6b2o18b2o18b2o18b2o18b
2o18b2o28b3o17b3o17b3o\$103b2o10b2o18b2o6b2o10b2o3b2o13b2o3b2o13b2o3b2o
13b2o3b2o23bo19bo19bo\$12b4o36b4o26b4o18b2o6b3obo15b3obo6bobo6b3obo4bo
10b3obo4bo10b3obo4bo10b3obo4bo20b3obo15b3obo15b3obo\$11bo4bob2o31bo4bob
2o21bo4bob2o21bo2bobob2o11bo2bobob2o3bo7bo2bobob3o10bo2bobob3o10bo2bob
ob3o10bo2bobob3o20bo2bobo14bo2bobo14bo2bobo\$10bobo3bobo31bobo3bobo21bo
bo3bobo21bobobobobo11bobobobobo11bobobobobo11bobobobobo11bobobobobo11b
obobobobo21bobobobob2o10bobobobob2o10bobobobob2o\$10bobo3bobo31bobo3bob
o21bobo3bobo21bobo3bobo11bobo3bobo11bobo3bobo11bobo3bobo11bobo3bobo11b
obo3bobo3bo17bobo3bo2bo10bobo3bo2bo10bobo3bo2bo\$9b2obo4bo31b2obo4bo21b
2obo4bo21b2obo4bo11b2obo4bo11b2obo4bo11b2obo4bo11b2obo4bo11b2obo4bo4bo
bo14b2obo4bo11b2obo4bo11b2obo4bo\$13b4o36b4o3b2o21b4o3b2o21b4o16b4o16b
4o16b4o16b4o16b4o5b2o19b4o16b4o16b4o\$59bo2bo26bo2bo\$11b4o36b4o5bobo18b
4o5bobo18b4o16b4o16b4o16b4o16b4o16b4o26b4o16b4o16b4o\$11bo3bo35bo3bo5bo
19bo3bo5bo19bo3bo15bo3bo15bo3bo15bo3bo15bo3bo15bo3bo25bo3bo15bo3bo15bo
3bo\$14b2o38b2o28b2o28b2o18b2o18b2o18b2o18b2o18b2o28b2o18b2o18b2o2\$42bo
58bo119b3o\$39bo2bobo55b2o119bo\$37bobo2b2o56bobo119bo\$38b2o2\$84b2o\$85b
2o\$18b2o64bo\$17bobo\$19bo5\$103bo\$101b2o\$96bo5b2o\$94bobo9bo6bo\$95b2o9bob
o4bobo\$106b2o5b2o\$12bo198bo\$12bobo81bo112bobo\$12b2o83bo112b2o\$95b3o\$
10b2o\$10bobo46bo33b2o\$12bo19bo19bo6bobo10bo5b2o12bobo7bo5b2o24b2o28b2o
18b2o29bo8b2o18b2o\$12b3o17b3o17b3o4b2o11b3o3b2o14bo7b3o3b2o8bo15bo29bo
19bo31b2o6bo19bo\$15bo19bo19bo6b2o11bo29bo11b2o16bo13bo15bo19bo29b2o8bo
19bo\$12b3obo15b3obo15b3obo5bobo7b3obo25b3obo10bobo12b3obo13bo11b3obo
15b3obo19bobo2b3o8b3obo15b3obo\$11bo2bobo14bo2bobo14bo2bobo5bo8bo2bobo
24bo2bobo24bo2bobo11b3o10bo2bobo14bo2bobo20b2o4bo7bo2bobo12bobo2bobo\$
10bobobobob2o10bobobobob2o10bobobobob2o10bobobobob2o20bobobobob2o20bob
obobob2o20bobobobob2o10bobobobob2o17bo4bo7bobobobob2o9b2obobobob2o\$10b
obo3bo2bo10bobo3bo2bo10bobo3bo2bo10bobo3bo2bo20bobo3bo2bo20bobo3bo2bo
11bo8bobo3bo2bo10bobo3bo2bo30bobo3bo2bo12bo3bo2bo\$9b2obo4bo11b2obo4bo
11b2obo4bo11b2obo4bo21b2obo4bo21b2obo4bo13b2o6b2obo4bo11b2obo4bo31b2ob
o4bo14bo4bo\$13b4o16b4o16b4o16b4o26b4o26b4o13bobo10b4o9bo6b4o29bo6b4o
16b4o\$175bobo37bobo\$11b4o16b4o16b4o16b4o26b4o26b4o26b4o11b2o3b4o31b2o
3b4o18b2o\$11bo3bo15bo3bo15bo3bo15bo3bo25bo3bo25bo3bo17b3o5bo3bo15bo3bo
35bo3bo17b2o\$14b2o18b2o18b2o18b2o28b2o28b2o19bo8b2o18b2o38b2o\$154bo3\$
204bo4bo\$204b2o3b2o\$203bobo2bobo\$215b3o15bo\$217bo14b2o\$216bo15bobo!
``````
Don't worry about the parts where the rotor changes yet.

EDIT: Griddle with tub and hook in 74 gliders and one LWSS:

Code: Select all

``````x = 414, y = 72, rule = B3/S23
283bo\$281bobo\$282b2o16\$297bo\$271bo24bo6bo\$272bo23b3o4bobo\$270b3o30b2o
2\$127bo\$125bobo16bo\$67bo58b2o15bo\$65b2o76b3o126bo63bo\$66b2o205bo61bo
49bo\$58bo108bo103b3o57bo3b3o46bo\$58bobo104bobo7bo129bo26b2o7bo42b3o5bo
\$16bo41b2o88bo17b2o7bobo125bobo25b2o6b2o34bo14b2o\$14bobo89bobo38bo27b
2o127b2o34b2o34b2o13b2o\$15b2o89b2o39b3o101bobo53bo67b2o\$107bo2b2o116bo
22b2o54b3o39bobo\$18bobo41b3o38b3o4bobo17bo39b2o13bobo38bobo23bo33b2o
22bo38b2o\$18b2o42bo42bo4bo18bobo37bo2bo5bo6b2o21b2o17b2o3b2o52b2o2b2o
17b2o39bo24bo\$2bo16bo25bo17bo40bo25b2o38b3o5bobo5bo21b2o14b2o6b2o19b3o
34b2o81b2o13b2o\$obo40bobo132b2o3bo39bobo27bo83bo36b2o6b2o4bobo20bo\$b2o
41b2o10bo21b2o26b2o22b2o38b3o9b2o24b4o13bo6b4o18bo35b4o41b3o31bobo8b3o
5bo20bobo\$16b2o36b3o20bo2bo24bo2bo20bo2bo36bo3bo8bobo22bo4bo18bo4bo52b
o4bo39bo5bo29b2o7bo4bo23bo4bo\$2b3o10bo2bo3bo23b3o4bo22bob3o23bob3o19bo
b3o35bob4o13bo2bo15bob5o17bob5o51bob5o38bob6o29bo7bob5o22bob5o\$2bo13bo
bo3bobo3bo19bo5bob3o18bo27bo23bo39bo16bo20bo23bo57bo44bo25b3o16bo28bo\$
3bo13bo4b2o4bobo16bo7b2o2bo18bob3o23bob3o19bob3o35bob4o10bo3bo17bob3o
19bob3o53bob3o40bob4o21bo17bobo26bobo\$28b2o28b2o19b2o2bo23b2o2bo19b2o
2bo35b2o2bo10b4o19b2o2bo19b2o2bo53b2o2bo40b2o2bo20bo19b2o27b2o\$25b2o
55b2o26bobo21bobo44b2o29b2o22bobo55bobo49b3o\$25bobo59bo23bo23bo8bo36bo
bo33bo19bo57bo50bo23b3o\$25bo26b3o30b2o56b2o36bo33b2o130bo24bo\$52bo23b
2o8b2o55bobo4b3o24b2o27b2o8b2o153bo\$53bo23b2o2bo68bo26bobo27b2o2bo127b
o\$76bo3b2o69bo25bo28bo3b2o127b2o\$80bobo87b2o38bobo60b2o30bo32bobo\$87b
3o81b2o44b3o52bobo28b2o\$87bo82bo46bo56bo29b2o\$88bo63bo65bo125b3o\$84b3o
53bobo8b2o61b3o127bo\$86bo53b2o9bobo62bo128bo\$85bo55bo73bo121b3o\$315b2o
22bo\$140b2o172b2o22bo\$140bobo173bo\$140bo2\$303b3o\$303bo\$304bo\$131bo\$
131b2o\$130bobo2\$287b2o\$288b2o\$287bo!
``````

### Re: Synthesising Oscillators

Posted: December 7th, 2013, 10:09 am

Code: Select all

``````x = 33, y = 11, rule = B3/S23
9bo13b2o\$2b2o5bobo11bo\$2bo5b2obo12b3obo\$3b3o2b6o12bo\$5bo2bo2bo\$29bo\$2b
o2bo2bo18bob3o\$6o2b3o21bo\$2bob2o5bo19b2o\$2bobo5b2o\$4bo!``````
Here is an mindblowing way to synthetize a 18-cell object using 2 eaters. I tried to make a spark, but the generator I found could win the prize of the ugliest one ever made.

### Re: Synthesising Oscillators

Posted: December 7th, 2013, 8:31 pm
Assorted three-glider syntheses:

Code: Select all

``````x = 263, y = 160, rule = B3/S23
48bo77bo\$41bo5bo71bo5bo\$42bo4b3o70bo4b3o\$40b3o75b3o3\$134b2o\$52b2o79b2o
\$51b2o82bo\$53bo23\$18bo\$11bo5bo\$12bo4b3o\$10b3o6\$17b2o\$16b2o\$18bo118bo\$
130bo5bo\$131bo4b3o\$129b3o2\$140b2o\$139b2o\$80bo60bo\$73bo5bo\$74bo4b3o\$72b
3o2\$89b2o\$88b2o\$90bo2\$184bo\$177bo5bo\$178bo4b3o\$176b3o3\$187bo\$186b2o\$
186bobo5\$91bo\$84bo5bo\$85bo4b3o\$83b3o16b2o\$8bo92b2o\$bo5bo95bo\$2bo4b3o\$
3o3\$19b2o\$18b2o\$20bo2\$214bo\$207bo5bo\$208bo4b3o\$206b3o3\$127bo\$120bo5bo
80b3o\$121bo4b3o78bo\$119b3o64bo21bo\$179bo5bo\$135b3o42bo4b3o\$135bo42b3o\$
136bo\$260bo\$253bo5bo\$183b3o68bo4b3o\$183bo68b3o\$184bo5\$261bo\$260b2o\$
260bobo2\$36bo\$29bo5bo\$30bo4b3o\$28b3o\$151bo\$144bo5bo\$96bo48bo4b3o\$89bo
5bo47b3o\$39b3o48bo4b3o\$39bo48b3o\$40bo\$156b3o\$98b3o55bo44bo\$98bo58bo36b
o5bo\$99bo95bo4b3o\$193b3o5\$196b3o\$196bo\$197bo\$230bo\$223bo5bo\$224bo4b3o\$
222b3o4\$166bo\$159bo5bo63b3o\$160bo4b3o61bo\$158b3o69bo2\$53bo\$46bo5bo\$47b
o4b3o\$45b3o111b3o\$159bo\$160bo4\$56b3o\$56bo\$57bo!
``````
EDIT: Remember the very last 15-bitter? It's back for more:

Code: Select all

``````x = 44, y = 42, rule = B3/S23
41bo\$10bo30bobo\$8bobo30b2o\$9b2o\$21bo\$21bobo\$21b2o2\$10bo\$11b2o\$10b2o3\$
4bobo\$5b2o22bo\$5bo22bo\$28b3o\$25bo\$26b2o\$18b2o5b2o\$14b2obo2bo8b3o\$15bob
ob2o8bo\$15bo2bo11bo\$2o14bobo\$b2o14bo\$o3\$4b2o\$5b2o\$4bo\$16b2o14b2o\$16bob
o12b2o\$16bo16bo\$3b2o\$4b2o\$3bo3\$19b2o\$19bobo\$19bo!
``````

### Re: Synthesising Oscillators

Posted: December 8th, 2013, 3:51 am
Is there a "lexicon" of 3g collisions?

### Re: Synthesising Oscillators

Posted: December 8th, 2013, 1:45 pm
No. It is unknown how many three-glider collisions there are. But a way to search is to simply add one more glider to a messy two-glider reaction.

### Re: Synthesising Oscillators

Posted: December 9th, 2013, 1:19 pm
I guess the 2G mess may have itself thousands, possibly millions of possibilities...

### Re: Synthesising Oscillators

Posted: December 10th, 2013, 8:42 pm
Predecessor to one sixteen-bitter:

Code: Select all

``````x = 9, y = 8, rule = B3/S23
5bo\$2bo\$3b3o2bo\$2bobobo\$2bobobo\$o2b3o\$6bo\$3bo!
``````
EDIT: A different sixteen-bitter in 16 gliders:

Code: Select all

``````x = 149, y = 26, rule = B3/S23
63bo\$61b2o\$62b2o4\$56bobo21bo\$57b2o19b2o\$9bobo45bo21b2o46bobo\$9b2o83b2o
b2o17b2ob2o6b2o13b2ob2o\$10bo23bo60bobobo17bobobo6bo14bobobo\$27b2o6b2ob
obo18b2o5bo28bo2bobob2o13bo2bobob2o17bo2bobo\$4bo4b3o15bo2bo3b2o2b2o19b
o2bo3bo29bobob2obo14bobob2obo18bobobo\$5b2o2bo18b3o8bo20b3o3bo30bo21bo
25bobo\$4b2o4bo135bo\$28b3o29b3o\$bo25bo2bo28bo2bo57b2o2b2o\$b2o25b2o30b2o
35b3o20b2ob2o\$obo53b3o40bo25bo\$58bo14b2o23bo\$57bo15bobo24b3o\$73bo26bo\$
101bo\$67b2o\$66bobo\$68bo!
``````

### Re: Synthesising Oscillators

Posted: December 10th, 2013, 11:02 pm
Sokwe wrote:The griddle with two blocks can be done by a somewhat messy method. Here are the nontrivial steps (some of it can likely be reduced):
The last step can, indeed, be simplified, reducing the final solution by 4 gliders, for a total of 34 (both new and old methods instantiated):

Code: Select all

``````x = 152, y = 124, rule = B3/S23
34bo23bo71bo\$35boo19boo70boo\$34boo21boo70boo\$\$6bo118bo\$4bobo116bobo\$5b
oo117boobbo\$128bobo\$7bo120boo\$7bobo\$7boo27bo19bo\$24booboo5bobo7booboo
7bobo90boo\$24bo3bo6boo7bo3bo7boo5bobbobbo13bobbobbo13bobbobbo13bobbobb
o13bobbo3bo\$25b3o17b3o15b7o13b7o13b7o13b7o13b7o\$37b3o13b3o\$27b3o9bo7b
3o3bo9boobb3o13boobb3o13boobb3o13boobb3o13boobb3o\$27bobbo7bo8bobbo3bo
8boobbobbo12boobbobbo12boobbobbo12boobbobbo12boobbobbo\$29boo18boo18boo
18boo18boo18boo18boo\$6boo\$5bobo56boo18boo\$7bo56boo18boo\$boo34boo\$obo5b
oo26bobo43boo\$bbo5bobo27bo42bobo\$8bo74bo\$50b3o\$50bo\$51bo8\$127bo\$80bo
45bo\$81boo43b3o\$80boo21boo18boo18boo\$85bo16bobbo16bobbo16bobbo\$85bobo
14bobo17bobo17bobo\$85boo16bo19bo19bo\$50bo\$51bo31bo\$49b3o32bo\$82b3o\$52b
obo\$52boo\$53bo\$\$70bo19bo15bo3bo15bo3bo15bo3bo\$49boo4b3o11bobo17bobo12b
3obbobo12b3obbobo12b3obbobo\$43bobbo3bo4bo7bobbo3bo12bobbo3bo12bo6bo12b
o6bo12bo6bo\$43b7o6bo6b7o13b7o13b7o13b7o13b7o\$\$43boobb3o13boobb3o13boo
bb3o13boobb3o13boobb3o13boobb3o\$43boobbobbo12boobbobbo12boobbobbo12boo
bbobbo12boobbobbo12boobbobbo\$48boo18boo18boo18boo18boo18boo14\$88bobo\$
88boo\$80bo8bo\$81bo52bo\$79b3o12bobo37bobo\$94boo38boo\$95bo16bo19bo\$78bo
32bobo17bobo\$77bo34bo19bo\$77b3o6bo3bo14bo19bo19bo\$75bo8b3obbobo13bobo
17bobo17bobo\$73bobo7bo6bo12bo4bo14bo4bo14bo4bo\$74boo7b7o5b3o5b6o14b6o
14b6o\$95bo\$83boobb3o6bo6boobboo14boobboo14boobboo\$83boobbobbo12boobboo
14boobboo14boobboo\$75bo12boo\$75boo\$74bobo\$\$94b3o\$94bo\$95bo6\$72boo\$71b
oo\$67bobo3bo44bobo\$68boo48boo\$68bo41bo8bo\$111bo17bo\$20bo88b3o16bo\$20bo
bo105b3o\$20boobboo\$23boo67boo14bo13boo\$25bo15bo19bo29bobo13bo13bobo\$
16bo3bo15bo3bobo13bo3bobo23bo3bobo14b3o6bo3bobo22bo\$14b3obbobo12b3obbo
bo12b3obbobo22b3obbobo13bo8b3obbobo23bobo\$13bo6bo12bo6bo12bo6bo22bo6bo
12bobo7bo6bo22bo4bo\$13b7o13b7o13b7o11boo10b7o14boo7b7o23b6o\$70boo54boo
\$13boobb3o13boobb3o13boobb3o12bo10boobb3o23boobb3o5boo16boobboo\$13boo
bbobbo12boobbobbo12boobbobbo22boobbobbo22boobbobbo6bo15boobboo\$18boo
18boo18boo28boo15bo12boo\$105boo\$104bobo\$\$124b3o\$124bo\$125bo!
``````
A hard 16-bit still-life from 55 gliders. (Note the cute pseudo-heisenburp in the last cleanup glider) (UPDATE: totally obviated by your 16-glider solution):

Code: Select all

``````x = 141, y = 147. rule = B3/S23
44bobo\$45boo\$45bo4\$62bobo\$62boo\$63bo48bobo\$108bo3boo\$109boobbo\$108boo\$
76bo\$75bo19bo19bo18boo\$65bo9b3o16bobo17bobo17bobo\$64bo30boboboo14bobob
oo14boboboo\$64b3o26boboboobo12boboboobo12boboboobo\$93boo18boo18boo\$67b
oo\$67bobo\$42boo23bo\$41bobo\$43bo\$\$61boo\$61bobo\$61bo\$\$43boo\$42bobo\$44bo\$
62bo\$61boo\$61bobo9\$21bo9bo\$22boo5boo\$21boo7boo\$\$32bo\$31boo\$31bobo75bo\$
107boo\$37bo20bobo47boo\$37bobo19boo44bo\$37boo20bo46bo\$24boo18boo3boo13b
oo3boo13boo3boo13b3o7boo3boo13boo3boo\$24bobo17bobobbo7boo5bobobbo14bob
obbo24bobobbo14bobobbo\$25boboboo14bobobo8boo5bobobo15bobobo25bobobo5b
ooboo5bobobo\$23boboboobo12boboboo8bo5boboboo14boboboo24boboboo7bobo4bo
boboo\$23boo18boo18boo17bobo27bobo11bobo3bobo\$53bo29bo29bo13bo5bo\$51bob
o7bo43bo\$52boo6boo43boo\$55boo3bobo41bobo\$31boo21bobo\$32boo22bo50b3o\$
31bo75bo\$108bo10\$105bo\$104bo\$104b3o\$102bo\$52bobo41bo3bobo\$52boo43bo3b
oo\$53bo41b3o\$51bo\$14boo3boo13boo3boo11bo11boo3boo13boo3boo23boo3boo13b
oo3boo\$14bobobbo14bobobbo10b3o11bobobbo14bobobbo24bobobbo14bobobbo\$5b
ooboo5bobobo5booboo5bobobo15booboo5bobobo5booboo5bobobo15booboo5bobobo
8boo5bobobo\$6bobo4boboboo6boobo4boboboo16boobo4boboboo5bobobo4boboboo
15bobobo4boboboo9bo4boboboo\$6bobo3bobo13bo3bobo16bo6bo3bobo10bobbo3bob
o20bobbo3bobo10boobo3bobo\$7bo5bo14boo3bo17boo5boo3bo14boo3bo24boo3bo
11booboo3bo\$50bobo4\$oo5boo\$boo5boo6boo81boo\$o6bo7boo81bobo\$11b3o3bo82b
o\$13bo\$12bo97boo\$109boo\$111bo6\$61bo61boo\$60bo41bobo17bobbo\$60b3o40boo
17bobbo\$58bo44bo19boo\$59bo\$57b3o18boo22boo4boo18boo\$78boo21bobo4boo18b
oo\$64boo3boo13boo3boo12bo10boo3boo13boo3boo\$64bobobbo14bobobbo24bobobb
o14bobobbo\$58boo5bobobo8boo5bobobo18boo5bobobo8boo5bobobo\$58bo4boboboo
9bo4boboboo19bo4boboboo9bo4boboboo\$55boobo3bobo10boobo3bobo20boobo3bob
o10boobo3bobo\$55booboo3bo11booboo3bo21booboo3bo11booboo3bo8\$13boo18boo
28boo9bo\$12bobbo16bobbo26bobbo6boo\$12bobbo16bobbo26bobbo7boo\$13boo18b
oo28boo\$\$18boo18boo28boo\$18boo18boo22b3o3boo57bo\$24boo3boo13boo3boo13b
o9boo3boo10booboo3boo10booboo3boo4boo4booboo\$24bobobbo14bobobbo13bo10b
obobbo12bobobobbo12bobobobbo6boo4bobobo\$18boo5bobobo8boo5bobobo18boo5b
obobo12bobbobobo12bobbobobo12bobbobo\$18bo4boboboo9bo4boboboo19bo4bobob
oo14boboboo14boboboo14bobobo\$15boobo3bobo10boobo3bobo20boobo3bobo19bo
19bo19bobo\$15booboo3bo11booboo3bo21booboo3bo61bo\$62boo\$45boo14bobo11b
oo4bo40boo\$25b3o17boo10boo4bo11boobboo26bo3boo9bobo\$25bo30bobo10boo9b
oo25booboo10bo\$26bo31bo11boo34bobo3bo6bo\$22b3o44bo6bo41boo\$24bo50boo
41bobo\$23bo51bobo!
``````
This could be done much more cheaply (15+) if the eater could be dropped into place after the fact; unfortunately, all the mechanisms I am aware of that can do this either add a boat or block, and later convert it into a snake/carrier/eater (unusable because a boat or block in that position would get attacked before it could be transformed), or add an eater/snake/carrier with one forward bit first (unusable because they would attack the still-life before being added), or the one glider approaching from the northwest snags the top of the still-life on the way in. This glider needs to hit the dying spark in just the right way to turn it into an eater. The failing middle step is shown working below on a less obtrusive object (a beehive). Perhaps someone can figure out how to make this troublesome glider less obtrusive (perhaps by replacing it by an equivalent spark)?:

Code: Select all

``````x = 135, y = 66, rule = B3/S23
38bobo\$38boo\$39bo3\$o\$boo\$oo6\$81bo\$82bo\$80b3o3bo\$76bo7boo\$77boo6boo\$76b
oo\$\$73bo\$71bobo\$72boo\$\$124bo\$48booboo15booboo7bobo13boo10booboo3boo4b
oo4booboo\$18boobboo25bobo17bobo8boo14bo12bobobobbo6boo4bobobo\$17bobob
oo26bobbo16bobbo8bo12bobo12bobbobobo12bobbobo\$19bo3bo26bobo17bobo21boo
14boboboo14bobobo\$51bo19bo39bo19bobo\$132bo\$\$119boo\$76bo27bo3boo9bobo\$
76boo26booboo10bo\$75bobo25bobo3bo6bo\$115boo\$115bobo6\$81bo\$82bo\$80b3o3b
o\$76bo7boo\$77boo6boo\$76boo\$\$73bo\$71bobo\$72boo3\$80bobo13boo\$71bo8boo9bo
4bo\$70bobo8bo8bobobobo\$70bobo17boboboo\$71bo19bo4\$76bo\$76boo\$75bobo!
``````
This is another 16-bit still-life that I haven't been able to quite put together. I have both top and bottom halves; unfortunately, one glider from each piece passes through the other piece. I'm sure the two pieces can both be made more efficiently, and likely in a non-conflicting way. (Shown are generations 0, 25, 26, 27 of both halves, plus combined result. The key part to the bottom also has a simpler predecessor, shown below it):

Code: Select all

``````x = 140, y = 96, rule = B3/S23
27bo\$27bobo\$27boo5\$19bo89bo\$18bo9bo20boo21bo5b3o27boo\$18b3o5boo13b3o4b
oo22bo5bo23boo3bobbo\$27boo20bo23bo4boo\$43bo6booboo21b6o3bo16b3oboobboo
\$17b3o21bo3b4o3b4o16boobo6bo3bo15b3ob3o6boo\$17bo25b3ob4o3b3o15boo6bo5b
o18bo5bo3b3o\$18bo24bobobboo6bo16bob3obbo3bobbo14b3obo10bo\$55boo28boo
19bo7b3o\$54bo30bo29boo\$48bo\$9booboo25booboo4bo20booboo3bo21booboo\$10bo
bo27bobo3bo23bobo3bo23bobobobo\$10bobbobboo22bobbobboo22bobbobo24bobbob
oo\$11bobobboo23bobobboo23bobobobbo22bobo\$12bo29bo3boo24bo29bo\$47boo29b
o29boo\$46bobo29boo27b3o\$48bo28bo30bo4\$11bo\$11boo\$10bobo7\$129booboo\$
130bobobobo\$130bobboboo\$131bobo\$132boo\$137boo\$136bobbo\$130bo5bobbo\$
129bobo5boo\$129bobbo\$130boo8\$bo\$bbo\$3o6booboo8bo16booboo25booboo25boob
oo\$10bobo8bo18bobo27bobo27bobo\$10bobbo7b3o16bobbo26bobbo26bobbo\$11bobo
27bobo27bobo27bobo\$12bo29bo29bo29boo\$36bobo29bobobo\$37b6o23bo4b4o22bo
7bo\$37boboobb3obo19bo4b4o24bo4bo\$40bo4boo23boobo3bo22bo5bo\$40bo3bobo
23boobbobo23b3o\$41bobo8\$11bo\$10b3o\$10boboo\$11b3o\$11boo8\$39booboo\$40bob
o\$40bobbo\$41bobo\$42bo\$39bo\$40b3o\$39boobboo!
``````
For the still-life that can make griddles on both sides, this predecessor can make it. Unfortunately, getting the blinker where it needs to be will be problematic. (It might be possible to do something equivalent by tying a boat or something similar onto the corner of the pre-block, and then flipping it up, but I haven't been able to find anything that works yet).
Actually, for the desired results, the two arms could just as easily end up pointing in opposite directions, if making that would be any easier, although it's likely to be similarly difficult. I have a partial attempt; it needs three sparks. Unfortunately, two of them need to be too close together: the problematic barge-lengthener (same problem as with the first method), and a blinker+plus+bit. I'm sure the latter can be made much less obtrusively from below, which might make this actually possible.

Code: Select all

``````x = 97, y = 36, rule = B3/S23
71boo18boo\$72b3o17b3o\$70bo4bo14bo4bo\$69bob4obo12bob4obo\$70bo5bo13bo4bo
\$72bo19b3o\$71boobo16boo\$74bo\$74bo12\$11boo28boo12b3o13boo18boo\$12b3o27b
3o9bo3bo13b3o17b3o\$10bo4bo11bo12bo4bo12bo11bo4bo14bo4bo\$3bo5bob4o10boo
12bob4o11boo11bob4obo12bob4obo\$4boo4bo15boo12bo15bo13bo5bo13bo4bo\$3boo
7bo5bo23bo29bo18b3o\$11boo5bobo20b3o12bo14b3o19boo\$18boobb3o12boo4bobo
21boo4bobo\$22bo13bo6boo21bo6boo\$23bo12bo4b3o22bo4b3o\$37bo3boo24bo3boo\$
38bo11bo17bo11bo\$oo47bo29bo\$boo3boo\$o6boo\$6bo!
``````
Towerator wrote:Here is an mindblowing way to synthetize a 18-cell object using 2 eaters. I tried to make a spark, but the generator I found could win the prize of the ugliest one ever made.
Congratulations. You've figured out the most important step in trying to synthesize something - i.e. identifying a possible predecessor. The next part is trying to determine whether it's viable or not (i.e. can you find ITS predecessor, and so on, back to the point where you can cut and paste known mechanisms like gliders or standard sparks.)

Here, look at your first predecessor, and try to think of how you could get that in place. Just think back one generation. Look at the top right bit in the bottom left spark. Think about how that bit could possibly get there without having touched either either before. This will likely be a challenging problem. (Sometimes, you CAN get away with having such sparks come from attached pieces, like inducting blocks, boat bits, etc. that can be used as springboards for bringing in sparks.

Don't worry too much about "ugly". Ugly is worse than "elegant", but much better than "impossible". Once you have a viable solution for something, THEN comes the process of optimization. First do something correctly, then only later try to do it better.

Another thing that comes with time is determining the relative cost of adding pieces. In this particular case, turning an eater head into a claw takes 2 gliders, so it may be easier to start with the simpler "two back to back siamese eaters" still-life, and then add the two claws later. But as I said earlier, this is an optimization, and only something to worry about once you actually have found a viable solution first. It's likely that many syntheses you come up with first won't be optimal (i.e. they won't push the state of the art forward) but they can be good practice in learing how to do things, so once you're proficient, you may well advance the art.

I used to have a web site with thousands of syntheses on it. Unfortunately, it's down at the moment, but I'm working on a massive overhaul which should be hopefully be up sometime early next year. Right now, you can download many synthese directly from the front page of the Lifewiki on this site. Looking at those can be quite informative. Some syntheses are "atomic" (i.e. a few gliders smash together to do something), but most are composed of many small steps, and looking at all the steps can be quite educational.
Extrementhusiast wrote:Griddle with tub and hook in 74 gliders and one LWSS:
Great! I've always had trouble synthesizing that diagonal hook. I wonder if something like this could be used to make the related 16-bit still-life?
Extrementhusiast wrote:Remember the very last 15-bitter? It's back for more:
48 and counting!
Extrementhusiast wrote:Predecessor to one sixteen-bitter:
Good! The interior is easily buildable. It may be possible to build it (say) from the closed tube between two houses or bookends, which can be selectively destroyed. I'm not sure whether this will work, but it's much better than before (i.e. I had no clue how one could build this)!
Extrementhusiast wrote:A different sixteen-bitter in 16 gliders:
This totally obviates my 55-glider solution from a few days ago (see above)

### Re: Synthesising Oscillators

Posted: December 11th, 2013, 12:34 pm

Code: Select all

``````x = 10, y = 11, rule = B3/S23
7bo\$2o5bo\$o5b2o\$b3o2b3o\$3bo2bo2\$3bo2bo\$b3o2b3o\$2b2o5bo\$2bo5b2o\$2bo!``````
Better, but it's not over yet... Also, this:

Code: Select all

``````x = 10, y = 9, rule = B3/S23
2o\$o\$b3obo\$3bobo2\$4bobo\$4bob3o\$9bo\$8b2o!
``````
is a predecessor of another unsynthetized object... They seem related.

### Re: Synthesising Oscillators

Posted: December 11th, 2013, 1:23 pm
towerator wrote:Better, but it's not over yet...
Yes, it seems as if any predecessor with an ON cell in line with the eaters' tails -- even the simplest variant, like this:

Code: Select all

``````x = 10, y = 11, rule = B3/S23
8bo\$2o6bo\$o5bobo\$b3o2bo\$3bo2bo2\$3bo2bo\$3bo2b3o\$bobo5bo\$bo6b2o\$bo!``````
-- begs the question of how to get that key cell to turn on without affecting either of the two eaters. If you're allowed to start with four eaters, you might be able to collapse two of them -- a small spark added to the following pattern might produce the above six-cell spark:

Code: Select all

``````x = 10, y = 11, rule = B3/S23
\$2o6bo\$o8bo\$b3o2b3o\$3bo2bo2\$3bo2bo\$b3o2b3o\$o8bo\$bo6b2o!``````
But building those four eaters is starting to look pretty expensive...?

### Re: Synthesising Oscillators

Posted: December 11th, 2013, 8:16 pm
Obvious three-glider reduction:

Code: Select all

``````x = 126, y = 59, rule = B3/S23
38bobo\$38b2o\$39bo3\$o\$b2o52bobo\$2o53b2o\$56bo7\$45bo\$43b2o\$44b2o7\$104bobo
\$71b2ob2o17b2ob2o6b2o13b2ob2o\$18b2o2b2o48bobobo17bobobo6bo14bobobo\$17b
obob2o49bo2bobob2o13bo2bobob2o17bo2bobo\$19bo3bo49bobob2obo14bobob2obo
18bobobo\$74bo21bo25bobo\$123bo2\$97b2o2b2o\$74b3o20b2ob2o\$76bo25bo\$75bo\$
77b3o\$77bo\$78bo4\$42bo\$41b2o\$41bobo8\$49b3o\$49bo\$50bo2\$10b3o\$12bo\$11bo!
``````
This is now the first formerly unknown sixteen-bitter that uses less than one glider per bit.

EDIT: A different way to synthesize two of the three sparks:

Code: Select all

``````x = 25, y = 16, rule = B3/S23
11b2o\$12b3o\$10bo4bo\$3bo5bob4o\$4b2o4bo\$3b2o7bo9bobo\$11b2o9b2o\$23bo4\$18b
2o\$2o16bobo\$b2o3b2o10bo\$o6b2o\$6bo!
``````
EDIT 2: A possible predecessor to towerator's second predecessor:

Code: Select all

``````x = 20, y = 21, rule = B3/S23
17bo\$17bobo\$17b2o\$13bobo\$14b2o\$14bo\$5b2o\$5bo7b2o\$6b3obo3bo\$8bob4o2\$6b
4obo\$5bo3bob3o\$5b2o7bo\$13b2o\$5bo\$4b2o\$4bobo\$b2o\$obo\$2bo!
``````
EDIT 3: That SL in 44 gliders and one LWSS:

Code: Select all

``````x = 274, y = 29, rule = B3/S23
227bo\$226bo\$226b3o\$24bo\$22bobo2bobo87bo24bo79bo33bo\$23b2o2b2o58bo24bo
3bo19b2o4bobo78b2o31bobo\$28bo56bobo25b2ob3o16bo2bo3b2o64bo13b2o3bo28b
2o\$24bo61b2o24b2o21bo2bo64bo3bo17b2o25bobo\$7bobo13bo19bo19bo12bo12bo
31bo14b2o36bo29b2ob3o16b2o25b2o\$3bo3b2o14b3o16bobo17bobo10bo12bobo30bo
bo20b2o27bo29b2o48bo\$4b2o2bo33bobo17bobo10b3o10bobo18b2o10b2o10b2o9b2o
17b2o5bo2b3o16b2o25b2o23b2o18b2o\$3b2o38bo19bo25bo19bo14b2o7bo29bo5bobo
20bo5b2o19bo24bo7b2o10bo\$19bobo4bo2bo14b3o2bo14b3o2bo20b3o2bo14b3o2bo
8bobo7b3o2bo24b3o3bo2b3o17b3o3bo5b2o13b3obo2bo17b3obo3bo11b3o\$20b2o4b
4o16b4o16b4o22b4o16b4o8bo11b4o11bo2bo11b4o3bo21b4o6bobo14bob4o19bob4o
14bo\$20bo54bo70b2o2bo23bo13bo16bo62b2o\$2o24b4o16b4o16b4o4b2o16b4o16b4o
20b4o6bobobo3bo11b4o16bobo6b4o21b4obo19b4obo19bo\$b2o23bo2bo16bo2bo15bo
3bo4bobo14bo3b3o13bo3b3o17bo3b3o4bo3b4o11bo3b3o15b2o5bo3b3o19bo2bob3o
16bo3bob3o17b3o\$o6b3o55b2o24b2o5bo12b2o5bo16b2o5bo22b2o5bo21b2o5bo26bo
15b2o7bo19bo\$7bo10b3o76bobo17b2o22b2o28b2o27b2o25b2o23b2o18b2o\$8bo11bo
49b3o24bobo89b2o53bo\$19bo26b2o24bo25bo85b3ob2o30b2o21b2o\$47b2o22bo28b
2o84bo3bo30b2o20bobo\$46bo3b2o15bo32bobo82bo34bo3b2o14b2o\$49b2o16b2o2b
2o27bo122b2o14bobo\$51bo14bobo2bobo151bo15bo\$71bo\$45b3o103b2o66b3o\$47bo
103bobo67bo\$46bo104bo68bo!
``````

### Re: Synthesising Oscillators

Posted: December 12th, 2013, 1:19 am
I'm not sure if this one has been done yet, but here's a 16-bit still life from a 15-bit still life and four gliders:

Code: Select all

``````x = 20, y = 23, rule = B3/S23
2o2bo\$o2bobo\$b3o2bo\$4bobo\$3bobo\$4bo8\$8b2o\$4b2o2bobo\$3bobo2bo\$5bo4\$4b3o
10b2o\$4bo12bobo\$5bo11bo!``````
Unrelated converter:

Code: Select all

``````x = 16, y = 17, rule = B3/S23
2o\$o\$b3o3bo\$3bo3bo\$7bo2\$4b2o3b3o\$3bobo\$2bobo\$3bo2\$7b2o\$6b2o\$8bo\$14bo\$
13b2o\$13bobo!``````

### Re: Synthesising Oscillators

Posted: December 12th, 2013, 8:18 am
Great job! Another one has been solved!

### Re: Synthesising Oscillators

Posted: December 12th, 2013, 8:55 pm
I found this:

Code: Select all

``````x = 21, y = 24, rule = B3/S23
6bo\$4bobo\$5b2o2\$9bo\$7bobo\$obo5b2o\$b2o\$bo8bo\$8b2o\$9b2o6bo\$17bobo\$2bo14b
2o\$2b2o\$bobo3b2o3b2o\$8bo4bo\$8bob3o\$9b2o3\$12b3o\$14bo3b2o\$13bo4bobo\$18bo
!
``````
Not sure how useful it will be.

EDIT: I've noticed that the boat-turning component is unnecessarily large:

Code: Select all

``````x = 108, y = 45, rule = B3/S23
78bo\$79bo\$77b3o12bo\$31bobo3bobo11bo9b2o18b2o8bo\$8bobo21b2o4b2o11bobo6b
o2bo16bo2bo7b3o\$9b2o21bo5bo12b2o8b2o5b2o11b2o5b2o\$9bo25b2o30bo2bo16bo
2bo\$11bo15bo6bobo10bo20b2o18b2o\$b2o3bo3bo10b2o3bobo7bo4b2o3bobo13b2o
18b2o18b2o\$o2bobobo2b3o7bo2bobobo12bo2bobobo13bobo2bo14bobo2bo14bobo2b
o\$bobob2o14bobob2o14bobob2o3bobo8bobobobob2o10bobobobob2o10bobobobo\$2o
bo16b2obo16b2obo6b2o8b2obo2b2ob2o9b2obo2b2ob2o9b2obo2b2o\$3bo19bo19bo7b
o11bo19bo8b2o9bo\$3b2o18b2o18b2o18b2o18b2o7bobo8b2o\$92bo2\$50b2o\$49b2o\$
51bo8\$78bo\$79bo\$77b3o\$31bobo3bobo21b2o18b2o\$32b2o4b2o20bo2bo16bo2bo\$
32bo5bo22b2o18b2o\$35b2o\$34bobo\$36bo4b2o3bo15b2o18b2o18b2o\$40bo2bobobo
13bobo2bo14bobo2bo14bobo2bo\$41bobob2o3bobo8bobobobob2o10bobobobob2o10b
obobobo\$40b2obo6b2o8b2obo2b2ob2o9b2obo2b2ob2o9b2obo2b2o\$43bo7bo11bo19b
o8b2o9bo\$43b2o18b2o18b2o7bobo8b2o\$92bo2\$50b2o\$49b2o\$51bo!
``````

### Re: Synthesising Oscillators

Posted: December 13th, 2013, 5:27 am
Here is a potential starting point for one of the 16-bit still lifes. It is currently missing a crucial step, but I've provided some possibly useful predecessors:

Code: Select all

``````x = 330, y = 90, rule = B3/S23
275b3o\$274bo3bo\$278bo\$277bo\$231bo44bo\$230bo45bo\$230b3o\$276bo\$94bo\$95bo
\$93b3o\$97bo\$97bobo173bo\$64bo32b2o5bo169bo3b2o\$63bo38b2o170bo3b2o\$63b3o
37b2o167b3o2\$12b2o36bo39bo39bo39bo39bo59bo48b2o\$3bobo7bo35bobob2o34bob
ob2o34bobo6bobo28bobo37bobo57bobo45b3o2bo4bo\$4b2o4bo2bobo31b3obobobo
31b3obobo33b3obo6b2o27b3obo35b3obo55b3obo5b3o36bo4b2o4bobo\$4bo3bobo3b
2o30bo4bo2bo31bo4bobo32bo4bob2o4bo26bo4bob2o31bo4bob2o51bo4bob2o5bo36b
3obo5b2o\$9b2o31bo4b3obo35b3obob2o32b3obob2o7b3o22b3obobobo31b3obobo53b
3obobo6bo38bobo\$40bobo6b2o38bobo37bobo10bo26bobo2bo34bobobo55bobobo5bo
41bob2o\$bo39b2o47b2o15b2o21b2o11bo26b2o38b2ob2o56bobob2o2b2o39b2ob2o\$b
2o103b2o30b2o130b2obo2bo2bo\$obo11bo52b2o39bo28b2o35b3o97b2o51b2o\$13b2o
52bobo32b3o34bo36bo2bo36b2o60bo42bo5bobo\$13bobo31b2o12b2o4bo34bo72bo2b
o36bo2bo58b2obo39b2o5bo\$46bobo11b2o41bo74b3o34bo2bo56b3obo40bobo\$48bo
13bo153b2o62bo34b2o\$50b3o261bobo\$50bo149bo115bo\$51bo146bobo\$199b2o31b
2o\$232bobo\$232bo\$203b2o\$204bo\$204bobo\$205b2o12bo\$220bo14bo\$218b3o13b2o
\$234bobo\$219bo56b2o\$219b2o54b4o\$218bobo53b2ob2o\$275b2o\$270bo\$269bobo\$
267b3obo\$266bo4bob2o4bo\$267b3obobo4b3o\$269bobobo5b2o\$192bo78bobob2o\$
192b2o76b2obo2bo\$191bobo80b2o\$278b3o\$277bo\$275b3o2bo\$277bo14\$276b2o\$
275b4o\$274b2ob2o\$275b2o\$270bo\$269bobo\$267b3obo\$266bo4bob2o\$267b3obobo
4b3o\$269bobobo5b2o\$271bobob2o\$270b2obo2bo\$274b2o3bo\$279b2o\$277bobo\$
276bob3o\$274b2o3b2o!``````
Extrementhusiast wrote:Griddle with tub and hook in 74 gliders and one LWSS
Doing the last two steps simultaneously gives a slight reduction:

Code: Select all

``````x = 27, y = 31, rule = B3/S23
16bo\$15bo\$15b3o\$6bo\$7b2o\$6b2o\$26bo\$24b2o\$6bo18b2o\$4b2o\$5b2o6bo\$obo8b3o
\$b2o7bo5bo\$bo7bob6o\$10bo\$11bob4o\$12b2o2bo5b2o\$22bobo\$b3o18bo\$3bo\$2bo\$
15b2o\$16b2o\$15bo2\$20b2o\$20bobo\$20bo\$14b2o\$13bobo\$15bo!``````
Extrementhusiast wrote:I've noticed that the boat-turning component is unnecessarily large
Another reduction by one glider:

Code: Select all

``````x = 74, y = 21, rule = B3/S23
9bo\$9bobo\$2bo6b2o\$obo\$b2o2bo\$5bobo\$5b2o4\$7b2o3bo15b2o18b2o18b2o\$6bo2bo
bobo13bobo2bo14bobo2bo14bobo2bo\$7bobob2o3bobo8bobobobob2o10bobobobob2o
10bobobobo\$6b2obo6b2o8b2obo2b2ob2o9b2obo2b2ob2o9b2obo2b2o\$9bo7bo11bo
19bo8b2o9bo\$9b2o18b2o18b2o7bobo8b2o\$58bo2\$16b2o\$15b2o\$17bo!``````
Unrelated converters:

Code: Select all

``````x = 165, y = 51, rule = B3/S23
101bo\$50bo48bobo8bo17bo\$48b2o50b2o7bo16b2o7bo\$49b2o58b3o9bobo3b2o5bo\$
122b2o10b3o\$122bo2\$8b2o28b2o28b2o28b2o29b2o27b2o\$8bo2bo26bo2bo26bo2bo
26bo2bo26bo2bo26bo2bo\$9b3o27b3o27b3o27b3o27b3o27b3o2\$7b7o23b7o6bo16b7o
23b7o23b7o23b7o\$7bo2bo3bo22bo2bo3bo4b2o16bo2bo3bo22bo2bo3bo21bo7bo22bo
2bo3bo\$13bobo27bobo3bobo21b2o4bo23bobo21b3ob2o2bo27b2o\$14bo29bo34bobo
22bo24bobob2o\$79b2o\$10b2o28b2o28b2o28b2o58b2o\$5b2o3bobo22b2o3bobo22b2o
2b2o24b2o2b2o37b3o14b2o2b2o\$bo3bobo2bo20bo3bobo2bo8b2o10b2ob2o5bo19b2o
b2o5bo36bo12b2ob2o5bo\$b2o2bo25b2o2bo12b2o10bobo3bo23bobo3bo10b2o30bo
10bobo3bo\$obo27bobo17bo11bo14b3o12bo13b2o44bo\$77bo30bo\$78bo8\$100bo\$
101b2o\$100b2o7bobo\$109b2o\$110bo3\$8b2o88b2o\$8bo2bo86bo2bo\$9b3o87b3o2\$7b
7o83b7o\$7bo2bo3bo82bo2bo3bo\$13bobo87bobo\$14b2o88b2o2\$10b2o88b2o\$5b2o2b
2o9b2o73b2o2b2o10bo\$b2ob2o5bo8bobo68b2ob2o5bo8b2o\$obo3bo13bo69bobo3bo
13bobo\$2bo89bo!``````

### Re: Synthesising Oscillators

Posted: December 13th, 2013, 1:30 pm
Found the missing step for one of the Elkies's P5 variants:

Code: Select all

``````x = 43, y = 27, rule = B3/S23
15bo\$15bobo\$15b2o\$3bo\$bobo\$2b2o10bo\$14bobo\$14b2o2\$8bo\$6bobo10bobo\$7b2o
10b2o\$2b2o16bo16b2o\$bo2bo31bo2bo\$2bobo32bobo2bo\$b2ob3o29b2ob4o\$o2bo3bo
27bo2bo\$bobo2b2o28bobo2b2o\$2bo19b3o12bo3b2o\$22bo\$23bo2\$15b2o\$15bobo\$
15bo5b2o\$21bobo\$21bo!``````
Sokwe wrote:
Extrementhusiast wrote:I've noticed that the boat-turning component is unnecessarily large
Another reduction by one glider:

Code: Select all

``````x = 74, y = 21, rule = B3/S23
9bo\$9bobo\$2bo6b2o\$obo\$b2o2bo\$5bobo\$5b2o4\$7b2o3bo15b2o18b2o18b2o\$6bo2bo
bobo13bobo2bo14bobo2bo14bobo2bo\$7bobob2o3bobo8bobobobob2o10bobobobob2o
10bobobobo\$6b2obo6b2o8b2obo2b2ob2o9b2obo2b2ob2o9b2obo2b2o\$9bo7bo11bo
19bo8b2o9bo\$9b2o18b2o18b2o7bobo8b2o\$58bo2\$16b2o\$15b2o\$17bo!``````
I was just referring to the part on the right, otherwise copying it verbatim from one of Niemiec's posts.

EDIT: Yet another 16-bitter in 21 gliders:

Code: Select all

``````x = 122, y = 58, rule = B3/S23
92bo\$91bo\$91b3o\$77bo\$78bo\$76b3o3\$90bobo\$90b2o\$91bo\$98bo\$96b2o\$97b2o\$
68bo\$62bo6bo\$63bo3b3o\$61b3o2\$29bo19bo\$27b2o15bo3bo32b2o\$28b2o15b2ob3o
29bo2bo\$44b2o34bo2bo\$27bo53b2o\$26b2o\$3bo13bo4bo3bobo20b2o35b2o\$2bo12bo
bo3bobo23bo2bo33bo2bo27b2o2b2o\$2b3o11b2o2bo2bo22bob2o33bob2o28bo2bo2bo
\$21b2o22bobo34bobo32b2ob2o\$b2o42bobo34bobo33bobo\$obo43bo36bo34bobo\$2bo
116bo\$22b2o\$21bobo3bo\$23bo2b2o72b2o\$26bobo70b2o\$101bo2\$64b3o5bo\$66bo5b
2o\$65bo5bobo4\$83bobo\$83b2o\$84bo2\$83b2o\$83bobo\$83bo5\$74b2o\$73bobo\$75bo!
``````

### Re: Synthesising Oscillators

Posted: December 13th, 2013, 10:47 pm
Extrementhusiast wrote:EDIT: Yet another 16-bitter in 21 gliders:

Code: Select all

``````x = 122, y = 58, rule = B3/S23
92bo\$91bo\$91b3o\$77bo\$78bo\$76b3o3\$90bobo\$90b2o\$91bo\$98bo\$96b2o\$97b2o\$
68bo\$62bo6bo\$63bo3b3o\$61b3o2\$29bo19bo\$27b2o15bo3bo32b2o\$28b2o15b2ob3o
29bo2bo\$44b2o34bo2bo\$27bo53b2o\$26b2o\$3bo13bo4bo3bobo20b2o35b2o\$2bo12bo
bo3bobo23bo2bo33bo2bo27b2o2b2o\$2b3o11b2o2bo2bo22bob2o33bob2o28bo2bo2bo
\$21b2o22bobo34bobo32b2ob2o\$b2o42bobo34bobo33bobo\$obo43bo36bo34bobo\$2bo
116bo\$22b2o\$21bobo3bo\$23bo2b2o72b2o\$26bobo70b2o\$101bo2\$64b3o5bo\$66bo5b
2o\$65bo5bobo4\$83bobo\$83b2o\$84bo2\$83b2o\$83bobo\$83bo5\$74b2o\$73bobo\$75bo!
``````
Hold on... doesn't that look like the p7 oscillator that can be perturbed to p8?

### Re: Synthesising Oscillators

Posted: December 14th, 2013, 4:52 am
Two related 16-cell still lifes from an easily constructable larger still life:

Code: Select all

``````x = 70, y = 41, rule = B3/S23
36bobo\$36b2o\$37bo4\$67bo\$18bo48bobo\$16bobo41bo6b2o\$17b2o39bobo\$20bo38b
2o2bo\$20b3o40bobo\$23bo39b2o\$22b2o3\$5b2o58b2o\$5bobo57bo2bo\$6b2o58b2obo\$
68bo\$4b4o56b3o\$3bo4bo54bo2b2o\$3b2o2bobo53b2o\$8bo10\$23b2o\$22b2o\$24bo2\$
2o\$b2o21b2o\$o23bobo\$24bo!``````
Edit: These syntheses are possibly already known:

Code: Select all

``````x = 69, y = 17, rule = B3/S23
2bo\$obo\$b2o2\$25bo39bo\$7b3o13b2o22b3o13b2o\$9bo14b2o23bo14b2o\$8bo39bo\$
14b3o37b3o\$14bo39bo\$15bo39bo\$3b3o37b2o\$5bo3b3o30bobo4b3o\$4bo6bo15b2o
15bo6bo15b2o\$10bo10b2o3b2o22bo10b2o3b2o\$20b2o6bo31b2o6bo\$22bo39bo!``````
Edit 2: Here is a sequence of sparks that may work to synthesize the 16-bit still life I mentioned in my previous post (marked with the number of generations between each step). getting all of these sparks together at the right time might be difficult (or impossible), but it might lead to better ideas:

Code: Select all

``````x = 215, y = 20, rule = B3/S23
31b3o47b3o48bo\$31bo49bo25bo23b2o\$31b3o47b3o23bo3bo20bo23b2ob2o\$33bo47b
obo23b4o21bo23b5o\$4bo26b3o20bo26b3o21bo25b3o21b5o\$3bobo47bobo48bobo47b
obo\$b3obo45b3obo46b3obo45b3obo47b2o\$o4bob2o24bo16bo4bob2o4bo19bo17bo4b
ob2o3b2o18bo17bo4bob2o2b4o36b3o2bo4bobo\$b3obobo26bo16b3obobo5bo20bo17b
3obobo2b2ob2o18bo17b3obo4bo2b2o17bo17bo4b2o4b2o\$3bobobo22b6o17bobobo5b
o16b6o18bobob2ob2o17b6o18bobob6o20bo17b3obo6bo\$5bobob2o23bo20bobob2o3b
o19bo21bobo25bo21bobob2o18b6o18bobo\$4b2obo2bo22bo20b2obo2bo22bo21b2obo
bo22bo21b2obo25bo21bob2o\$8b2o8bo39b2o49bo42bo6b2o22bo22bobobo\$18bobo
42bobo44bo2bo37bob2o5bo44b2obo2bo\$14b2o2b2o42bo2bo45bo55bo41b2o\$14bobo
44b2o2bo50b3o47bobo\$9b2o3bo49bo48bo2b3o49bo38bo\$10b2o49bobo48bo2b2o45b
o2b2o39b2o\$9bo52bo49b3o47bo43bobo\$113b2o47bobo!``````

### Re: Synthesising Oscillators

Posted: December 14th, 2013, 2:45 pm
Predecessor to another 16-bitter:

Code: Select all

``````x = 57, y = 51, rule = B3/S23
3\$24b3o\$17bo8bo4b3o\$15bobo7bo5bo\$16b2o14bo3\$12bobo\$13b2o\$13bo8\$28b2o\$
28bo2b2o\$29b2obo17bo\$26bo6b2o13bobo\$25bobo6bo14b2o\$26bo2bo3bo\$27b2obo
2bobo\$29bo4b2o\$25bo3bobo\$24bobo3bobo17b2o\$24bo2bo3bo17bobo\$25b2o24bo2\$
10b2o\$9bobo\$11bo3\$48b3o\$48bo\$49bo\$44b2o\$11b3o29b2o\$13bo31bo\$12bo7b3o\$
22bo\$21bo!
``````
I couldn't figure out how to make the proper pre-beacon in any other way. Is there a better way, like from a ship, instead of this difficult-to-place 14-bitter? (A good way to edgeshoot a boat would also work, as we would then simply use two of them at once to get from a tub to that 14-bitter.)

EDIT: Found the missing step to solve at least one of the 16-bitters:

Code: Select all

``````x = 39, y = 24, rule = B3/S23
26bo\$24b2o\$25b2o4\$o\$b2o\$2o3\$25bo4bo\$26b2obo\$25b2o2b3o4\$15bo\$11b2obobo\$
11bo3bobo\$12b3o2bo\$10bobo4b2o18b2o\$10b2o24b2o\$38bo!
``````
I did it completely differently than what was suggested.

EDIT 2: Finished yet another of the 16-bitters in 48 gliders:

Code: Select all

``````x = 259, y = 46, rule = B3/S23
124bo\$124bobo\$124b2o105bo\$108bobo118b2o\$84bo24b2o119b2o7bo\$85b2o22bo
127b2o\$84b2o3bo134bo13b2o\$81bo7bobo130bobo5bo\$79bobo7b2o132b2o6b2o\$80b
2o33bo61bo52b2o\$71bobo42b2o7bo49bobo20bo\$50bo21b2o41b2o6b2o51b2o20bobo
34bobo\$29bobo19b2o19bo51b2o72b2o36b2o\$29b2o19b2o63bo5bo103b2o9bo\$30bo
2b2o12b2o60b2o3b2o3b2o21b2o18b2o11b3o4b2o15bo4b2o19bobo3b2o\$26b3o4bobo
10bobo7bo23b2o27bo4bobo3b2o20bo19bo14bo4bo16bo4bo21b2o3bo\$28bo4bo14bo
6bobo21bo2bo27bo32bo19bo12bo6bo15bo5bo26bo\$27bo28b2o21b4o24b4o29b4o16b
4o16b4o18b4o15bobo5b4o\$72bo34bo32bo19bo19bo21bo19b2o5bo10b2o10b2o\$29b
2o25b2o15bo7b2o26b2o31b2o18b2o18b2o20b2o16bo8b2o6b2o11bo2b2o\$2bo4bo21b
obo24bobo12b3o7bobo16bo7b2obo29b2o2bo12bo2b2o2bo15b2o2bo17b2o2bo22b2o
2bo6bo12b2o2bo\$3bob2o24bo26bo24bo17bo9bo32b2o10bobo5b2o18b2o20b2o12bo
12b2o22b2o\$b3o2b2o19b4o23b4o21b4o16b3o6b3o30b3o13b2o2b3o16bob2o18bob2o
12bobo8bob2o20bob2o\$27bo26bo24bo28bo31bo2bo16bo2bo16b2obo18b2obo13b2o
8b2obo20b2obo\$14bo13bo26bo24bo59b2o17bobo\$7bo5bo13b2o25b2o23b2o55bo9bo
9b2o2bo60bo\$8b2o3b3o81b2o38b2o5b2o9bobo63b2o\$7b2o87bobo37b2o7b2o10bo
62bobo\$98bo22b2o37b2o\$120b2o22bo14b2o\$73bo12bo35bo20b2o16bo\$73b2o10b2o
15bo32b3o5bobo\$72bobo10bobo14b2o31bo\$101bobo32bo2\$2o\$b2o110b3o\$o112bo\$
114bo5\$119b3o\$119bo\$120bo!
``````
On another note, I kinda want to run a statistics package on this data set (where the data are the minimum numbers of gliders required).

EDIT 3: Predecessor to yet another 16-bitter:

Code: Select all

``````x = 87, y = 47, rule = B3/S23
58bo\$39bo18bobo\$37bobo18b2o\$38b2o4\$56bo\$54b2o\$46bo8b2o\$45bo14b2o\$45b3o
2b3o7bobo\$50bo9bo\$51bo5\$2ob2o39b2ob2o31b2ob2o\$bobo2bo38bobo2bo30bobo\$b
o2b3o38bo2b3o30bo2b3o\$2b2o42b2o34b2o2bo\$4bo43bo35bo\$2b3o41b3o35b2o\$bo
43bo\$b2o35bo6b2o\$39bo\$37b3o3\$52b2o\$18b2o33b2o\$17bobo22bo9bo13b2o\$19bo
22b2o22bobo\$41bobo22bo3\$65bo\$64b2o\$64bobo2\$59bo\$58b2o\$58bobo\$22b2o\$21b
obo\$23bo!
``````
EDIT 4: Same as above, yet different:

Code: Select all

``````x = 100, y = 32, rule = B3/S23
62bo\$63bo\$61b3o2\$37bo\$36bo32bobo\$36b3o30b2o\$34bo35bo\$35bo\$33b3o26b2o\$
62b2o2\$69bobo\$2o3b2o20b2o3b2o21b2o3b2o7b2o20b2o3b2obo\$obo2bobo19bobo2b
obo20bobo2bobo7bo20bobo2bob2o\$2b3o2bo21b3o2bo22b3o2bo30b3o\$bo5b2o19bo
5b2o20bo5b2o8bo19bo\$b2o25b2o26b2o14bobo17b2o\$60bo11b2o\$60b3o\$63bo7bo\$
24bo37b2o6b2o\$22bobo45bobo\$23b2o2\$30b2o34b2o\$31b2obobo28b2o\$30bo3b2o
16b3o12bo\$35bo6bo11bo6b2o\$16b2o23b2o10bo8b2o\$15bobo23bobo17bo\$17bo!
``````

### Re: Synthesising Oscillators

Posted: December 14th, 2013, 6:54 pm
I wrote:Here is a sequence of sparks that may work to synthesize the 16-bit still life I mentioned in my previous post...
It wasn't as difficult as I thought it might be. The penultimate step is certainly more dense than it needs to be:

Code: Select all

``````x = 418, y = 58, rule = B3/S23
346bo\$344bobo\$345b2o4\$299bo74bo\$298bo74bo8bobo\$298b3o72b3o6b2o\$355bo
14bo12bo\$122bo233b2o11bo\$123bo231b2o12b3o\$121b3o239bo14bo\$125bo238bo
11b2o\$125bobo234b3o12b2o\$92bo32b2o5bo235bo\$91bo38b2o234bobo\$91b3o37b2o
211bo22b2o\$345bo\$40b2o36bo39bo39bo39bo39bo39bo39bo24b3o12bo\$31bobo7bo
35bobob2o34bobob2o34bobo6bobo28bobo37bobo37bobo37bobo7bo29bobo47b2o\$2o
30b2o4bo2bobo31b3obobobo31b3obobo33b3obo6b2o27b3obo35b3obo35b3obo35b3o
bo8b2o17bo7b3obo45b3o2bo4bobo\$b2o29bo3bobo3b2o30bo4bo2bo31bo4bobo32bo
4bob2o4bo26bo4bob2o31bo4bob2o31bo4bob2o31bo4bob2o4b2o19b2o4bo4bob2o15b
o25bo4b2o4b2o\$o3b2o31b2o31bo4b3obo35b3obob2o32b3obob2o7b3o22b3obobobo
31b3obobo33b3obobo33b3obobo25b2o6b3obobo5b2o7b2o27b3obo6bo\$4bobo61bobo
6b2o38bobo37bobo10bo26bobo2bo34bobobo35bobobo35bobobo35bobobo5bobo7b2o
28bobo\$4bo24bo39b2o47b2o15b2o21b2o11bo26b2o38b2ob2o35b2ob2o36bobob2o3b
3o28bobob2o3bo40bob2o\$29b2o103b2o30b2o150b2obo2bo3bo29b2obo2bo44bobobo
\$28bobo11bo52b2o39bo28b2o35b3o117b2o5bo32b2o44b2obo2bo\$41b2o52bobo32b
3o34bo36bo2bo76b2o126b2o\$41bobo31b2o12b2o4bo34bo72bo2bo37b2o37bo2bo\$
74bobo11b2o41bo74b3o30b3ob2o38bo2bo123bo\$76bo13bo150bo3bo38b2o123b2o\$
78b3o159bo168bobo\$78bo189bo\$79bo186bobo104b2o\$267b2o31b2o70b2o\$300bobo
55b3o13bo\$300bo42b2o4bo10bo\$271b2o71b2o3b2o8bo\$272bo70bo4bobo\$231b2o
39bobo\$232b2o39b2o12bo50b3o\$231bo3b2o51bo14bo36bo\$235bobo48b3o13b2o35b
o\$235bo66bobo\$287bo\$287b2o\$286bobo8\$260bo\$260b2o\$259bobo!``````

### Re: Synthesising Oscillators

Posted: December 14th, 2013, 7:23 pm
Extrementhsuiast wrote:Two completely separate but related converters:
It's interesting that they both slide one space. Combining two copies of the table-to-cap one can make both cis- and trans- versions of cap on cap (depending on whether you use line or point symmetry) from 8 gliders, and since the trans- version already takes 8, this makes this at least equivalent as the best solution so far.
Extrementhusiast wrote:Griddle with tub and hook in 74 gliders and one LWSS:
This can be reduced by 3 gliders, by attaching the bookend-with-tub directly. (I didn't have this mechanism, but seeing how you did it, I remembered that a common mechanism for puffing out a tub-like protrusion was to attach a diagonal bit to a corner block just as it's attaching. In this case, it takes 2 gliders to do then, rather than 5 later.) It turns out that both primary ways of making this still-life take 5 gliders, and the tub can be added for 2 more to both of them:

Code: Select all

``````x = 109, y = 48, rule = B3/S23
46bo\$47bo41bo\$45b3o41bobo\$49bo39boo\$48bo17boo18boo\$48b3o15boo18boo\$45b
o\$46bo5boo\$44b3o5bobo12bo19bo19bo\$52bo13bobo17bobo17bobo\$38bo26bobo17b
obo17bobo\$4bo34boo24bo19bo19bo\$4bobo17boo12boo4boo16booboo15booboo15b
ooboo\$3oboo17bobbo16bobbo16bobbo16bobbo16bobbo\$bbo20bobo8b3o6bobo17bob
o17bobo17bobo\$bo22bo11bo7bo19bo19bo19bo\$35bo18\$54boo\$50bobboo\$48bobo4b
o\$49boo\$o66bo\$boo41bobo19bobo\$oo36bo6boo18bobo\$5bo33boo4bo19bo\$3boo3b
3o27boo22booboo\$4boobbo14boboo16boboo16bobbo\$9bo13boobo7b3o6boobo16bob
o\$7bo28bo27bo\$7boo26bo\$6bobo!
``````
Extrementhusiast wrote:Predecessor to one sixteen-bitter:
Thanks! This is indeed viable, and here is a 30-glider synthesis (based on a 26-glider synthesis of the related 18-bit still-lifes with boats instead of hooks; I couldn't remove the one-bit sparks, but at least they were benign):

Code: Select all

``````x = 135, y = 76, rule = B3/S23
48bo\$46bobo\$47boo11bobo18bo\$60boo20bo\$51bo9bo18b3o\$51bobo\$51boo\$\$67boo
booboo32booboo15boobooboo\$3bo63bo3boboo32bo3bo15bo3boboo\$4boo62b3o37b
3o17b3o\$3boo53bo\$57boo9b3o37b3o17b3o\$bo26bo19bo8bobo7bo3bo35bo3bo15bo
3bo\$boo25bo19bo18bo3bo35bo3bo15bo3bo\$obo25bo19bo19b3o37b3o17b3o\$\$53bo
14b3o37b3o17b3o\$44bo7boo13bo3bo25boobboo4bo3bo12boobo3bo\$42bobo7bobo
12booboo24boboboo5booboo12boobooboo\$43boo53bo3bo\$\$47boo\$46bobo\$48bo3\$
48b3o\$50bo\$49bo5\$57b3o\$57bo\$58bo16\$59bo\$53bo6bo6bo\$54boobb3o5bo\$53boo
11b3o\$108bobo\$106bobobobo\$43bobo11boobooboo42booboo\$44boo6bo4bo3boboo\$
44bo5bobo5b3o28bo19bo\$47bo3boo35bobo17bobo17bobo\$47boo9b3o27boobo16boo
bo16boobo\$46bobo8bo3bo24boo3bo14boo3bo14boo3bo\$57bo3bo8bobo14bo3boo14b
o3boo14bo3boo\$58b3o9boo15boboo16boboo16boboo\$66boo3bo16bobo17bobo17bob
o\$58b3o5bobo5bo14bo19bo\$54boobo3bo4bo6boo\$54boobooboo11bobo31booboo\$
106bobobobo\$108bobo\$50b3o11boo\$52bo5b3obboo\$51bo6bo6bo\$59bo!
``````
I just found a simple 3-glider beehive-to-boat converter, which is better than the previous 2 step beehive-to-block-to-boat method, saving 2 gliders. This improves at least 8 candelfrobra-variant syntheses. I'm not sure where else it would come in handy:

Code: Select all

``````x = 105, y = 20, rule = B3/S23
o3bo45bo\$boobobo42bo\$oobboo16bo19bo6b3o10bo19bo19bo\$21bobo17bobo17bobo
17bobo17bobo\$6b3o13bo19bo19bo19bo19bo\$6bo56bo19bo19bo\$7bo55bo19bo19bo\$
60bo3bo15bo3bo15bo3bo\$60b4o16b4o16b4o\$37bobo\$38boo6b3o11boo18boo5bo12b
oo\$38bo7bo12bobbo16bobbo3bo13bobo\$47bo12boo18boo4b3o12bo\$40boo\$41boo\$
40bo40b3o\$83bo\$82bobb3o\$85bo\$86bo!
``````
At first, this was one of the 16-bit still-lifes that I thought would be very difficult to synthesize, as it forms a loop, and such objects always pose problems. But then I thought that since it was trivial to turn a carrier into a canoe, perhaps both sides could be turned simultaneously? This turns out to be the case, just needing a slightly-customized spark, so this can be made from merely 12 gliders:
(UPDATE: This obviates Extrementhusiast's subsequent candidate predecessor)

Code: Select all

``````x = 113, y = 21, rule = B3/S23
16bo\$15bo\$15b3o4\$28boo18boo18boo18boo18boo\$28bobbo16bobbo16bobbo16bobb
o16bobo\$26boobboo14boobboo14boobboo14boobboo14boo3bo\$11bobo12bo19bo19b
o19bo19bo5bo\$11boo15bo19bo19bo19bo18bo3boo\$12bo14boo18boo3bobo12boobb
oo14boobboo3bobo9bobo\$52boo17bobo17bobobboo11boo\$9b3o41bo18bo19bo4bo3b
o\$9bo90boo\$boo7bo39b3o47bobo\$obo42bo4bo41b3o\$bbo42boo4bo36bo5bo\$44bobo
41boo3bobboo\$87bobo6bobo\$96bo!
``````
Sokwe wrote:I'm not sure if this one has been done yet, but here's a 16-bit still life from a 15-bit still life and four gliders:
No, this is new! In the past, I had tried various different approaches to make this, without success. This mechanism also looks like it might be useful in some other places too.
Extrementhusiast wrote:I found this:
Interesting. This was previously buildable (bun-on-snake, and add tail), but this mechanism is still interesting. It also looks like this mechanism might be adaptible to other situations. I'm always interesting in anything that can make an inducting snake (in any orientation), as a large percentage of unsolved pseudo-still-lifes involve inducting snakes.
Exrementhusiast wrote:I've noticed that the boat-turning component is unnecessarily large:
Great! I'll have to see where this is used. I remember a fair number of 16-bit still-lifes use this either directly, or indirectly.
Sokwe wrote:Another reduction by one glider:
I always figured that the top part should be doable with 3 gliders. This should reduce many other things as well!
Extrementhusiast wrote:Found the missing step for one of the Elkies's P5 variants:
This is so simple and obvious, I wonder why it was never found before. There are quite a few synthesis that turn an eater into a block-on-table using a convoluted round-about method (that doesn't fit here), and I think many of them can be greatly optimized by doing them this way!
Sokwe wrote:These syntheses are possibly already known:
Both of these create an interesting T-shaped omino, which just happens to be a exactly the component I was just looking for yesterday while trying to synthesize an obscure c/2 spaceship with an odd tag-along. I will have to see if this can fit there. The first one is new. It uses 9 gliders, the same as the existing synthesis. The second one is new, but at 8 gliders is not optimal. Here are (I think?) Dave Buckingham's earlier 7-glider synthesis, plus a new 5-glider one from Boris Shemyakin from last year:

Code: Select all

``````x = 147, y = 66, rule = B3/S23
82bo\$83bo\$81b3o32bo\$114boo\$115boo5bo\$120boo\$121boo7\$69bo29bo\$69bo29bo
41boo\$50b3o16bo29bo37boobobbo\$52bo84boobobbo\$51bo88booboo\$72boo28boo
36bobbobbo\$51boo18bobbo26bobbo36boobboo\$51bobo17bobo27bobo\$51bo20bo25b
o3bo\$98boo\$97bobo4\$84b3o\$86bo\$85bo38boo\$118boo3boo\$117boo6bo\$119bo16\$
87bo\$88bo\$38bobo45b3o30bo\$bbo36boo76bobo\$obo36bo40bo37boo\$boo3bo74boo
18bo19bo\$4boo17boo18boo16boo17boo18bobo17bobo18boo\$5boo16bobo17bobo15b
obo36boobo16boobo17bobo\$25bo19bo17bo18bo20bo19bo19bo\$25boo18boo16boo
16bo21boo18boo18boo\$38boo8boo11bobobbo14b3o10bo6bobobbo14bobobbo14bobo
bbo\$39boo7bobo10boobboo26boo6boobboo14boobboo14boobboo\$38bo9bo33bo10bo
bo\$81boo\$81bobo\$90b3o\$90bo\$91bo!
``````
Extrementhusiast wrote:Predecessor to another 16-bitter:
I'm not sure how easy it would be to put the two bridged shillelaghs there in place. While this particular synthesis has now been obviated (see my synthesis from yesterday above), this does bring up an interesting way of making a single canoe, which may prove useful in some situations where a canoe wraps closely around something else.
Extrementhusiast wrote:Finished yet another of the 16-bitters in 48 gliders:
Nice! I'll need to remember this method. One problem I frequently run into is wanting to use a mechanism that's ridiculously easy with a trans-carrier, but impossible with a cis-carrier. In many cases (like this one), the trans-carrier can't just be put in place and flipped later because it's unstable per se. However, this way of building in place with scaffolding, and then removing the scaffolding while flipping it, might be expensive, but it may make some other previously unbuildable objects possible. One I was looking at this morning can't use this exactly as shown, but might be amenable to a modified version of it:

Code: Select all

``````x = 8, y = 7, rule = B3/S23
oo\$bo4boo\$boboobbo\$bboboo\$\$3boobo\$3boboo!
``````
Extrementhusiast wrote:Same as above, yet different:
Nice! When I had posted my attempts to make this, I had tried all the old things, plus dozens of new variants to do this eater-to-snake reduction, but all of them snagged the hook on the bottom left. This less obtrusive version might also be useful in some other cases where the old ones were inadequate.
Sokwe wrote:It wasn't as difficult as I thought it might be. The penultimate step is certainly more dense than it needs to be:
I think this now brings us down to only 39 unsynthesized 16s!

### Re: Synthesising Oscillators

Posted: December 14th, 2013, 7:54 pm
mniemiec wrote:I think this now brings us down to only 39 unsynthesized 16s!
I only count 35. Did you see these four by Extrementhusiast?

Code: Select all

``````x = 189, y = 122, rule = B3/S23
92bo\$93bo\$91b3o2\$67bo\$66bo32bobo\$66b3o30b2o\$64bo35bo\$34bobo28bo\$32bobo
bobo24b3o26b2o\$33b2ob2o54b2o2\$5bo29bo63bobo\$2o2bobo23b2o2bobo20b2o3b2o
21b2o3b2o7b2o20b2o3b2obo\$obo2bo6bo17bobo2bobo19bobo2bobo20bobo2bobo7bo
20bobo2bob2o\$2b3o6b2o19b3o2bo21b3o2bo22b3o2bo30b3o\$bo9bobo17bo5b2o19bo
5b2o20bo5b2o8bo19bo\$b2o28b2o25b2o26b2o14bobo17b2o\$6b2o82bo11b2o\$5bobo
6bo75b3o\$7bo5b2o78bo7bo\$13bobo38bo37b2o6b2o\$52bobo45bobo\$10b3o40b2o\$
12bo\$11bo48b2o34b2o\$61b2obobo28b2o\$60bo3b2o16b3o12bo\$65bo6bo11bo6b2o\$
46b2o23b2o10bo8b2o\$45bobo23bobo17bo\$47bo3\$129bo\$130bo\$128b3o\$138bobo\$
131bobo4b2o\$131b2o6bo\$132bo2\$136bo\$120b2o3b2obo6b2o13b2o3b2o\$120bobo2b
ob2o6bobo12bobo2bo2bo\$122b3o27b3o2b2o\$121bo29bo\$121b2o28b2o\$128b2o\$
129b2o3b2o\$128bo5bobo\$134bo14\$56bo\$54b2o\$55b2o3\$88bo\$30bo58bo\$31b2o54b
3o\$30b2o2\$95bobo\$55bo4bo34b2o\$56b2obo36bo\$55b2o2b3o\$88b2o\$88b2o2\$5bo
39bo49bobo\$b2obobo34b2obobo35b2o2b2o7b2o24b2o2b2obo22b2o2b2obo\$bo3bo6b
o28bo3bobo34bo3bobo7bo24bo3bob2o22bo3bob2o\$2b3o6b2o29b3o2bo35b3o2bo33b
3o27b3o\$obo8bobo26bobo4b2o18b2o12bobo4b2o8bo21bobo27bobo\$2o38b2o24b2o
13b2o15bobo19b2o28b2o\$6b2o60bo29b2o29b2o\$5bobo6bo114b2o\$7bo5b2o82bo\$
13bobo80b2o33b2o\$82b2o12bobo32bobo\$10b3o68bobo47bo\$12bo70bo8b3o\$11bo
80bo\$93bo8\$159bo\$160bo\$158b3o\$168bobo\$161bobo4b2o\$161b2o6bo\$162bo2\$
166bo\$151b2o2b2obo6b2o14b2o2b2o\$151bo3bob2o6bobo13bo3bo2bo\$152b3o27b3o
2b2o\$150bobo27bobo\$150b2o28b2o\$158b2o\$159b2o3b2o\$158bo5bobo\$164bo!``````

### Re: Synthesising Oscillators

Posted: December 14th, 2013, 8:26 pm
Sokwe wrote:
mniemiec wrote:I think this now brings us down to only 39 unsynthesized 16s!
I only count 35. Did you see these four by Extrementhusiast?
Oops! I saw all of these, but I only counted them as 1. i didn't pay close enough attention to notice that the "same as above, only different" was a different still-life rather than a different synthesis. I also forgot about the two derived snake-to-carrier variants. It would have all eventually gotten settled when I went to merge them all into the synthesis database on my home computer.

I think I have 46 outstanding there, and I count 10 new ones here, leaving 36. Perhaps I miscounted, but it should become pretty clear when I merge all the wonderful new posts into the database. Regardless of the exact count, a 25% reduction in one week is quite impressive. At this rate, by the end of the year, they may all be finished!

### Re: Synthesising Oscillators

Posted: December 15th, 2013, 2:15 pm
Here is a handy-dandy chart I just made that indexes predecessors for the unsolved 16-bitters:

Code: Select all

``````x = 1079, y = 94, rule = B3/S23
962b2ob2o31b2o33b2o34b2o\$963bobo31bo2bo31bo2bo32bo2bob2o\$962bo3bo31b2o
32b2obo31bobob2obo\$963b3obo31bobob2o29bob2obo28bobo\$716b2o30b2o2bo33b
2o31b2o33b2o3bo29b2ob2o32b2o37bo2bo29bo2b2obo29bobob2o30bo\$6b2o2b2o30b
obobo30bob2o30bob2o31b2o2bobo28bo3b2o29b2ob2o30b2o2bo30b2ob2o32b2ob2o
34b2o35b2ob2o29bobo32b2o33b2o33b2o32b2o3b2o28b2o2b2o29b2o2b2o29b2ob2o
32b3obo29bo3b3o30bobo32bo33bo2b3o29bo3bo31bobo2b2o35b2o29b2o35bo34b2o\$
6bobo2bo29bob3obo28bob2obo29b2obo31bo2bob2o28b3o2bo30bobobobo27bo2bobo
30bobo34bobo34bobo34bobobo30b2obo31bo2b2o30bo2b2o30bo2b2obo27bobobobo
28bo2bo2bo28bo2bo2bo29bobo32bo5bo29bo5bo28bo2bobo30bob2o31b2o33bobo31b
o6bo\$8b2o31bo5bo28bo5bo31bob2o29bobo34b2o31bo2bob2o28b2o2bo29bo3bo32bo
3bo32bo2bob2o31bo5bo31bo32b2obo31b2obo31b2o2b2o29bobo31bobob2o29b2obob
o29bo2b3o30bo5bo29bo3b2o29b2obobo30bo2bo32bo33b2obo30b2o3bo\$6bo2bobo
30b3obo30bob2obo28b2o2bobo30bo2b2o30bo2b3o29bobo32bobo30bob2o33bob2obo
31b2obo2bo32bo3b2o28b2obob2o30bobobo30bobobo31bo31bob2o32bobo33bobo31b
2o2bo31bob3o31bobo33bo2bo31bobo32b3o33bobo30bo2bo\$6b2o2b2o32b2o32b2obo
29bob2o34b2obo30b2o3bo30b2o31bo2b2o30bobobo32bobobo34bobo34bobo30bobob
obo30bo2b2o28bo4b2o31bob2o28bo37bo33bo35bo34b2o34b2o33bobo30bobob2o34b
o32bobo30bobo\$252b2o36b2o35bo35b2o36b2o33bo32b2o32b2o37bobo27b2o37b2o
31b2o35b2o105bo31b2o37b2o33bo32bo34b2ob2o31b2o32b2o2bo30b2o2b2o\$963bob
o31bo2bo31bo2bobo29bo2bo2bo\$962bo3bo31b2o3b2o29b2obo31b2obobo\$963b3obo
31bobo2bo31bob2o31bobo\$965bo2bo29bo2b2o33bo2bo31bo\$966b2o30b2o37b2o31b
2o4\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o8\$108bob2o35bobo2b2o
386b2ob2o2b2o\$108b2obo35b2obo2bo169b2ob2o213bobo2b2o\$111bob2o35bobo
100b2o69bobo213bo2bo4bo\$108b3obobo32b3obo97b2obobo68bo3bo212bobo10bo\$
108bo2bo35bo2bo98bob2o70bob2o69bo144bo9b2o\$109b2o37b2o103bo70bobobo4bo
63bo3bo150b2o\$250b3obo72b2o4bobo59b3ob2o143b2o2b2o\$119bo38bo91bo2bo79b
2o65b2o142b2ob2o\$118bo38bo93b2o296bo143bo\$118b3o36b3o170b3o60b2o10bob
2o265bo18bobo298b4o\$115b2o37b2o105bo68bo63b2o9b2obo263bobo18b2o298bo4b
o8bo\$111bo3bobo32bo3bobo103bo70bo61bo15b2o262b2o323bo9bo\$109bobo3bo32b
obo3bo105b3o147bo585b2o8b2o\$110b2o37b2o106b2o144b2obobo136bo458b2ob3o\$
253bo3bobo143bob2ob2o135bo452b2o5b2o\$251bobo3bo285b5o143bo306bo2b2o\$
252b2o291bo143b2o308b2obo\$545bo135bo8b2o308bobob2o\$680bo14b2o302bo2b2o
bo\$396b2o282b3o2b3o7bobo301b2o\$395bobo287bo9bo\$397bo288bo\$540b2ob2o\$
541bobo\$540bo2bo\$540bobo\$541bo137b2ob2o\$680bobo2bo\$399bobo135bo3bo138b
o2b3o\$395bo3b2o134bobo2bobo138b2o\$396b2o2bo4bob2o123b2o2b2o2bobo140bo\$
395b2o8b2obo122bobo7bo139b3o\$409b2o122bo9b3o134bo\$402b2o6bo126b3o3bo
129bo6b2o\$402bobobobo130bo4bo129bo\$405b2ob2o128bo133b3o\$400bo\$395bo3b
2o\$393bobo3bobo285b2o\$394b2o257b2o33b2o\$652bobo22bo9bo13b2o\$654bo22b2o
22bobo\$676bobo22bo3\$700bo\$699b2o\$402bo296bobo\$401bo\$401b3o290bo\$693b2o
\$400bo292bobo\$401bo255b2o\$399b3o254bobo\$658bo2\$398bo6bob2o\$398b2o5b2ob
o\$397bobo9b2o\$402b2o6bo\$401bo2bobobo\$401b2o2b2ob2o3\$396b2o\$395bobo\$
397bo!
``````
Use dotted lines to separate different predecessors.