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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 mniemiec » June 2nd, 2016, 12:47 am

22-glider synthesis for one of the unsolved 18-bit P2s, griddle w/beehive and pre-block, based on this soup: http://catagolue.appspot.com/hashsoup/C1/n_E6sZsbs2bGTb4154167/b3s23. Because the corner bit of the stator exists before the activation step, this lends itself to other variations, such as 2 related griddles (w/loaf and mango), also for 22 gliders.
x = 163, y = 129, rule = B3/S23
11bo54bo$10bo55bobo27b2o$10b3o49b3ob2o27bo2bo$41b2o21bo6b2o22bobo3b2o$
10bo29bobo20bo6bobo23bo3bobo$10b2o29bo29bo29bo$9bobo9$115bo$116b2o$
115b2o$128bo$129bo$127b3o2$122bo$123bo6bobo$121b3o6b2o$131bo2$118bo24b
o$116bobo17bo4b2o$117b2o15bobo5b2o$135b2o$6b2o28b2o28b2o28b2o28b2o$5bo
2bo26bo2bo26bo2bo26bo2bo26bo2bo$5bobo3b2o22bobo3b2o22bobo3b2o22bobo3b
2o11bo10bobo3b2o$6bo3bobo23bo3bobo23bo3bobo3bo19bo3bobo9bobo11bo3bobo$
11bo29bo29bo4bobo22bo11b2o16bo8bo17bo$bo74b2o2b3o34b2o20b2o17bobo$2bo
77bo37b2o19bobo14bo4bo$3o33bo29bo9bo4bo14bo20bo8bo28bob4obo$35bobo27bo
bo7b2o18bobo6b2o19bobo6b2o19bobo3bo$3b2o2b2o27bo29bo8bobo18bo7bobo19bo
7bobo19bo3bo$2bobob2o97b2o28b2o23b2o$4bo3bo2$129b2o$128bobo$130bo2b3o$
133bo$134bo7$115bo$116b2o$115b2o$128bo$129bo$127b3o2$122bo$123bo6bobo$
121b3o6b2o$131bo2$118bo24bo$116bobo17bo4b2o$117b2o15bobo5b2o$135b2o$6b
2o28b2o28b2o28b2o28b2o$5bo2bo26bo2bo26bo2bo26bo2bo26bo2bo$5bobo3b2o22b
obo3b2o22bobo3b2o22bobo3b2o11bo10bobo3b2o$6bo3bobo23bo3bobo23bo3bobo3b
o19bo3bobo9bobo11bo3bobo$11bo29bo29bo4bobo22bo11b2o16bo8bo17bo$76b2o2b
3o34b2o20b2o17bobo$80bo37b2o19bobo14bo4bo$36bo29bo9bo4bo14bo20bo8bo28b
ob4obo$35bobo27bobo7b2o18bobo6b2o19bobo6b2o18bo2bo3bo$35b2o28b2o8bobo
17b2o7bobo18b2o7bobo18b2o3bo$105b2o28b2o23b2o$6b2o$5bobo2b2o$7bo2bobo
116b2o$10bo117bobo$130bo2b3o$133bo$8bo125bo$8b2o$7bobo5$115bo$116b2o$
115b2o$128bo$129bo$127b3o2$122bo$123bo6bobo$121b3o6b2o$131bo2$118bo24b
o$116bobo17bo4b2o$117b2o15bobo5b2o$135b2o$6b2o28b2o28b2o28b2o28b2o$5bo
2bo26bo2bo26bo2bo26bo2bo26bo2bo$5bobo3b2o22bobo3b2o22bobo3b2o22bobo3b
2o11bo10bobo3b2o$6bo3bobo23bo3bobo23bo3bobo3bo19bo3bobo9bobo11bo3bobo$
11bo29bo29bo4bobo22bo11b2o16bo8bo17bo$76b2o2b3o34b2o20b2o17bobo$80bo
37b2o19bobo14bo4bo$36bo29bo9bo4bo14bo20bo8bo28bob4obo$8b2o25bobo27bobo
7b2o18bobo6b2o19bobo6b2o18bo2bo3bo$7b2o25bobo27bobo8bobo16bobo7bobo17b
obo7bobo17bobo3bo$3b3o3bo25bo29bo29bo9b2o18bo9b2o18bo4b2o$5bo$4bo$8b3o
118b2o$8bo119bobo$9bo120bo2b3o$133bo$134bo!
mniemiec
 
Posts: 1038
Joined: June 1st, 2013, 12:00 am

Re: Synthesising Oscillators

Postby tennisplayer » June 17th, 2016, 12:35 am

synthesis of a p3 oscillator
x = 85, y = 353, rule = B3/S23
27bo23bo$28bo6bo15bobo$26b3o7bo14b2o$34b3o2$75bo$74bobo$41bo32b2o$41b
2o$40bobo$64b2o5b2o$64b2o5b2o$44bo$45bo$37b3o3b3o3bo24b2o$29b3o7bo8b2o
24bobo$31bo6bo9bobo24bo$30bo8$71bo$46bo23bobo$37bo8bobo21bobo$38b2o6b
2o23bo$37b2o$66b2o$65bo2bo$66b2o$50bo$49bobo$49b2o19b2o$70bo$68bobobo$
39b2o5b2o19bobobobob2o$39b2o5b2o19bobobobob2o$68bobobo$70bo$49b2o19b2o
$49bobo$50bo$66b2o$65bo2bo$66b2o$37b2o$38b2o6b2o23bo$37bo8bobo21bobo$
46bo23bobo$71bo7$42bo$41bobo$41bobo13bo$42bo14bobo$57b2o$37b2o8b2o$36b
o2bo7bobo$37b2o8bo3$41b2o26b2o$41bo27bo$39bobobo23bobobo$38bobobobob2o
18bobobobo$38bobobobob2o18bobobobo$39bobobo8bo14bobobo$41bo10bobo14bo$
41b2o9b2o15b2o3$37b2o$36bo2bo$37b2o2$42bo$41bobo$41bobo$42bo7$34bo$32b
obo$33b2o3$45bo$44bo$44b3o4$40b3o26b2o$42bo3b2o20bobo$35b3o3bo4bo22bo$
37bo6bobobo18bobobo$36bo6bobobobo16bobobobo$43bobobobo16bobobobo$44bob
obo18bobobo$46bo22bo$46b2o21b2o7$46b2o21b2o$45bobo20bobo$46bo22bo$44bo
bobo18bobobo$43bobobobo16bobobobo$36bo6bobobobo16bobobobo$37bo6bobobo
18bobobo$35b3o3bo4bo22bo$42bo3b2o20bobo$40b3o26b2o4$44b3o$44bo$45bo3$
33b2o$32bobo$34bo5$50bobo$50b2o$47bo3bo$48bo$46b3o3$46b2o21bo$45bobo
20bobo$46bo22bo$44bobobo18bobobo$43bobobobo16bobobobo$43bobobobo16bobo
bobo$44bobobo18bobobo$46bo22bo$45bobo20bobo$46b2o21bo3$46b3o$48bo$47bo
3bo$50b2o$50bobo12$46bo$44bobo$41b2o2b2o$42b2o$41bo26bo$46bo20bobo$45b
obo20bobo$46bo22bo$44bobobo18bobobo$43bobobobo16bobobobo$43bobobobo16b
obobobo$44bobobo18bobobo$46bo22bo$45bobo20bobo$46bo22bo8$45bo22bo$44bo
bo20bobo$45bobo20bobo$46bo22bo$44bobobo18bobobo$43bobobobo16bobobobo$
43bobobobo16bobobobo$44bobobo18bobobo$46bo22bo$45bobo20bobo$46bo20bobo
$41bo26bo$42b2o$41b2o2b2o$44bobo$46bo2$9bo$7bobo$8b2o3$2bo$obo$b2o2$
33bo$31b2o$32b2o$17bo$18b2o$17b2o2$26bo41bo$27bo20bo18bobo$25b3o19bobo
18bobo$48bobo18bo$49bo17bobobo$47bobobo14bobobobo$46bobobobo13bobobobo
$46bobobobo14bobobo$47bobobo17bo$49bo18bobo$22b3o23bobo16bobo$24bo22bo
bo16bobo$23bo24bo17bo$65b2o2$27b2o$28b2o2b2o$27bo4bobo$32bo18$32bo$27b
o4bobo$28b2o2b2o$27b2o2$65b2o$23bo24bo17bo$24bo22bobo16bobo$22b3o23bob
o16bobo$49bo18bobo$47bobobo17bo$46bobobobo14bobobo$46bobobobo13bobobob
o$47bobobo14bobobobo$49bo17bobobo$48bobo18bo$25b3o19bobo18bobo$27bo18b
obo18bobo$26bo19bo19bobo$45b2o19bo$17b2o46b2o$18b2o$17bo$32b2o$31b2o$
33bo2$b2o$obo$2bo3$8b2o37bo$7bobo29b2o4bobo24b2o$9bo30bo5b2o25bo$40bob
o9bo20bobo$41bobo8bobo19bobo$42bobo7b2o21bobo$43bo32bo6b2o$41bobobo28b
obobo4b2o$40bobobobo26bobobobo$40bobobobo26bobobobo$41bobobo28bobobo4b
2o$43bo32bo6b2o$42bobo7b2o21bobo$41bobo8bobo19bobo$40bobo9bo20bobo$40b
o5b2o25bo$39b2o4bobo24b2o$47bo8$60bo$49bo9bo$49bobo7b3o$49b2o2$34b2o
31b2o$35bo32bo$35bobo30bob2o$36bobo11bo18bo2bo$37bobo9bo20bobo$38bo6b
2o2b3o$36bobobo4b2o22bo2bo$35bobobobo26bobob2o$35bobobobo26bobob2o$36b
obobo4b2o22bo2bo$38bo6b2o2b3o$37bobo9bo20bobo$36bobo11bo18bo2bo$35bobo
30bob2o$35bo32bo$34b2o31b2o2$49b2o$49bobo7b3o$49bo9bo$60bo!
tennisplayer
 
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Re: Synthesising Oscillators

Postby mniemiec » June 17th, 2016, 5:06 am

tennisplayer wrote:synthesis of a p3 oscillator...

Very nice! The last 3 steps use 10 gliders to activate the still-life by hitting it with an interchange-like predecessor. The test tube baby-to-fumarole activation does the same thing from 5 gliders with an actual interchange predecessor, and that same mechanism can work here. The previous 2 steps each use 8 gliders to add a tail, while the standard 4-glider mechanism also works. This reduces the synthesis by 13 gliders from 57 to 44:
x = 84, y = 34, rule = B3/S23
4bo$3bo$3b3o$$obo$boo5bo$bo6bobo$8boo$64bo$bbobo22boo18boo13boo13boo$
3boo23bo19bo14boo13bo$3bo6bo17bobo17bobo27boboo$9bobo17bobo17bobo27bo
bbo$10bobo17bobo17bobo27bobo$11bo19bo19bo$9bobobo15bobobo15bobobo25bo
bbo$8bobobobo13bobobobo13bobobobo23boboboo$8bobobobo13bobobobo13bobobo
bo23boboboo$9bobobo15bobobo15bobobo25bobbo$11bo19bo19bo$10bobo17bobo
17bobo13boo12bobo$9bobo17bobo17bobo13boo12bobbo$3bo6bo17bobo17bobo16bo
10boboo$3boo23bo19bo29bo$bbobo22boo18boo6bo21boo$55boo$8boo44bobo6bo$b
o6bobo51boo$boo5bo53bobo$obo$60bo$3b3o54boo$3bo55bobo$4bo!
mniemiec
 
Posts: 1038
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Re: Synthesising Oscillators

Postby BobShemyakin » June 17th, 2016, 2:22 pm

mniemiec wrote:
tennisplayer wrote:synthesis of a p3 oscillator...

Very nice! The last 3 steps use 10 gliders to activate the still-life by hitting it with an interchange-like predecessor. The test tube baby-to-fumarole activation does the same thing from 5 gliders with an actual interchange predecessor, and that same mechanism can work here. The previous 2 steps each use 8 gliders to add a tail, while the standard 4-glider mechanism also works. This reduces the synthesis by 13 gliders from 57 to 44:
x = 84, y = 34, rule = B3/S23
4bo$3bo$3b3o$$obo$boo5bo$bo6bobo$8boo$64bo$bbobo22boo18boo13boo13boo$
3boo23bo19bo14boo13bo$3bo6bo17bobo17bobo27boboo$9bobo17bobo17bobo27bo
bbo$10bobo17bobo17bobo27bobo$11bo19bo19bo$9bobobo15bobobo15bobobo25bo
bbo$8bobobobo13bobobobo13bobobobo23boboboo$8bobobobo13bobobobo13bobobo
bo23boboboo$9bobobo15bobobo15bobobo25bobbo$11bo19bo19bo$10bobo17bobo
17bobo13boo12bobo$9bobo17bobo17bobo13boo12bobbo$3bo6bo17bobo17bobo16bo
10boboo$3boo23bo19bo29bo$bbobo22boo18boo6bo21boo$55boo$8boo44bobo6bo$b
o6bobo51boo$boo5bo53bobo$obo$60bo$3b3o54boo$3bo55bobo$4bo!


Synthesis is wonderful!
However, it contains an error in the first tennisplayer's step. Gliders, marked the point cannot pass each other, if you start early. Error can easily be corrected (it is necessary to push 6 gliders)
x = 59, y = 99, rule = B3/S23
6$7bo23bo$8bo6bo15bobo$6b3o7bo14b2o$14b3o2$22bo32bo$54bobo$21bo32b2o$
21b2o$20bobo$25bo18b2o5b2o$44b2o5b2o$24bo$25bo$17b3o3b3o3bo24b2o$9b3o
7bo8b2o24bobo$11bo6bo9bobo24bo$10bo32$32bo$2bobo25b2o$3b2o5bobo18b2o$
3bo7b2o$11bo2$55bo$54bobo$54b2o3$17b2o25b2o5b2o$16bobo25b2o5b2o$18bo2$
21bobo30b2o$22b2o2b2o26bobo$14bo7bo3bobo26bo$6bo7b2o10bo$6b2o5bobo$5bo
bo!
:
The first mniemiec's step can be reduced by 2 glider (to add the tail enough 3 gliders):
x = 44, y = 42, rule = B3/S23
3$14bo$13bo$7bo5b3o$8bo$6b3o3$9b2o20b2o$10b2o20bo$9bo4bo17bobo$13bobo
17bobo$14bobo17bobo$15bo19bo$13bobobo15bobobo$12bobobobo13bobobobo$4bo
7bobobobo13bobobobo$5b2o6bobobo15bobobo$4b2o9bo19bo$14bobo17bobo$13bob
o17bobo$14bo17bobo$32bo$31b2o8$b3o$3bo$2bo15b3o$18bo$19bo!

This reduces the synthesis by a further 2 gliders from 44 to 42:
x = 252, y = 116, rule = B3/S23
5$161bo$161bobo$161b2o$176bo$174bobo$119bo19bo35b2o$92bo25bobo17bobo$
53bo29bo8bobo23bobo17bobo$23bobo25b2o31b2o6b2o25bo19bo47bo$24b2o5bobo
18b2o29b2o101bo$24bo7b2o80b2o18b2o50b3o$32bo80bo2bo16bo2bo$114b2o18b2o
$76bo19bo59bo$75bobo17bobo58bobo23b3o18b2o18b2o$75b2o18b2o21b2o18b2o
16b2o10b2o14bo3b2o12bobo17bobo$118bo19bo29bo8b3o3bo4bo14bo19bo$116bobo
bo15bobobo10b2o13bobobo8bo6bobobo10bobobo15bobobo$38b2o25b2o5b2o11b2o
5b2o21bobobobob2o10bobobobob2o6bobo11bobobobo6bo6bobobobo8bobobobo13bo
bobobo$37bobo25b2o5b2o11b2o5b2o21bobobobob2o10bobobobob2o6bo13bobobobo
13bobobobo8bobobobo6bo6bobobobo$39bo76bobobo15bobobo25bobobo15bobobo
10bobobo8bo6bobobo$118bo19bo29bo19bo14bo8b3o3bo4bo$42bobo30b2o18b2o21b
2o18b2o28b2o18b2o13b2o14bo3b2o$43b2o2b2o26bobo17bobo119b3o$35bo7bo3bob
o26bo19bo$27bo7b2o10bo66b2o18b2o$27b2o5bobo76bo2bo16bo2bo$26bobo85b2o
18b2o85b3o$83b2o136bo$84b2o6b2o25bo19bo82bo$83bo8bobo23bobo17bobo$92bo
25bobo17bobo$119bo19bo70b2o$209bobo$211bo20$155bo$154bo$148bo5b3o$40bo
bo106bo$40b2o105b3o$37bo3bo34bo$38bo35bobo132bo$36b3o32b2o2b2o73b2o20b
2o18b2o13b2o13b2o$72b2o77b2o20bo19bo14b2o13bo$71bo23bo19bo19bo14bo4bo
17bobo17bobo27bob2o$16b2o18b2o18bo19bo17bobo17bobo17bobo17bobo17bobo
17bobo27bo2bo$15bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo
17bobo27bobo$16bo19bo19bo19bo19bo19bo19bo19bo19bo19bo$14bobobo15bobobo
15bobobo15bobobo15bobobo15bobobo15bobobo15bobobo15bobobo15bobobo25bo2b
o$13bobobobo13bobobobo13bobobobo13bobobobo13bobobobo13bobobobo13bobobo
bo13bobobobo13bobobobo13bobobobo23bobob2o$13bobobobo13bobobobo13bobobo
bo13bobobobo13bobobobo13bobobobo13bobobobo5bo7bobobobo13bobobobo13bobo
bobo23bobob2o$14bobobo15bobobo15bobobo15bobobo15bobobo15bobobo15bobobo
7b2o6bobobo15bobobo15bobobo25bo2bo$16bo19bo19bo19bo19bo19bo19bo8b2o9bo
19bo19bo$15bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo
13b2o12bobo$16b2o18b2o18bo19bo19bo19bo17bobo17bobo17bobo17bobo13b2o12b
o2bo$111bo23bo19bo17bobo17bobo16bo10bob2o$112b2o59bo19bo29bo$36b3o72b
2o2b2o55b2o18b2o6bo21b2o$38bo75bobo83b2o$37bo3bo74bo82bobo6bo$40b2o
165b2o$40bobo164bobo2$205bo$205b2o$142b3o59bobo$144bo$143bo15b3o$159bo
$160bo!


Bob Shemyakin
BobShemyakin
 
Posts: 214
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Re: Synthesising Oscillators

Postby Extrementhusiast » June 17th, 2016, 3:09 pm

BobShemyakin wrote:The first mniemiec's step can be reduced by 2 glider (to add the tail enough 3 gliders):
RLE

Your tails are facing the wrong way. However, it still works if the reaction is flipped the right way:
x = 40, y = 31, rule = B3/S23
9bo$7bobo$8b2o$12bobo$12b2o$13bo18b2o$33bo$6b2o7bo17bobo$5bobo6bobo17b
obo$7bo7bobo17bobo$16bo19bo$2bo11bobobo15bobobo$obo10bobobobo13bobobob
o$b2o10bobobobo13bobobobo$14bobobo15bobobo$16bo19bo$15bobo17bobo$14bob
o17bobo$15bo17bobo$33bo$32b2o5$18bo$17b2o$17bobo$3b2o$2bobo$4bo!


---

Here are a few more oscillators:
x = 1466, y = 652, rule = B3/S23
1027b2o$1027bobo$25bo189bo812b2o$23bobo190bo813b2o$24b2o188b3o718bo86b
2o2b3obobo$936bo85bo2bo3bob2o$934b3o86bobo3bo$1022b2obo3bob2o$896bo44b
o7bo76b3o2bo$444bobo449bobo40bobo5b2o82bo$445b2o449b2o42b2o6b2o78b3o$
271bo173bo582bo$272bo617bobo$95bo28bo26bo6bo33bo50bo26b3o6bo43bo19bobo
9bo26bo22bo35bo59bo37bo38bo31bo31bo22bo13bo29bo27bo31bo14bo7bo29bo20bo
26bo20b2o7bo37bo$94bobo26bobo24bo6bobo31bobo48bobo33bobo41bobo19b2o8bo
bo24bobo20bobo33bobo57bobo35bobo36bobo29bobo29bobo22b2o10bobo27bobo25b
obo29bobo11bobo6bobo27bobo20bo24bobo19bo7bobo35bobo27b2o$94bo2bo25bo2b
o16bo6b3o4bo2bo30bo2bo47bo2bo32bo2bo40bo2bo18bo9bo2bo23bo2bo19bo2bo32b
o2bo56bo2bo34bo2bo35bo2bo28bo2bo28bo2bo20b2o11bo2bo26bo2bo24bo2bo23bo
4bo2bo11b2o6bo2bo26bo2bo17b3o24bo2bo26bo2bo34bo2bo26bobo$95b2obo25b2ob
o15b2o13b2obo30b2obo47b2obo20bobo9b2obo40b2obo28b2obo23b2obo19b2obo32b
2obo56b2obo34b2obo35b2obo28b2obo28b2obo33b2obo26b2obo24b2obo20bobo5b2o
bo13b2o4b2obo26b2obo29bo14b2obo26b2obo27b2o5b2obo19b2o5b2o$97bobo26bob
o13bobo15bobo31bobo48bobo20b2o11bobo41bobo14b2o13bobo24bobo20bobo33bob
o57bobo35bobo36bobo29bobo29bobo34bobo27bobo25bobo20b2o7bobo12b2o6bobo
27bobo28bobo14bobo27bobo26bobo6bobo18bobo6b2o$93b3obo2bo18b2ob3obo2bo
23b2ob3obo2bo18bo2bob2ob3obo2bo33b2o2b2o4b3obo2bo19bo5b2ob3obo2bo36b3o
bo2bo12bobo9b3obo2bo19b3obo2bo15b3obo2bo28b3obo2bo52b3obo2bo30b3obo2bo
31b3obo2bo24b3obo2bo24b3obo2bo29b3obo2bo22b3obo2bo20b3obo2bo16b2o6b3ob
o2bo15b3obo2bo22b3obo2bo27b2o11b3obo2bo14bo3bo3b3obo2bo27bo2b3obo2bo
19bo2b3obobo$89b2o2bo2bob2o18bobobo2bob2o23bobobo2bob2o17bobo2b2obobo
2bob2o33bobob2o5bo2bob2o26b2obo2bob2o29bo6bo3bob2o15bo8bo3bob2o19bo3bo
b2o15bo3bob2o28bo3bob2o7bo44bo3bob2o30bo3bob2o31bo3bob2o24bo3bob2o24bo
3bob2o23bo5bo3bob2o22bo3bob2o20bo3bob2o16bobo5bo3bob2o11bo3bo3bob2o19b
2obo3bob2o25bo11b2obo3bob2o14bobobobobo3bob2o27b2obo3bob2o19b2obo3bob
2o$27b2o61b2o4bo22bo5bo26b2o5bo21b2o6bo3bo38bo3bo5bobo20b3o10bobo27bo
2bobo6b3obo28bo2bo22b2o2bo18b2o2bo31b2o2bo10bobo42b2o2bo33b2o2bo34b2o
2bo27b2o2bo27b2o2bo27bo4b2o2bo25b2o2bo23b2o2bo21bo5b2o2bo14b2o2b2o2bo
21bobob2o2bo29b2o8bobob2o2bo13b2o2bobobobob2o2bo31bob2o2bo25bo3bo26bob
obo$28b2o59bo5b2ob2o24b2ob2o29b2ob2o29b2ob2o46b2ob2o19bo11b2ob2o24b2o
2b2o7b2obob2o17bo8bobob2o21bobob2o17bobob2o30bobob2o7b2o45bobob2o32bob
ob2o33bobob2o26bobob2o26bobob2o22b3o6bobob2o24bobob2o22bobob2o26bobob
2o10bobo4bobob2o19bo4bobob2o25b2o9bobo3bobob2o11b2o2b2obobo3bobob2o28b
o3bobob2o22bo3bob2o$27bo3b3o33bo2bo27bobo11b2o13bobo31bobo18bo12bobo
48bobo17bo15bobo22bobo9bo2b2o2bobo16b2o8bo2bobo20b2o2bobo16b2o2bobo29b
2o2bobo53b2o2bo33b2o2bo34b2o2bo27b2o2bo27b2o2bo32b2o2bo25b2o2bo23b2o2b
o27b2o2bo18b2o2bo25b2o2bo38b2o3b2o2bo11bo8b2o3b2o2bo28b2o3b2o2bo24b3o
2bo$19b2o10bo34bo31bobo12b2o2bo9bobo31bobo18b2o5b2o4bobo48bobo33bobo
34b2o5bobo15bobo11bobo17bo6bobo20bobo33bobo3b3o51bobo35bo38bo15bo15bo
31bo21b2o13bo29bo27bo3bobo25bo22bo29bo47bo29bo37bo29bo$18bobo11bo33bo
3bo28bo12bo3b2o10bo20b2o11bo18bobo5bobo4bo50bo35bo43bo31bo19bo6bo17b2o
3bo30b2o3bo4bo49b4ob2o31b4o35b4o17b2o9b4o28b4o21bobo9b4o24b6o22b6o4b2o
20b6o17b6o17bo6b6o42b6o24b6o32b6o27b3o$20bo45b4o46bobo26b2o2bobo3b3o
31bo187b3o24bobo33bobo8bo48bo2bo34bo38bo19b2o3bobo4bo24b3o3bo27bo8bo
28bo27bo10bo20bo2bo19bo2bo19b2o5bo2bo44bo2bo11b2o13bo2bo34bo2bo29bo$
146b2obo5bo30b2o83b3o38bo69b3o20bo35b2o20b4o34bobo35bo38b3o22b2o5b3o
23bo4bob2o31bobob2o26bob2o24bob2o71bobo69b2o41b2o$30bo19b2o93bo10bo18b
2o8bobo85bo38b2o68bo80bo3bo34bo37bo39bo22bo9bo21bo4b2ob2o32b2ob2o25b2o
b2o23b2obobo141bo4b2o36bobo$29b2o18b2o125b2o9bo84bo38bobo37b2o26b2o2bo
27b2o50bo28bo20b2o24b2o31bo39b2o23bo94bo6bo74b3o71b2o37bo2b2o95b2o$29b
obo19bo123bo103b3o70b2o6b2o16bobo26bo2b2o43b3o6bo2bo22bobo19b2o34b2o
23bo62b2o92bobo14bo66bo72bo41b2o96bobo$279bo71bo7b2o19bo26b2o3bo42bo
31b2o2b2o21bo29b2o2bobo20b3ob2o40b2o17bobo65b2o2b2o2b2o13b2o2b2o12b2o
68bo115bo96b2o$280bo25b2o47b3o3bo44bobo42b2o3bo29bobo56b2obo26bobo39bo
bo57b3o25b2ob2ob2o15b2o5b2o4b3o2b2o282b2o$272b3o30bobo49bo77bo14b2o36b
o20b3o32bo7b2o21bo25bo15bo61bo24bo8bo13bo8b2o3bo284b3obobo$274bo32bo
48bo78b2o15bo42bo13bo42bobo46b2o10b3o62bo56bo6bo279b2obo3bob2o$273bo
160bobo58b2o13bo21bo19bo18b3o26bobo12bo64b3o27b2o311bobo3bo$439b3o12bo
39bobo35b2o39bo40bo65bo28bobo24b2o284bo2bo3bob2o$49b2o390bo11b2o14b2o
29b2o29bobo38bo108bo29bo24bobo283b2o2b3o2bo$49bobo388bo12bobo13bobo27b
obo234bo5bo288bo$49bo419bo31bo239b2o285b3o$8b2o500b3o228bobo284bo$9b2o
499bo$8bo502bo5$60b3o$60bo$61bo66$309bo$174bobo132bobo310bo$175b2o132b
2o312bo$175bo445b3o$171bo20bobo$56bo115b2o18b2o627bo$57b2o112b2o20bo
436bo188bobo$56b2o62bo455bo54b2o187b2o3bo$66bobo50bo457bo7bo44b2o191b
2o$66b2o51b3o132bobo318b3o5bobo39bo198b2o$67bo49bo136b2o40bo287b2o40b
2o4bo195bo$115bobo137bo40bobo294bo31b2o4bo182bobo11bobo$35bo80b2o8bo
95bo30bo42b2o157bo67bo19bo42bo4b2o38b3o181b2o11b2o$34bo14bo74b2o96bobo
29bo198b2o69b2o18bo40bo6b2o221bo$34b3o10bobo14bobo58b2o95b2o28b3o199b
2o67b2o17b3o40b3o77b2o32b2o44b2o45b2o18bo9b2o$32bo15b2o15b2o150bo398bo
31bo16b2o32b2o44b2o45b2o16bobo9b2o$7bo25bo31bo152bo3bo232bo158bobo32b
2o160b2o41bo$7bobo21b3o22b2o23b2o29b2o67b2o3b2o28b3o2bobo3b2o19b2o4b2o
23b2o2bo15bo31b2o2bo24b2o2bo27b2o2bo27b2o2bo26b2o4b2o2bo27b2o2bo38b2o
2bo34b2o2bo35b2o9b2o2b2o16b2o11b2o2b2o28b2o2b2o40b2o2b2o41b2o2b2o24b2o
2b2o29bobo$7b2o47b2o5b2o16bobob2o25bobob2o63bobobobo33bo2bobobo19bo2bo
bobo23bo2bobo13bo32bo2bobo23bo2bobo26bo2bobo26bo2bobo24bobo4bo2bobo26b
o2bobo37bo2bobo7bo25bo2bobo45bo2bobo29bo2bobo28bo2bobo40bo2bobo41bo2bo
bo24bo2bobo29bobo$62b2o18b2obo27b2obo65b2obo36b3obo22b3obo26b3obo13b3o
31b3obo2b2o20b3obo2b2o23b3obo2b2o23b3obo2b2o28b3obo27b3obo38b3obo6bo
27b3obo8bo37b3obob2o27b3obob2o26b3obob2o38b3obob2o39b3obob2o22b3obob2o
25b2obob2o$8b2o39b2o13bo20bo7bo22bo68b2o39b2o25b2o29b2o9bo40b2o2bo24b
2o2bo27b2o2bo27b2o2bo32b2o30b2o21b3o17b2o5b3o29b2o7bobo39bobo32bobo31b
obo43bobo44bobo27bobo29bobo$7bobo24b2o12bobo4b2ob2o22b3o8bobo17b3o66b
3o2bo36b2o2bo22b2o2bo26b2o2bo9b2o36b2o2b2o23b2o2b2o26b2o2b2o26b2o2b2o
31b2o2bo27b2o2bo22bo15b2o2bo34b2o2bo6b2o38b2o2bo30b2o2bo29b2o2bo41b2o
2bo27bo14b2o2bo25b2o2bo27b2o2bo$9bo2bo17b2o2bo2bo12bo3bobobo2bo19bo2bo
bo6b2o17bo2bobo11b2o37bo12bo2bobo2b3o30bo2bobo2b3o16bo2bobo2b3o20bo2bo
bo2b3o4b2o35bo2bobo17bobo3bo2bobo26bo2bobo26bo2bobo6b2o23bo2bob2o22b2o
bo2bob2o21bo11b2obo2bob2o7b2o18bob2obo2bobobo38bob2obo2bobo26b2obo2bob
o25b2obo2bobo37b2obo2bobo26bobo9b2obo2bobo21b2obo2bobo23b2obo2bobo$12b
obo16b2o3b2o17bo4b2o19b2o2b2o3b2o20b2o2b2o2b2o7bobo34bobo12b2o2bo36b2o
2bo22b2o2bo26b2o2bo14b3o30b2o2b2o18b2o3b2o2b2o26b2o2b2o26b2obobo5b2o
15b3o6b2obobo22bobob2obobo33bobob2obobo8bobo17b2obob2obobobo38b2obob2o
bob2o22bobobob2obob2o16bo6bobob2obob2o27bobo5bobob2obob2o26b2o8bobob2o
bob2o19bobob2obob2o22b2ob2obob2o$12b2o16bo59bobo27b2o7bo37b2o3bo126bo
29bo26bo71b2o8bo16bo9bobo23bo5bobo24b2o7bobo4bobo8bo22bobo2bo2bo42bobo
2bo25b2o2bobo2bo17bobo6bobobo2bo31b2o5bobobo2bo39bobobo2bo22bobobo2bo
24bo3bo2bo$90bo82bo126bo29bo30b2o30b2o30b2o27bo10b2o30b2o26b2o7b2o4b2o
32b2o2b2o32bo12b2o2b2o29b2o2b2o18b2o5b2ob2o2b2o26b3o2bo5b2ob2o2b2o7bob
o28b2ob2o2b2o20b3ob2o2b2o22b3ob2o2b2o$13b2o156b3o154b3o26bo3bobo29bo
31bo98bo88b2o113bo24b2o22b2o4bo2bo25bo3bo27bo3bo$12bobo318b3o21b2o3bo
28bobo6bobo16bo3bobo8b2o25bo25bo124b2o71bo41bo3b2o21bo16b2o3bobo5bobo
25bobobo27bobobo$14bo40b3o114bo160bo22bobo32b2o7b2o15bobo3b2o5bo2b2o
25b2o25b2o163bobo30b2o43bo2bo9b2o25bobo5bo6bo27bobo29bobo$55bo116b2o
156b2o2bo27b2o31b3o3bo16b2o10b2o3bo24bobo23bobo99b2o29b2o32b2o29bobo
10b2o31bo2bo4bo3bo2bo3bo22bo41bo31bo$56bo75b3o36bobo155bobo30bobo32bo
31bobo156bobo23b3ob2o33bo38b3ob2o33b2o5b2o2bo2bo2b2o$115b2o15bo198bo
30bo33bo4b2o21bo64b3o96bo27bo3bo73bo3bo38bobo3b2o3bobo$114bobo16bo146b
o119bobo21b2o63bo37b2o19bo66bo37b3o37bo37bo$116bo163b2o120bo20bobo64bo
35bobo18b2o106bo75b2o$127b2o150bobo13bo232bo18bobo104bo75bobo6b3o37b3o
5b2o$126b2o166b2o443bo41bo4b2o$128bo165bobo353b3o87bo39bo7bo$652bo$
278b2o371bo129b2o$279b2o499b2o$278bo503bo8b3o$791bo$792bo2$180b3o$179b
o2bo$182bo$182bo$179bobo18$757b3o$757bo$758bo34$42bo$40b2o$22bo18b2o$
20bobo$21b2o$25bo$23b2o5bo176bo136bo179bo19bo$24b2o2b2o175b2o22bo112bo
bo177b2o21bo$29b2o11bo106bobo54b2o22bo11bo100b2o34bo143b2o18b3o$33bo7b
2o101bo4b2o51bo25b3o10bo71bo32bo32bobo39bo131bobo$32bobob2o3bobo98bobo
5bo22bobo27b2o5bo21bo8b3o33bo36bo31bobo26b2o2b2o40bobo129b2o$33b2ob2o
35b2o20b2o18b2o21b2o3b2o21b2o8bo18b2o5b2o4b2o14b2o5bo32b2o9b2o8bo18b2o
6b3o3bo19b2o6b2o20b2o4bo2bo26b2o15b2o20b2o42b2o21bo29b2o12bo22b2o$73bo
bo19bobo17bobo20bobo25bobo7bo18bobo11b2o13bobo4b3o30bobo4b2o3b2o5b2o
19bobo9b2o20bobo27bobo4b2o27bobo9bo26bobo41bobo13bo4b2o30bobo14bobo17b
obo$21bo53bo21bo19bo22bo7bo19bo4bo2bo20bo7bo20bo39bo4b2o7b2o2b2o20bo
10b2o21bo29bo12bobo20bo10bo2b2o23bo43bo14b2o3b2o31bo14b2o20bo$22bo4bo
7b2o28bo9b2o20b2o18b2o21b2o5bo20b2o4b3o20b2o5bo21b2o38b2o12bobo23b2o
32b2o28b2o11b2o21b3o6b3o2bobo22b3o41b3o11b2o7b2o28b3o13bo20b3o$20b3o5b
o5bo2bo28bo6b2o2bo17b2o2bo4bo10b2o2bo18b2o2bo4b3o16b2o2bo24b2o2bo4b3o
17b2o2bo35b2o2bo11bo23b2o2bo29b2o2bo3bo21b2o2bo3bo7bo19b2o5b2o7bo22b2o
5b2o3b2o30b2o5b2o3b2o11bobo25b2o5b2o28b2o5b2o$2bobobo19b3o4bob2o27b3o
5bo2b2o17bo2b2o5bobo7bo2b3o17bo2b3o22bo2b3o5bo17bo2b3o23bo2b3o34bo2b3o
7bo26bo2b3o2b2o3bo20bo2b3o2bobob2o16bo2b3o2bobob2o22bo2b2o5bo28bo2b2o
5bobobo29bo2b2o5bobobo11bo26bo2b2o5bob2o23bo2b2o5bo$34bo38b2o19b3o7b2o
8b3o20b3o25b3o6b2o18b3o13bo12b3o6b2o9b2o18b3o6b2obobo25b3o5bobobobo19b
3o5bobobobo15b3o5bobobobo4b2o15b3o5bobo2bo25b3o5bobobo31b3o5bobobo40b
3o5bobob2o23b3o5bobo$35b2o38b2o20b2o18b3o20b3o25b2obo3b2o20b2obo8b2o
15b2obobobo9bobo20b2obobobobobo28b2obobobobobo22b2obobobobobo18b2obobo
bobobo3b2o19b2obobobobobo27b2obobobobobo9bo22b2obobobobo43b2obobobo11b
o17b2obobob2o$36bo38bobo18bo2bo3bo12bo2bo19bo3bo23bo2b2o24bo2b2o8bobo
13bo2b2obo11bo21bo2b2obobo2bo28bo2b2obobo2bo22bo2b2obobo2bo18bo2b2obob
o2bo6bo17bo2b2obobo2b2o26bo2b2obobo2b2o8bo22bo2b2obobobob2o39bo2b2obob
ob2o7b2o16bo2b2obobo$35bo40bo20b2o3b2o13b2o20b2ob2o23b2o9b3o15b2o3b2o
22b2o3bobo32b2o3bo2bo31b2o3bo2bo7b2o16b2o3bo2bo21b2o3bo2bo27b2o3bo2bo
30b2o3bo2bo12b3o20b2o3bo2bobo2bo39b2o3bo2bob2o7bobo15b2o3bo2bo$24b3o8b
2o65bobo42bobo28bo22bobo26bobo37bobo37bobo7b2o22bobo27bobo33bobo36bobo
41bobo3b2o45bobo34bobo$26bo92bo27b2o25b2o3bo22bo3b2o23bo8b2o29bo39bo
10bo22bo29bo35bo38bo43bo52bo10bo25bo$25bo68bo23b2o28bo24b2o30b2o33bobo
314b2o$66b2o26b2o22bobo49bo4bo25b2o4bo32bo218b2o46b3o47bobo$30b2o10b2o
21bobo25bobo19bo33b3o18b2o28bobo256bobo45bo46bo$31b2o9bobo22bo4b2o41b
2o32bo19bobo30bo256bo48bo44b2o$30bo11bo30b2o6b2o31bobo24b3o6bo80b2o
222b3o95bobo$72bo7b2o61bo88b2o223bo46b3o38bo$76b3o3bo59bo88bo224bo47bo
40b2o$78bo426bo38bobo$77bo158b3o$236bo262b2o$237bo262b2o64bo$499bo65b
2o$234b3o328bobo$236bo$235bo51$984bo$984bobo$984b2o5$942bo$943b2o23bo$
942b2o23bo$960bo6b3o449b2o$958bobo458b3o$959b2o450bo6bob2o4bo$945bo18b
o444bobo6b3o5bobo$559bo199bo186b2o14bobo445b2o7bo6b2o$558bo65bo132bobo
185b2o16b2o436bobo$468bo89b3o64b2o131b2o9bo632b2o$4bo103bo237bo29bo35b
o53b2o56bo24bo74b2o144b2o186bo13bobo427bo3bobo$2bobo104b2o233b2o26bob
2o34bobo44bobo7b2o51bo2bo26bo6bo71bo30bo30bo77b2o188b2o11b2o341bo91b2o
$3b2o103b2o235b2o23bobo2b2o4bobo27b2o45b2o61bob3o22b3o4bobo60bo10bobo
27bo32b2o69bo86bo3bo99bo3b2o13bo340bo92bo12bo$15bo325bo24bo4b2o8b2o75b
o41bobo16b3o34b2o3bo57b2o2bo5b2o28b3o29b2o68bobo10bo45bo30b2obobo85bo
2bo6bobo355bo3b3o102bo$15bobo321bobo10bo14bo14bo27bo64bobo23b2o58bobo
54b2o4b2o23bo80bo31b2o4bo5bobo43bobo27b2o2b2o90bo6b2o356b2o7bo5bobo90b
3o$15b2o241bo27bo53b2o5bo2b2o13b3o6bo26bo7b2o64b2o16b2o6bo22b2o22b2o
11b2o60b2o7bobo15b2o79bo35bo6b2o44b2o120bo3bo247bobob4o108b2o6b2o6b2o
80bobo$3bo254bobo24bo59b2o4b2o16b3o3b2o6b2o17b2o5bobo64bo15bo2bo7bo19b
o2bo3bo18b2o2b2ob2o56bo5bo11b2o15b2o44bobo31b3o35b3o173b4o247b2o2bo3bo
116b2o6bo27bo53b2o$bobo254b2o21bo3b3o48bobo7b2o23bo2b2o6b2o17b2o3bo24b
2o34b2o23b2obo2bo3bo20b2obo2bobo16bo4b2obo2bo32b2o20b2o4b2o6b2o3bo12b
2o7b2o34bo3b2o36bo72bo48bo339bo2bo86bo70b2o51bo$2b2o96bobo94bo36bo47b
2o53b2o11bo5bo13bo13bo20bobo23bo35bo9b2o16bobobo2b3o21bobobo25bob2o4b
2o25bobo19bobo3bobo5bobo15bobo7bo36b2o2bo36bobo69bobo9bobo34bobo49b2o
58b2o49b2o18bo34b2o66b2o43bo4b2o7bo2bo83b2obobo63b2o64bobo5bo$100b2o
96b2o35bo3bo17bo3b2o18b2o29b2o4bo18bo3b2o6b2o4b2o21b2o21b2o3bobo23bo8b
obo24bo7bo2bo15bo2bo27bo2bo3b2o21bo6b2o21bo4bo35bo19bo8bo30bo3b2o32bo
7b2o28bobo7bo30bo2bo9b2o34bo2bo47bo2bo56bo2bo50bo16b2o36bo67bo44b2o3bo
35b2o35bo4b2o14b2o2b2o130b2o5bo$101bo95b2o34b3ob2o16bobo2bo2bo48bobo3b
obo20bobo5bobo3bobo21bo22b2o4bo22b2o8b2o24b2o7bo2bo14b2o29b2o5b2o21b2o
8bo18bobo3b2o34b2o27b2o28b3o35b3o38b2o5b3o30b3o11bo34b3o39bobo6b3o57b
3o51bob2o14b2o35bob2o64bob2o12bo27b2o4bob2o31bo2bob2o32b2obo2bob2o15bo
20b2o54b2o36b2o15bo5b3o4b2o13b2o$238b2o16b2o2bo2bo23bo26bo3b2o23bo34bo
22bo5bo22bo11bo23bo10b2o14bo30bo9bo19bo26b2o2b2o2bo34bo28bo30bo9bobo
25bo41bo5bo45bo43bo30bo3b2o14bo59bo45b2obobo6bo42b2obobo6b2o54b2obobo
6b2o2bo4b3o26b2obobo6b2o22bo2bobobo6b2o22b2o2bo2bobobo6b2o27bobo6b2o
26bo18bobo35bobo27bobo12bobo$172bo88b2o3bo20b3o24b3o26b2o33b2o27b2o22b
2o34b2o25b2o29b2o28b2o25b2o6b2o32b4o25b4o27b4o6b2o3bobo20b4o44b4o3b2o
25b3o3b2o3b2o36b3o3bobob2o27b2o2bo7b3o3bobob2o48b3o3bobob2o46b3o3bobob
2o43b3o3bobo6bo52b3o3bobo2b3o2bo19b3o11b3o3bobo23b2o4b3o3bobo27b2o4b3o
3bobo29b3o3bobo24bobo20b3o35b3o16bo8bo16b3o2b2o$44b2o30b2o42b2o51b2o
90bo24bo26bo27bo34bo28bo23bo8b2o25bo26bo30bo29bo23bo10bo35bo28bo30bo6b
o3b2o25bo47bo2bo25bo3bo2bo4bobo5b2o27bo3bo2bobob2o26b2o10bo3bo2bobob2o
25b2o12b2o6bo3bo2bobob2o45bo3bo2bobob2o42bo3bo2bo8bobo49bo3bo2bo10bo
20bo10bo3bo2bo30bo3bo2bo19b2o13bo3bo2bo25b2o3bo3bo2bo27b2o14b2o3bo3bo
33bo3bo14bo25bo3bo2bo$44bo31bo43bo34b2o15b2o10b2o26b2o20b2o21b2o6b3o
19b2obo23b2obo25b2obo31b2obo25b2obo20b2obo7bobo22b2obo23b2obo27b2obo
26b2obo31b2obo32b2obo25b2obo27b2obo10bo23b2obob2o41b2obobo24bobobobobo
11b2o27bobobobobobo40bobobobobobo25b3ob2o12b2o4bobobobobobo47bobobobob
obo44bobobobob2o7b2o8b3o30bo7bobobobob2o29bo10bobobobobobo27bobobobobo
bo18b2o11bobobobobobo23bobobobobobob2o42bobobobobobob2o28bobobobob2o
10b3o22bobobob2o$45bo31bo21b3o2b2o15bo29b2obobo12b2o9b2obobo22b2obobo
16b2obobo17b2obobo2b3o19b2obobob2o3bo14b2obobob3o19b2obobob3o25b2obobo
b3o19b2obobob3o14b2obobob3o5bo20b2obobob3o17b2obobob3o21b2obobob3o20b
2obobob3o25b2obobob3o26b2obobob3o19b2obobob3o21b2obobob3o28b2obobob2ob
o22bo14b2obobob2o21b2o2bo3bob2o14bo22b2o2bo3bobo2b2o36b2o2bo3bobo2b2o
25b5o12bo6bo3bobo2b2o47bo3bobo2b2o40b2o2bo3bobo6bo12b5o23b3o4bo2b2o2bo
3bobo7b3o29b2o2bo3bobo2b2o23b2o2bo3bobo2b2o17bo9b2o2bo3bobo2b2o9bo15bo
bo3bobobo45bobo3bobobo29bo3bobobo36bo3bobo$15bo4bo23b2o30b2o23bob2o15b
2o27bo2bob2o12bobo8bobob2o20bobobob2o16bobob2o17bobob2o3bo20bobob2o7bo
bo11bobob2o5bo17bobob2o5bo23bobob2o5bo17bobob2o5bo12bobob2o5bo24bobob
2o5bo15bobob2o5bo19bobob2o5bo18bobob2o5bo23bobob2o5bo24bobob2o5bo17bob
ob2o5bo19bobob2o5bo26bobob2o29b2o11bobob2o25bobobob2o41bobobob3obo40bo
bobob3obo30b3o8b2o7b2obob3obo48b2obob3obo44bobobob3obo4b2o12b2ob3o25bo
2b3o2bobobob3obo7bo31bobobob3obo27bobobob3obo10bo20bobobob3obo11b2o15b
2obob3obobobo29b3o10b2obob3obobobo26b2ob3obobobo33b2ob3obo$16b2obo23bo
31bo24bo4bo13bo29b2o2bo16bo5bobo3bo22b2o3bo18bo2bo19bo2bo6bo19bo2bo9b
2o12bo2bo6b2o17bo2bo6b2o23bo2bo6b2o17bo2bo6b2o12bo2bo6b2o24bo2bo6b2o
15bo2bo6b2o19bo2bo6b2o18bo2bo6b2o23bo2bo6b2o24bo2bo6b2o17bo2bo6b2o19bo
2bo6b2o3b3o20bo2bo30b2o5bobo4bo2bo24b2obobo2bo40b2obobo2bo3bo38b2obobo
2bo3bo41bobo8bo2bo3bo35b2o4bo8bo2bo3bo10b2o35bo2bo3bo6b2o12b2o27bo10bo
2bo3bo9bo32bo2bo3bo30bo2bo3bo10bo23bo2bo3bo13b2o15bo2bo3bo3b2o31bo14bo
3bo3b2o25bo2bo3bo3b2o14b2o16bo2bo3bo$15b2o2b3o22b4o28b4o40b4o18b2o10b
4o18b2o5b4o24b4o13b2o3b4o14b2o3b4o21b2o3b4o18b2o3b4o20b2o3b4o26b2o3b4o
20b2o3b4o15b2o3b4o27b2o3b4o18b2o3b4o22b2o3b4o21b2o3b4o26b2o3b4o27b2o3b
4o20b2o3b4o22b2o3b4o7bo21b2o3b4o11b2o21b2o3b2o3b4o20b2obobo3b4o36b2obo
bo3b3o39b2obobo3b3o44bo6bobo3b3o37b2o4bo5bobo3b3o7bo2b2o35b2o3b3o60b2o
3b3o41bobo3b3o29bobo3b3o11b3o19bobo3b3o4b2o23bobo3b3o27bo8bo16b3o31b2o
2b3o20bobo15b2o2b3o$47bo31bo43bo19b2o2bo9bo28bo27bo21bo22bo29bo4bo21bo
28bo34bo28bo23bo35bo26bo30bo29bo34bo35bo28bo30bo8bo28bo11bobo20bo12bo
24bo7bo5bo34bo50bo58b2o43bo4b3o5b2o14b2o3bo95b3o11bobob2o36b2o6bobob2o
24b2o6bobob2o28b2o6bobobo2bo2b2o18b2o6bobo23bobo27bobo35bobo18bo23bobo
$8bo37bo31bo41b3o19bo3b2o6b3o26b3o25b3o19b3o20b3o27b3o4b2o18b3o26b3o
32b3o26b3o21b3o33b3o24b3o28b3o27b3o32b3o33b3o26b3o28b3o5b2o28b3o12bo
20bo11b3o30b3o5b2o39b3o35b2o11b3o57b3o55b3o6bobo43b3o55bo12b2obo46b2ob
o34b2obo4b2o16bo15b2obo2bob2o28b2o24b2o4b3o5bo15b2o36b2o43b2o$9bo5bo
30b2o29bo42bo25bobo5bo16b3o9bo17bobo7bo21bo22bo29bo6bobo17bo28bo34bo
28bo23bo35bo26bo30bo29bo34bo35bo28bo30bo6b2o29bo4bo30b2o10bo32bo7bobo
37bo2bo36b2o9bo2bo56bo2bo54bo2bo51bo2bo54bo16bo49bo37bo3b2o17b2o2b2o
14b2o4bo61bo5b2o$7b3o3b2o62b2o94bo28b2o490bo33b2o28bobo91bobo36bo11b2o
58b2o42b3o11b2o53b2o73b2o48b2o25bo2bo7b2o4bo15bobob2o82bo5bobo64b2o$
14b2o22bobo27b2o102bo29bo524bobo123bo155bo222bo2bo31bo101bo51b2o$39b2o
26bobo2b2o734b3o197bo88b4o127bo3bo2b2o64bo6b2o58b2o53bo$39bo29bob2o
129b3o551b2o44b2o6bo286bo3bo127b4obobo64b2o6b2o6b2o49bobo$64b2o7bo130b
o550bobo43bobo5bo4b2o37b2o2b2o230b2o6bo202bobo5bo7b2o39b3o$38b2o12b3o
8bobo137bo553bo45bo10bobo35bobob2o231bobo6bo2bo210b3o3bo40bo$37bobo12b
o12bo19bo728bo39bo3bo211bo13b2o3bo224bo43bo12bo$39bo3bo9bo30b2o113b3o
605b2o261b2o11b2o228bo56b2o$42b2o40bobo114bo604b2o261bobo13bo284bobo3b
o$21b2o19bobo80b2o73bo607bo9b2o555b2o$20b2o103bobo690bobo258b2o16b2o
276bobo$22bo102bo692bo260bobo14b2o253b2o6bo7b2o$1079bo18bo251bobo5b3o
6bobo$1083b2o267bo4b2obo6bo$1083bobo271b3o$1074b3o6bo274b2o$1076bo23b
2o$1075bo23b2o$1101bo5$1058b2o$1057bobo$1059bo39$466bobo458bobo$467b2o
458b2o$467bo51bo356bo51bo$518bo358bo$518b3o354b3o3$471bo452bo$469bobo
452bobo$470b2o452b2o$729bo358bo$728bo360bo$728b3o356b3o8$716bo384bo$
714bobo3bo376bo3bobo$183bo91bo154bo284b2o4b2o90bo281b2o4b2o$182bo90b2o
156bo288b2o90bo283b2o$182b3o85bo3b2o153b3o147bo232b3o150bo$132bo135bob
o309bo5bo135bo235bo5bo130bo$130bobo136b2o156bo17bo132b3o3bobo134bo76bo
17bo141bobo3b3o129bo$73bo21bo35b2o18bo25bo10bo239bo16bobo137b2o134b3o
72bobo16bo142b2o134b3o$72bo23bo44b2o8bobo21bobo8b2o83bo154b3o16b2o183b
o38bo127b2o16b3o179bo42bo$55bo16b3o19b3o16bo26b2o9b2o23b2o9b2o81bo247b
o68bo43bo37bobo205bo79bo38bo41bobo$56bo11bo31bo11bo24b2o3bo28bo98b3o
244bo62bo4b2o42b3o37b2o207bo79b2o4bo31b3o40b2o$54b3o11bobo27bobo11b3o
23b2o32bo344b3o61bo4b2o45bo242b3o78b2o4bo30bo$68b2o29b2o36bo32b3o94bob
o5bo239bo63b3o50bo34bo8bo203bo82b3o29bo37bo8bo96bobo$263b2o3b2o4bo169b
o69b2o116b3o33b2ob2ob2o123bo80b2o111b3o38b2ob2ob2o95bobobobo$168b2o6b
2o86b2o2bo5b3o165b2o70bobo150b2o2b2o2b2o123b2o77bobo151b2o2b2o2b2o95b
2ob2o$167bobo7bo85bo179b2o326b2o26b2o19b2o88b2o59b2o34b2o41b2o47b2o33b
2o9b2o26b2o9b2o$61bo45bo61bo4b3o34b2o94bo41bo33bo44bo61bo87bo5b2o39bo
38bo58bo4bo37bo5bo42bo5bo83bo5bo47b2o5bo5bo29bo5bo36bo5bo37bo4bo5bo33b
o5bo5bo26bo11bo$62bo43bo67bo8b2o24bo2bo56bob2o33bobo39bobo31bobo6bo35b
obo16bo42bobo85bobo3bo2bo3bo33bobo3b2ob2o28bobo3b2ob2o48bobo2bobob2o
25bo6bobo4bob2o21bo16bobo4bob2o79bobo4bob2o39bo3bo2bo3bobo4bob2o17b2ob
2o3bobo4bob2o24b2ob2o3bobo4bob2o30b2obobo2bobo4bob2o27b2obo4bobo4bob2o
20b2obo11bob2o$28b2o3b2o25b3o4b2o3b2o26b2o4b3o74bobo23b3o57b2obo34bo
41bo33bo8b2obobo30bo7bo8b2o43bo6b2o79bo4b2obo2bobo33bo4b2obo2bo27bo4b
2obo2bo47bo4b2obo2bo17bobob2o8bo4b2obo2bo19b2o8bo7bo4b2obo2bo70b2o6bo
4b2obo2bo36bobo2bob2o4bo4b2obo2bo13bo2bob2o4bo4b2obo2bo20bo2bob2o4bo4b
2obo2bo26bo2bob2o4bo4b2obo2bo23bo2bob2o4bo4b2obo2bo16bo2bob2o9b2obo2bo
$28bo2bo2bo32bo2bo2bo24bo2bo43bo29bo7bo207b2o2b2o39bo8bobo49bo88bobobo
42bob2o35bob2o55bob2o18b2o2b2o15bob2o18bobo8bo15bob2o71bo14bob2o37bobo
bo15bob2o13b2obo15bob2o20b2obo15bob2o26b2obo15bob2o23b2obo15bob2o16b2o
bo15bob2o$29b5o24b2o8b5o23b5o8b2o32b5o25b5o29b5o55b5o33b5o37b5o29b5o
10bo29b5o5bo51b5o5bo77b5o5bo2bo33b5o5bo28b5o5bo48b5o5bo21bo10b5o5bo32b
o5b5o5bo73bo5b5o5bo41bo2bo5b5o5bo19bo5b5o5bo26bo5b5o5bo32bo5b5o5bo29bo
5b5o5bo22bo5b5o5bo$obobo13bo25bo12bobo35bo13bobo30bo5bo23bo5bo27bo5bo
24bobobo24bo5bo31bo5bo35bo5bo27bo5bo38bo5bo55bo5bo3b2o76bo5bo3b2o35bo
5bo3b2o27bo5bo3b2o47bo5bo3b2o31bo5bo3b2o37bo5bo3b2o73b2o3bo5bo3b2o44b
2o3bo5bo3b2o19b2o3bo5bo3b2o26b2o3bo5bo3b2o32b2o3bo5bo3b2o29b2o3bo5bo3b
2o22b2o3bo2bo2bo3b2o$19b2o8b5o8b2o15bo8b5o21bob5o8bo31bob5obo21bob5obo
5b2o18bob5obo51bob5obo24bo4bob5obo4bo22bobo3bob5obo3bobo17bo3b5o3bo32b
o3b5o3bo49bo3b5o3bo75bo3b5o3bo9b3o22bo3b5o3bo26bo3b5o3bo46bo3b5o3bo30b
o3b5o3bo36bo3b5o3bo77bo3b5o3bo36b3o9bo3b5o3bo23bo3b5o3bo30bo3b5o3bo36b
o3b5o3bo33bo3b5o3bo26bo3b5o3bo$18b2o8bo2bo2bo8b2o22bo5bo20b2o5bo39b2o
5b2o21b2o5b2o5bobo17b2o5b2o51b2o5b2o22bobo4b2o5b2o4bobo16b3o2b2o3b2o5b
2o3b2o2b3o13b4o5b4o32b4o5b4o49b4o5b4o75b4o5b4o9bo24b4o5b4o26b4o5b4o46b
4o5b4o30b4o5b4o36b4o5b4o77b4o5b4o38bo9b4o5b4o23b4o5b4o30b4o5b4o36b4o5b
4o33b4o5b4o26b4o5b4o$23bo4b2o3b2o4bo27bob3obo23b3obo42b3o27b3o8bo22b3o
57b3o26b2o7b3o7b2o19bo2bo7b3o7bo2bo20b3o42b3o59b3o85b3o15bo28b3o36b3o
56b3o40b3o46b3o87b3o42bo15b3o33b3o40b3o46b3o43b3o36b3o$24b2o11b2o29bob
obo21b3obobo40b3obob3o21b3obob3o25b3obob3o51b3obob3o29b3obob3o24bo8b3o
bob3o8bo16b3obob3o36b3obob3o53b3obob3o79b3obob3o38b3obob3o30b3obob3o
50b3obob3o34b3obob3o40b3obob3o81b3obob3o52b3obob3o27b3obob3o34b3obob3o
40b3obob3o37b3obob3o30b3obob3o$23b2o13b2o54bo46bo7bo21bo7bo25bo7bo51bo
7bo24bo4bo7bo4bo23b2o3bo7bo3b2o20bo7bo36bo7bo53bo7bo79bo7bo38bo7bo30bo
7bo50bo7bo34bo7bo40bo7bo81bo7bo52bo7bo27bo7bo34bo7bo40bo7bo37bo7bo30bo
7bo$20bo21bo255b2o15b2o22bo2bo13bo2bo$18bobo21bobo252bobo15bobo21bo2bo
13bo2bo$19b2o21b2o296b2o15b2o152b3o368b3o$513bo368bo$69bo29bo242bo13bo
155bo370bo$68b2o29b2o241b2o11b2o$23b2o13b2o18bo9bobo27bobo9bo230bobo
11bobo$22bobo13bobo17b2o49b2o$24bo13bo18bobo49bobo2$70b2o25b2o$69b2o
27b2o$71bo25bo6$552b3o286b3o$552bo290bo$553bo288bo52$686bo398bo$685bo
400bo$685b3o396b3o$55bobo151bobo$56b2o151b2o$56bo153bo$72bo105bo15bo
105bobo52bo1076bo$52bobo15b2o106bobo14b2o15bobo86b2o25bobo22bobo122bob
o280bo185bobo257bo222b2o$53b2o16b2o19bobo83b2o14b2o16b2o26bobo34bo23bo
27b2o23b2o125bo280bo183bo259bo224b2o$53bo38b2o46bobo70bo27b2o33bo52bo
151bo278b3o183bo259b3o189bo35b2o$89bo3bo9bo36b2o89bo9bo3bo30b3o199bo2b
o274bo189bo2bo262bo180b2ob2o28bo7bobo$87bobo12bo18bo19bo90bo12bobo26bo
204b3o178bo93bobo189b3o162bo100bobo113bo63bobo2b2o26bobo6bo$88b2o12b3o
14bobo51bo56b3o12b2o28bo31bo24bobo25bo300b2o92b2o84bobo265b2o101b2o72b
obo39bobo63bo30b2o$40bo28bo50b2o7bo28bo14bobo21bo75b3o30bo16bobo6b2o
24bobo299b2o11bo119bobo36bo3bo4b2o255bo11b2o141bobo31b2o4bo3bo30b2o$
38b2o28bo20bo35bob2o30b2o12b2o23bo46bo32bo27b3o15b2o7bo25b2o117bo7bo
185bo121b2o37b2obobo3bo98bo7bo149bo153b2o32bo3bobob2o29bo28bo8bo$39b2o
27b3o18b2o32bobo2b2o28b2o36b3o45b2o31bo46bo154bo5bo149bo36b3o119bo37b
2o2b2o104bo5bo99bo48b3o154bo37b2o2b2o26bobo29bo2b2o2bo$88bobo33b2o118b
obo30b3o29b2o21b2o60bo12bo69b3o5b3o42bo49bo53bo161bo143b3o5b3o30bo27bo
39bo202bo72b2o27b3obo2bob3o30b2o28b2o$40bo30b2o60b2o23bo35b2o76b2o22b
2o2b2o7bobo15b2o2bo2bo60bo10bo124bo46b2o54b3o34bo50bo42b2o28bo184bo29b
2o35b3o50bo46bo54b2o49bo105b2o34bo2bo26bo2bo$7bobobo27b2o30bobo22b2o
35bo24b2o3bo11bo17bobo41b2o34bo23bo2b2o7bo18bo2bo2bo23bo11bo22b3o10b3o
120b3o47b2o89bobo48bo42b2o29b3o49bo132b3o26b2o88bobo46bo54b2o46b3o28bo
112bo2bo26bo2bo$39bobo19b3o7bo24bo37bo22bobo3b3o8bo20bo7b3o32bo33bo23b
o30bo4b2o25bo8b3o171bo88b3o36bobo48b3o42bo79bo122bo80b3o46bobo44b3o53b
o80bo112b2o28b2o27b4o$97bo37bo30bo7b3o60bo33bo23bo30bo30b3o7bo23b2o16b
2o131bobo86bo39bo89b2o74b2o7b3o58b2o41b2o15bobo16b2o36b2o26bo13b2o32bo
13b2o46b2o42b2o11b2o37b2o21b3o7b2o5b2o22b2o6b2o23b2o6b2o27b2o6b2o20b2o
6b2o22bo4bo$96b2o36b2o29b2o43b2o25b2o4b2o26b2o4b2o16b2o4b2o23b2o4b2o
33b2o4b2o15bobo4b2o4b2o4bobo16bo4bo5bo3bo34bo4bo10bo31bo6b2o4bo2b2o22b
o4bo2b2o42bo4bo8bo25bo4bo44bo4bo36bo4bo5bobo27bo4bo35bo5bo52bo3bo5bo5b
obo23bo10bo5bobo15b2o2bo4b2o7bobo25b2o2bo5bobo24bo8bo5bobo39bo5bobo39b
o5bobo40bobo5bo5bobo30bo5bobo30bo6bobo20bobo6bobo21bobo6bobo25bobo6bob
o18bobo6bobo18bobobo2bobobo$34bo2bo19bo2bo31bo2bo34bo2bo27bo2bo41bo2bo
bo27bo2bobo28bo2bobo18bo2bobo25bo2bobo35bo2bobo17bo4bobo2bobo4bo17bobo
2bobo5b2obobo31bobo2bobob2o5bo31bobo2bobo2bo2b2o25bobo2bobo2bo41bobo2b
obobo30bobo2bobobo40bobo2bobobo7bobo22bobo2bobobo3bo27bobo2bobob2o30bo
bo2bobob2o47bobob2o5bobo2bobob3o22bo5b2obobo2bobob3o17b2o2bo2bobo2bobo
b3o23bo2bobo2bobob3o28bobobo2bobob3o34bobobo2bobob3o24bobo7bobobo2bobo
b3o39bo3bobobo2bobob3o24b2obobo2bobob3o25b2obobo2bobob3o16b3obobo2bobo
b3o17b3obobo2bobob3o21b3obobo2bobob3o14b3obobo2bobob3o14b3obobo2bobob
3o$34b4o19b4o31b4o34b4o27b4o41b4o29b4o30b4o20b4o27b4o37b4o26b4o24bob4o
bo4b2o2b2o32bob4obob2o5b3o29bob4ob4o2bobo24bob4ob3o8bo33bob4ob2obo29bo
b4ob2obo39bob4ob2obo6b2o23bob4ob2obo11bo18bob4ob2o2bo29bob4ob2o2bo47b
2o2b2o4bob4ob2o3bo19b3o5b2obob4ob2o3bo15bobo2b4ob4ob2o3bo14bo8b3ob4ob
2o3bo26bob2ob4ob2o3bo32bob2ob4ob2o3bo24b2o6bob2ob4ob2o3bo29bo11bob2ob
4ob2o3bo22bo2b2ob4ob2o3bo23bo2b2ob4ob2o3bo14bo3b2ob4ob2o3bo15bo3b2ob4o
b2o3bo19bo3b2ob4ob2o3bo12bo3b2ob4ob2o3bo12bo3b2ob4ob2o3bo$32b2o4b2o15b
2o4b2o27b2o4b2o30b2o4b2o23b2o4b2o37b2o4bo26b2o4bo27b2o4bo17b2o4bo24b2o
4bo34b2o4bo24bo4bo24bo4bo44bo4bo42bo4bo34bo4bo11bobo32bo4bo3bo30bo4bo
3bo40bo4bo3bo7bo24bo4bo3bo10bo20bo4bo3b2o30bo4bo3b2o58bo4bo3b2o32bo4bo
3b2o25bo4bo3b2o13bobo11bo4bo3b2o27bo3bo4bo3b2o33bo3bo4bo3b2o25bo7bo3bo
4bo3b2o31bo10bo3bo4bo3b2o23b2o3bo4bo3b2o24b2o3bo4bo3b2o16b2o3bo4bo3b2o
17b2o3bo4bo3b2o21b2o3bo4bo3b2o14b2o3bo4bo3b2o14b2o3bo4bo3b2o$31bo2bo2b
o2bo13bo2bo2bo2bo25bo2bo2bo2bo28bo2bo2bo2bo21bo2bo2bo2bo4bo30bo2bo2bo
26bo2bo2bo27bo2bo2bo17bo2bo2bo24bo2bo2bo29bo4bo2bo2bo26bo2bo26bo2bo46b
o2bo8bo35bo2bo2bo33bo2bo2b2o8b2o4bo29bo2bo2b2ob2o29bo2bo2b2ob2o39bo2bo
2b2o34bo2bo2b2o11b3o19bo2bo2b2o33bo2bo2b2o61bo2bo2b2o26bo8bo2bo2b2o25b
o2bo2bo2b2o11bo4b2o8b2o2bo2bo2b2o27b2ob2o2bo2bo2b2o33b2ob2o2bo2bo2b2o
36b2o2bo2bo2b2o31b3o11b2o2bo2bo2b2o27b2o2bo2bo2b2o28b2o2bo2bo2b2o20b2o
2bo2bo2b2o21b2o2bo2bo2b2o25b2o2bo2bo2b2o18b2o2bo2bo2b2o18b2o2bo2bo2b2o
$32b2o4b2o15b2o4b2o27b2o4b2o30b2o4b2o23b2o4b2o5bobo29b2o4b3o24b2o4b3o
25b2o4b3o15b2o4b3o22b2o4b3o24bobo5b2o4b3o20b3o4b3o20b3o4b3o40b3o4b3o3b
2o33b3o4b2obo29b3o4b2obo13bo27b3o4b2obobobo25b3o4b2obobobo35b3o4b2obob
o7b3o19b3o4b2obobo28b3o4b2obo30b3o4b2obo6b2o50b3o4b2obo27b2o3b3o4b2obo
24bob2o4b2obo12bo13bob2o4b2obo26bobobob2o4b2obo32bobobob2o4b2obo24b3o
7bobob2o4b2obo43bobob2o4b2obo27bob2o4b2obo20b2o6bob2o4b2obo20bob2o4b2o
bo21bob2o4b2obo25bob2o4b2obo18bob2o4b2obo18bob2o4b2obo$172b2o38bo32bo
33bo23bo30bo25b2o13bo20bo8bo20bo8bo40bo8bo4b2o32bo9bo29bo23b3o25bo12b
2o25bo12b2o35bo10b2o7bo21bo10b2o28bo40bo15b2o51bo36b2o4bo34bo21b3o51b
2o46b2o40bo7b2o55b2o72b2o$534b2o42b3o5bo140bo41b3o4bo71bo127b2o25bo5b
3o130bo49bo4b3o81bo$492b2o36bo47bo6b2o182bo4b2o158b2o45bo21b2o6bo181b
2o4bo$492bobo28bo2bo3b2o47bo5bobo182bo4b2o65b3o88bobo44b2o3bo2bo13bobo
5bo181b2o4bo86b3o$166b2o198b2o124bo34bobobo312bo90bo44bobobo300bo$166b
obo196bobo117b3o35bo3bo315bo96b3o41bo3bo297bo$166bo200bo119bo36b4o412b
o43b4o$162b3o204b3o114bo3b2o444b2o3bo$164bo204bo112bo6b2o275b2o169b2o
6bo255b2o$163bo206bo111b2o7bo28bo245bobo167bo7b2o45bo208bobo$459b3o19b
obo36b2o140bo103bo106b3o68bobo43b2o117bo92bo$459bo59bobo140b2o211bo
114bobo115b2o$460bo200bobo210bo233bobo2$679b2o410b2o$679bobo90b2o316bo
bo102b2o$679bo92bobo317bo101bobo$772bo423bo37$69bobo$72bo$56bobo13bo$
57b2o10bo2bo$57bo12b3o2$65bo$63bobo$64b2o$81bo$68bo10b2o6b4o$53bobo11b
o12b2o5bo3bo$54b2o11b3o17bo$54bo33bo2bo$51bo28bo$52bo27bobo$50b3o27b2o
$73b2o$73bobo31b2o$74bo31bo2bob2o$61bo2bobo2bo36bobo3bo$61b4ob4o35b2ob
o$27bobobo$63b4ob4o36bob2o$63bo2bobo2bo32bo3bobo$58bo45b2obo2bo$57bobo
48b2o$58b2o$51b2o27b3o$50bobo27bo$52bo28bo$41bo2bo33bo$45bo17b3o11b2o$
41bo3bo5b2o12bo11bobo$42b4o6b2o10bo$51bo$67b2o$67bobo$67bo2$60b3o12bo$
60bo2bo10b2o$60bo13bobo$60bo$61bobo!
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Re: Synthesising Oscillators

Postby mniemiec » June 17th, 2016, 7:46 pm

BobShemyakin wrote:Synthesis is wonderful! However, it contains an error in the first tennisplayer's step. Gliders, marked the point cannot pass each other, if you start early. Error can easily be corrected (it is necessary to push 6 gliders) ...

I hadn't noticed this, as I only show combined steps when they can't influence each other, so I had already decomposed this into 4 separate steps. I couldn't find a way to make any pair of the still-lifes from 3 gliders.
BobShemyakin wrote:The first mniemiec's step can be reduced by 2 glider (to add the tail enough 3 gliders):...

This is significant! (I was unaware that there was a 3-glider mechanism to add a tail; is it new? If not, for some reason I didn't know about it; if it was in an existing synthesis, perhaps it's in one of the many that I haven't had time to assimilate yet?). This is also extremely frustrating, because it will improve hundreds (hopefully not thousands) of existing syntheses, creating a lot more work for me. I still haven't had time to assimilate (and propagate) all your improved 4..15-bit still-life syntheses and 4+ glider syntheses.

Extrementhusiast wrote:Here are a few more oscillators:...

These are amazing! I haven't had time to examine these yet in detail, but there is one minor technical error. In the first synthesis, the 3 final forms are not oscillators until 2 generations after the forms shown.
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Re: Synthesising Oscillators

Postby Sokwe » June 17th, 2016, 8:17 pm

mniemiec wrote:I was unaware that there was a 3-glider mechanism to add a tail

You may have already noticed this, but this mechanism doesn't work in all cases:
x = 30, y = 12, rule = B3/S23
8bo19bo$7bo19bo$bo5b3o11bo5b3o$2bo19bo$3o17b3o3$3b2o18b2o$4b2o18b2o$3b
o4bo14bo4bo$7bobo17bobo$8b2o18bo!
-Matthias Merzenich
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Re: Synthesising Oscillators

Postby BlinkerSpawn » June 17th, 2016, 9:56 pm

1-glider reduc by using the block from the beginning in the final step:
x = 187, y = 83, rule = B3/S23
153bo$151bobo$96bo19bo35b2o$69bo25bobo17bobo$30bo29bo8bobo23bobo17bobo
$obo25b2o31b2o6b2o25bo19bo47bo$b2o5bobo18b2o29b2o101bo$bo7b2o80b2o18b
2o50b3o$9bo80bo2bo16bo2bo$91b2o18b2o$53bo19bo59bo$52bobo17bobo58bobo
23b3o18b2o$52b2o18b2o21b2o18b2o16b2o10b2o14bo3b2o12bobo$95bo19bo29bo8b
3o3bo4bo14bo$93bobobo15bobobo10b2o13bobobo8bo6bobobo10bobobo$15b2o25b
2o5b2o11b2o5b2o21bobobobob2o10bobobobob2o6bobo11bobobobob2o3bo6bobobob
ob2o5bobobobob2o$14bobo25b2o5b2o11b2o5b2o21bobobobob2o10bobobobob2o6bo
13bobobobob2o10bobobobob2o5bobobobob2o$16bo76bobobo15bobobo25bobobo15b
obobo10bobobo$95bo19bo29bo19bo14bo$19bobo30b2o18b2o21b2o18b2o28b2o18b
2o13b2o$20b2o2b2o26bobo17bobo$12bo7bo3bobo26bo19bo$4bo7b2o10bo66b2o18b
2o$4b2o5bobo76bo2bo16bo2bo$3bobo85b2o18b2o$60b2o$61b2o6b2o25bo19bo$60b
o8bobo23bobo17bobo$69bo25bobo17bobo$96bo19bo20$96bo$94bobo$95b2o$107bo
bo$107b2o$108bo$61bobo$61b2o86bo$58bo3bo84bobo14bo$59bo63b2o18b2o3b2o
13bo9b2o$53bo3b3o64bo19bo8bo9b3o8bo$51bobo22bo29bo17bobo17bobo4bobo20b
ob2o$48b2o2b2o21bobo27bobo17bobo17bobo4b2o21bo2bo$17b2o18b2o10b2o6b2o
17bobo27bobo17bobo17bobo9bo17b3o$16bobo17bobo9bo7bobo18bo29bo19bo19bo
9bo19bo$17bo19bo19bo17bobobo13b2o10bobobo15bobobo15bobobo7b3o15bob2o$
15bobobo15bobobo15bobobo14bobobobob2o8bobo9bobobobob2o10bobobobob2o10b
obobobob2o20bobobo$14bobobobob2o10bobobobob2o10bobobobob2o10bobobobob
2o10bo9bobobobob2o10bobobobob2o10bobobobob2o20bobobo$7bo6bobobobob2o
10bobobobob2o10bobobobob2o11bobobo25bobobo15bobobo15bobobo25bob2o$8bo
6bobobo15bobobo15bobobo17bo29bo19bo19bo29bo$6b3o3bo4bo19bo19bo18bobo
19bo7bobo17bobo17bobo27b3o$13bo3b2o17bobo17bobo16bobo18bobo6bobo17bobo
17bobo4b2o21bo2bo$11b3o23b2o14bo3b2o17bo20b2o7bo17bobo17bobo4bobo20bob
2o$51bobo70bo19bo8bo20bo$48b2o2b2o50bo18b2o18b2o28b2o$49b2o6b3o43b2o$
15b3o30bo10bo43bobo$15bo42bo3bo36b2o$16bo44b2o35bobo$61bobo36bo2$4b2o$
3bobo$5bo!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: Synthesising Oscillators

Postby AbhpzTa » June 18th, 2016, 3:45 am

Reduced (from 41 to 37):
x = 418, y = 32, rule = B3/S23
302bo$303b2o$302b2o$316bo$116bo199bobo$69bo45bobo152bobo43b2o$30bo29bo
8bobo43bobo152b2o$obo25b2o31b2o6b2o45bo47bo100bo5bo$b2o5bobo18b2o29b2o
101bo102bo$bo7b2o100b2o50b3o94bo3b3o$9bo100bo2bo144bobo100b2o48b2o$
111b2o41bobo102b2o101bo49bo$73bo59bo21b2o157bo47bobo13bobo31bob2o$72bo
bo58bobo19bo3b3o53b2o38b2o8b2o46bobo47bobo12b2o33bo2bo$72b2o41b2o16b2o
26bo3b2o47bobo39b2o6bobo47bobo47bobo12bo34bobo$115bo44bo4bo49bo39bo9bo
49bo49bo$113bobobo10b2o33bobobo45bobobo45bobobo45bobobo45bobobo12b2o
31bo2bo$15b2o45b2o5b2o41bobobobob2o6bobo31bobobobob2o40bobobobob2o40bo
bobobob2o28b2o10bobobobob2o40bobobobob2o8bobo29bobob2o$14bobo45b2o5b2o
41bobobobob2o6bo33bobobobob2o40bobobobob2o40bobobobob2o29b2o9bobobobob
2o40bobobobob2o8bo31bobob2o$16bo96bobobo45bobobo45bobobo45bobobo32bo
12bobobo45bobobo9bo35bo2bo$115bo49bo44bo4bo49bo49bo49bo10b2o$19bobo50b
2o41b2o48b2o44bo3b2o47bobo39bo7bobo47bobo9bobo35bobo$20b2o2b2o46bobo
130bo3b3o49bo3b2o37bobo6bobo47bobo47bo2bo$12bo7bo3bobo46bo131b2o52bobo
43b2o7bo47bobo47bob2o$4bo7b2o10bo86b2o91bobo49b2o2b2o100bo49bo$4b2o5bo
bo96bo2bo143b2o6b3o44bo48b2o48b2o$3bobo105b2o100b3o40bo10bo43b2o$60b2o
151bo52bo3bo40bobo$61b2o6b2o45bo97bo54b2o36b2o$60bo8bobo43bobo151bobo
34bobo$69bo45bobo190bo$116bo!
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
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Re: Synthesising Oscillators

Postby gmc_nxtman » June 21st, 2016, 11:19 am

Some catalyst syntheses. Credit to AbhpzTa for the elk synthesis, and Extrementhusiast for the eater3 synthesis used in the 83-glider Rx202 catalyst synthesis. Does anyone know of a way to synthesize the Fx158 and R180 catalysts?

#C F172, Rx140, R197, Bx243, Rx202, and a B-to-G
x = 583, y = 503, rule = LifeHistory
318.BA$317.ABAB$318.2A2B$319.4B$320.4B$318.AB.4B$318.B2A.4B201.AB$
318.2A2B.4B199.BABA$319.4B.BA2B197.2B2A$320.6BA2B195.4B$321.3B3A3B
193.4B$322.9B191.4B$323.9B189.4B$324.9B5.AB180.4B$325.9B4.B2A178.4B$
326.9B3.2A2B176.4B$327.9B3.4B174.4B$328.9B3.4B172.4B$329.9B3.4B170.4B
$330.9B3.4B168.4B$329.BA7BAB3.4B166.4B$328.ABA5BABA2B3.4B164.4B$329.
2A6B2A3B3.4B162.4B$330.13B3.4B160.4B2.ABA$331.13B3.4B158.4B2.B2AB9.BA
$332.13B3.4B156.4B2.3BA9.2AB$333.3BA9B3.4B154.4B2.4B9.2B2A$334.3BA9B
3.4B152.4B2.4B9.4B$335.3A10B3.4B150.4B2.4B9.4B$336.5BA7B3.4B148.4B2.
4B9.4B$337.5BA7B3.4B146.4B2.4B9.4B$338.2B3A8B3.4B144.4B2.4B9.4B$339.
13B3.4B142.4B2.4B9.4B$340.13B3.4B140.4B2.4B9.4B$341.13B3.3BABA136.4B
2.4B9.4B$342.13B3.3B2AB134.4B2.4B9.4B$342.A5BABA5B3.2BA3B132.4B2.4B9.
4B10.BA$341.2BA5B2A6B3.6B130.4B2.4B9.4B10.2AB$341.3A5BA8B3.6B128.3BA
2.4B9.4B10.2B2A$342.17B3.6B126.3BA6B9.4B10.4B$343.17B3.6B124.4B3A3B9.
4B10.4B$344.17B3.6B122.10B9.4B10.4B$345.17B3.6B120.10B9.4B10.4B$346.
17B3.6B118.10B9.4B10.4B$347.17B3.6B116.10B9.4B10.4B$348.17B3.6B114.
10B9.4B10.4B$349.17B3.6B112.10B9.4B10.4B$350.17B3.6B110.10B9.4B10.4B$
351.17B3.6B108.10B9.4B10.4B$352.17B3.6B106.10B9.4B10.4B$353.17B3.6B
104.10B9.4B10.4B$354.17B3.6B102.10B9.4B10.4B$355.17B3.6B100.10B9.4B
10.4B$356.17B3.6B98.10B9.4B10.4B$357.17B3.6B96.10B9.4B10.4B$358.17B3.
6B94.10B9.4B10.4B$359.17B3.6B.A90.10B9.4B10.4B$354.ABA3.17B3.7BA88.
10B9.4B10.4B$354.B2AB3.10BABA4B3.4B3AB86.10B3.BA4.4B10.4B$355.A3BAB.
4BABA3B2A5B2.A8B84.10B3.2AB3.4B10.4B$356.4B2A.4B2A3BA7B.B2A7B82.10B3.
2B2A2.4B10.4B$357.2B2A2B.3BA13B2A9B80.10B3.4B2.4B10.4B$358.6B.28B78.
10B3.4B2.4B10.4B$359.6B.8BABA17B76.10B3.4B2.4B10.4B$360.6B.8B2A18B74.
10B3.4B2.4B10.4B$361.6B.7BA20B72.10B3.4B2.4B3.ABA4.4B$362.6B.15BA12B
70.10B.BA4B2.4B3.B2AB3.4B$363.6B.15BA12B68.10B.2A4B2.4B3.3BA3.4B$364.
6B.12B3A13B66.10B.2B2A2B2.4B3.4B3.4B$365.6B.18BA9B64.10B.6B2.4B3.4B3.
4B$366.6B.18B2A8B62.10B.6B2.4B3.4B3.4B$367.6B.16B2A10B60.10B.6B2.4B3.
4B3.4B$368.6B.28B58.10B.6B2.4B3.4B3.4B$369.6B.28B56.10B.6B2.4B3.4B3.
4B$370.6B.28B54.9BA7B2.4B3.4B3.4B$371.6B.28B52.10BABA4B2.4B3.2BABA2.
4B$372.6B.28B50.11B2A4B2.4B3.3B2AB.4B$373.6B.28B48.17B2.4B3.5BA.4B$
374.6B.28B46.17B2.4B3.6B.4B$375.6B.28B44.17B2.4B3.6B.4B$376.6B.28B42.
17B2.4B3.6B.4B$377.6B.28B40.17B2.4B3.6B.4B$378.6B.28B38.17B2.4B3.6B.
4B$379.6B.28B36.17B2.4B3.6B.4B$380.6B.28B34.17B2.4B3.4BAB.4B$381.6B.
28B32.17B2.4B3.4BA6B$382.6B.2BA25B30.17B2.4B3.5B3A3B$383.6BABA26B28.
17B2.4B3.11B$384.6B2A27B26.17B2.4B3.11B$385.35B24.17B2.4B3.11B$386.
35B22.17B2.4B3.11B$387.7BA27B20.17B2.4B3.11B$388.7BA4BA22B18.17B2.4B
3.11B$389.4B3A5BA22B16.17B2.4B3.11B$390.9B3A23B14.17B2.4B3.11B$391.
35B12.17B2.4B3.11B$392.35B10.17B2.4B3.11B$393.35B8.17B2.4B3.11B$394.
35B6.17B2.4B3.11B$395.35B4.17B2.4B3.11B$396.35B2.17B2.4B3.11B$397.52B
2.4B3.11B$398.50B2.4B3.11B$399.48B2.4B3.11B$400.46B2.4B3.11B$401.44B
2.4B3.11B$402.42B2.4B3.11B$403.40B2.4B3.11B$404.38B2.4B3.11B$405.36B
2.4B3.11B$406.29BA5B.4B3.11B$407.27BA5B.4B3.11B$408.19B2D5B3A7B3.11B$
409.18BD15B3.11B$410.18B3D4B2.6B.12B$411.19BD3B.AB2D3B2.11B$412.8BA9B
DB2DA.D2BD3B.10B$413.8BA7B2DBDB3ADBD13B$414.5B3A8BDBD5BD3BA9B$415.15B
DBDBCD2B2.2BABA6B$415.14B2DBDBAC3B.2B2A7B$414.19BCBA2BD13B$413.21B5D
14B$412.42B$411.25B3D16B$410.25BD2BD17B$409.27B2D19B$408.50B$407.52B$
406.54B$405.17B.38B$404.17B.40B$403.17B.12BA29B$402.17B.12B2A30B$401.
17B.13BABA30B$400.17B.48B$399.17B.2BA47B$398.17B.3B2A47B$397.17B.3BAB
A15B.32B$396.17B.4B2.15B3.32B$395.17B.4B2.15B5.32B$394.17B.4B2.15B7.
32B$393.17B.4B2.15B9.32B$392.17B.4B2.15B11.32B$391.8B2A7B.4B2.15B13.
32B$390.10B2A5B.4B2.15B15.32B$389.9B.A6B.4B2.15B17.32B$388.9B.7B.4B2.
15B19.32B$387.9B.7B.4B2.15B21.32B$386.9B.B3A3B.4B2.15B23.32B$385.9B.
4BA2B.4B2.15B25.32B$384.9B.4BA2B.4B2.15B27.32B$383.9B.7B.4B2.15B29.
32B$382.9B.7B.4B2.3BA11B31.8B2A22B$381.9B.7B.4B2.4B2A9B33.7BABA22B$
380.B2A6B.7B.4B2.2A2BABA8B35.6BA25B$379.3B2A4B.7B.4B2.ABAB2.9B37.32B$
378.3BA5B.7B.4B2.3BA2.9B39.32B$377.9B.7B.4B2.4B2.9B41.32B$376.9B.7B.
4B2.4B2.9B43.3B2A27B$375.9B.7B.4B2.4B2.9B45.2BABA27B$374.9B.7B.4B2.4B
2.9B47.BA30B$373.9B.7B.4B2.4B2.9B49.23BA8B$372.9B.7B.4B2.4B2.9B51.21B
2A9B$371.9B.7B.4B2.4B2.9B53.20BABA9B$370.9B.7B.4B2.4B2.9B55.2B3A15B.
11B$369.2BA6B.B2A4B.4B2.4B2.9B57.BA18B.11B$368.3B2A4B.BABA3B.4B2.4B2.
9B59.BA18B.9B2A$367.3BABA3B.4BA2B.2A2B2.4B2.9B61.20B.8BABA$366.9B.7B.
2B2A2.4B2.9B63.18B2A.7BAB$365.9B.7B.2BAB2.4B2.9B65.17BABA.7B$364.9B.
7B.4B2.4B2.4BA4B67.16BA3B.3BA3B$363.9B.7B.4B2.4B2.5B2A2B69.20B.B2A4B$
362.9B.7B.4B2.3AB2.5BABAB71.20B.ABA4B$361.3BA5B.7B.4B3.2BA2.9B73.20B
2.6B$360.4B2A3B.7B.4B5.A2.9B75.20B2.6B$359.4BABA2B.7B.4B8.9B77.20B2.
6B$358.9B.7B.4B8.9B79.20B2.6B$357.9B.7B.4B8.9B81.13B2A5B2.6B$356.9B.
7B.4B8.9B83.11B2A7B2.6B$355.9B.7B.4B8.9B85.12BA7B2.6B$354.9B.7B.4B8.
9B87.15B2A3B2.6B$353.9B.7B.4B8.3B2A4B89.13B2A5B2.6B$352.9B.7B.4B8.5B
2A2B91.14BA.4B2.6B$351.9B.7B.4B8.5BA3B93.14B2.4B2.6B$350.9B.7B.4B8.9B
95.14B2.4B2.6B$349.9B.7B.4B8.9B97.14B2.4B2.6B$348.9B.7B.4B8.9B99.14B
2.4B2.6B$347.9B.7B.4B8.9B101.14B2.4B2.6B$346.9B.7B.4B8.9B103.14B2.4B
2.6B$345.9B.7B.4B8.9B105.14B2.4B2.6B$344.9B.7B.4B8.9B107.14B2.4B2.6B$
343.9B.7B.4B8.9B109.14B2.4B2.4B2A$342.9B.7B.4B8.9B111.14B2.4B2.2B2AB$
341.9B.7B.3AB8.9B113.14B2.4B2.3BA$340.9B.7B2.2BA8.9B115.14B2.4B2.4B$
339.9B.7B4.A8.9B117.14B2.4B2.4B$338.9B.7B13.9B119.14B2.4B2.4B$337.5BA
3B.7B13.9B121.14B2.4B2.4B$336.6B2AB.7B13.9B123.14B2.4B2.4B$335.6BABA.
7B13.9B125.14B2.4B2.4B$334.9B.7B13.9B127.14B2.4B2.4B$333.9B.7B13.3B3A
3B129.14B2.4B2.4B$332.5B3AB.7B13.6BA2B131.14B2.4B2.4B$331.3A5BA.7B13.
6BA2B133.10B3AB2.4B2.4B$331.2BA4BA.7B13.9B135.9BA4B2.4B2.4B$330.2BA5B
.7B13.3B3A3B137.9BA4B2.4B2.4B$329.8B.7B13.6BA2B139.14B2.4B2.4B$328.8B
.7B13.4B.BA2B141.14B2.4B2.4B$327.8B.7B13.4B.4B143.14B2.4B2.4B$326.8B.
7B13.4B.4B145.14B2.4B2.4B$325.8B.7B13.2A2B.4B147.6B2A6B2.4B2.4B$324.
8B.7B13.2B2A.4B149.5BABA4B2A2.4B2.4B$323.8B.7B13.2BAB.4B151.4BAB2.3BA
BA2.4B2.4B$322.4B2A2B.7B13.4B.4B153.4B4.2BAB4.4B2.3BA$321.4BABAB.7B
13.2A2B.4B155.4B4.4B4.4B2.B2AB$320.4B2.BA.7B13.ABAB.4B157.4B4.4B4.B3A
2.ABA$319.4B5.7B15.BA.4B159.4B4.2B2A4.A2B$318.4B5.7B18.4B161.4B4.BABA
4.A$317.4B5.7B18.4B163.4B4.AB$316.2A2B5.7B18.4B165.4B$316.B2A5.7B18.
2A2B167.4B$316.AB5.7B18.ABAB169.4B$322.7B20.BA171.4B$321.3B3AB195.4B$
320.6BA197.4B$319.4B2.A199.2B2A$318.2A2B204.BABA$318.B2A206.AB$318.AB
3$258.A$257.A2B$256.B3A$196.A58.4B$195.2BA56.4B$195.3AB54.4B$196.4B
52.4B$197.4B50.4B$198.4B48.4B.ABA$199.4B46.4B.B2AB$200.4B44.4B.3BA3.A
$201.4B42.4B.4B3.A2B$202.4B40.4B.4B3.B3A$203.4B38.4B.4B3.4B$204.4B36.
4B.4B3.4B$40.A146.A17.4B34.4B.4B3.4B$39.A2B144.2BA17.4B32.4B.4B3.4B$
38.B3A144.3AB17.4B30.4B.4B3.4B$37.4B146.4B17.4B28.4B.4B3.4B$8.ABA25.
4B148.4B17.4B26.4B.4B3.4B42.ABA$8.B2AB23.4B150.4B17.4B24.4B.4B3.4B43.
B2AB$9.A3B21.4B152.4B17.4B8.A13.4B.4B3.4B45.A3B$10.3BAB18.4B154.4B17.
4B6.A2B11.4B.4B3.4B47.4B$11.3B2A16.4B156.4B17.4B4.B3A10.4B.4B3.4B49.
4B276.ABA$12.B2A2B14.4B158.4B17.4B2.4B10.4B.4B3.4B51.4B261.A12.B2AB$
13.5B12.4B160.4B17.8B10.4B.4B3.4B53.4B259.2BA10.3BA$14.5B10.4B162.4B
17.6B10.4B.4B3.4B55.4B258.3AB8.4B$15.5B8.4B164.4B17.3BABA8.4B.4B3.4B
57.4B5.B252.4B6.4B$16.5B6.4B166.4B15.4B2AB7.4B.4BA2.4B59.4B3.3B252.4B
4.BA2B$17.5B4.4B168.4B13.6BAB6.4B.4BA6B61.4B2.3B231.BA20.4B2.BA2B$18.
5B2.4B170.4B11.10B4.4B.5B3A3B63.9B2.ABA224.ABAB20.6B3A$19.9B172.4B9.
7B.4B2.4B.11B65.8B.B2AB225.2A2B19.8B$20.7B174.4B8.6B3.4B.3B.4BA6B67.
10BA227.4B11.A7.6B$21.5B176.4B5.7B5.5B2.5BABA3BABA65.3B2A5B229.4B9.2B
A4.7B$22.6B175.4B3.7B7.4B.6B2A4B2AB65.2B2A6B230.4B8.3AB3.7B$23.5BABA
173.4B2.7B8.17BA66.4BA6B230.4B8.4B3.4BABA$21.B.5B2AB171.16B8.16B66.B
2A10B230.4B8.4B2.4B2AB$17.AB.6BD2BA3.BA166.16B2D6.16B67.ABA2B2D2B2D2B
231.4B8.5B.2D2BA$17.B2A5BDBDB3.2AB165.18BD5.16B69.BA2BD3BD2B233.4B.B
6.4BD2BD3B$17.2A7BD3B.2B2A164.3A2B2A12BD.2D2.15B69.6B3D2BD234.7B.8BDB
D.3B$17.6BAB.B3D.2DB165.B.AB2A12B2D.D2BD14B69.4B3.2BDB2D235.14B2D2B2D
3B$16.8BA4BD.2D167.A.3BA12B.BDB2D13B69.4B5.BD2B237.B.13B2D2BD3B$15.7B
3A4BD173.13B2.2BD15B69.4B6.2D2B241.9B2D2B2D.4B$14.12BA2CD175.11B.2B2D
14B69.4B6.4B244.8BDBD2B2.2B2A$13.8B.4BDBA177.B2.11B.8B.4B69.4B6.4B
246.6BD2BD2B3.2AB$12.8B3.3BDC183.B2.6B.2B.9B69.4B6.4B246.3AB4.2D2B5.B
A$11.8B3.6B186.10B.7B69.4B6.4B247.2BA4.4B$10.8B5.5B185.12B.7B67.4B6.
4B249.A4.3A4B$9.8B7.4B183.B2A12B.6B66.4B6.3AB255.2BA4B$8.8B7.5B183.2B
2A17B2A64.4B7.2BA256.BA5B$7.4B3AB7.4B184.2BA4B3.11B2A2B62.4B9.A259.6B
$6.4B.2BA7.4B184.9B3.12BA2B60.2A2B269.8B$5.3AB3.A7.4B184.11B3.15B58.A
BAB270.6B3A$5.2BA11.2A2B184.8B.4B3.15B58.BA270.4B2.BA2B$6.A11.ABAB
184.7B4.4B3.15B328.4B4.BA2B$19.BA184.7B6.4B3.15B326.4B6.4B$204.7B8.4B
3.15B324.3AB8.4B$203.7B10.4B3.15B323.2BA10.3BA$202.7B12.4B3.15B323.A
12.B2AB$201.7B14.4B3.3BA11B336.ABA$200.A6B16.4B3.B2A6B3A3B$199.B2A4B
18.4B3.ABA.4BA6B$199.ABA3B20.2B2A7.4BA2.4B$200.4B22.BABA7.4B3.4B$199.
4B24.AB9.4B3.4B$198.4B37.4B3.4B$197.4B39.4B3.4B$196.4B41.4B3.4B$195.
4B43.4B3.4B$194.4B45.4B3.4B$193.4B47.4B3.4B$192.4B49.4B3.4B12.A$191.
4B51.4B3.4B$190.4B53.4B3.4B$189.4B55.4B3.B3A$188.4B57.4B3.A2B$187.4B
59.2B2A3.A$186.4B61.BABA$185.4B63.AB$184.4B$183.3AB$183.2BA$184.A16$
288.2D$289.D$289.D.DB$290.2DB$292.3B$292.4B$293.4B.B$294.7B$295.6B7.
2D$295.2B3D2B6.D$295.2BD4B3.BD.D$295.B3D4B2.B2D$295.11B119.2D$295.11B
120.D$295.11B120.D.DB$296.11B120.2DB$299.7B123.3B$298.8B4.2D2.D8.B
105.4B$191.2D18.4B82.8B5.D3.3D5.3D95.D9.4B.B$192.D17.4B84.7B2.BD.D6.D
4.BDB95.3D8.7B$192.D.DB13.4B84.9B.B2D6.2D3.2B3D97.D8.6B$193.2DB12.4B
85.11B8.10B96.2D8.2B3D2B123.B$195.3B9.4B86.11B10.9B95.B9.2BD4B122.4B$
195.4B7.4B85.2DB.9B.B3.B3.10B19.2D72.3B9.B3D7B118.4B$196.4B.B3.4B85.D
.DB2.26B15.B3.D.D70.6B8.12B110.2B3.7B$99.2D96.11B4.D81.D5.16BD13B7.6B
.B2D68.10B7.12B109.4B.8B$100.D97.9B3.3D80.2D5.16B2D13B.2B2.8B.B59.2B
2.2B3.16B.13B8.2D99.14B$100.D.DB94.2B3D3B3.D90.4B2D11B2D17B.6B.2B57.D
15B2D3BD20B6.D2.D98.B2D3B2D2BD3B$101.2DB94.2BD4B4.2D88.6B2D10BD29B54.
DBD15B2D2B2D21B5.D.D98.2B2D4B3D4B$103.3B92.B3D4B.4B4.D83.6BD10BD23B2D
6B52.B3D18B2D23B3.2D.2D97.9BD4B$19.B83.4B86.D4.11B4.3D81.2DB3.10B3.
23BD2BD5B53.D21BD22B5.B101.11B$18.3D3.2D78.4B.B75.D6.D.D3.12B2.D83.D.
DB.12B3.22B.B2D5B56.21BD23B.B2DB4D95.13B$18.BDB2.B2DB78.7B73.3D4.BD2B
.13B.B2D82.D4.2D2.3B.4B4.22B.7B58.4B.40B2D.D2.D95.14B$17.3D2B2.2B80.
6B76.D4.2B.18B81.2D5.D4.2B.3B4.6B.15B4.3B60.3B5.B.34B102.14B$17.5B3.
2B79.2B3D2B74.2D2.3B.4B3.10B87.3D4.BD2B.4B3.2B3.16B68.4B12.28B101.13B
$16.7B.2BCB78.2BD4B10.2C62.12B2.12B4.2C80.D6.D.D4.2C2.2C5.14B71.2C12.
27B103.14B3.2C$16.9BC.C78.B3D4B.2B6.C65.25B2.B.C88.D5.C3.C8.12B71.C
11.27B.B2D106.9B2.C2.C$17.8B.C79.13B.BC.C65.25B.2B.C.2C92.3C2.C5.13B
72.3C8.7B.13B7.BD.D105.10B2.C.C$17.6B4.3C.2C73.13B.B2C.2C60.D2.28B2C.
C2.C92.C.2C3.2DB.B2.6B76.C6.2C4B4.6B3.2B.3B8.D105.11B2C2.2C$16.6B7.C.
2C73.16B2.C.C57.3D2.30B.C.2C92.C5.D.DB4.6B76.C.2C2.C2BC7.4B9.2D8.2D
104.11B2.2C2.C$16.7B6.C77.14B3.C.C56.D5.28B3.C94.2C5.D8.5B75.2C.C3.BC
BC7.2B2DB8.D116.10B2C2.2C$11.2D4.6B4.3C71.2D7.11B2.2C.2C55.2D5.27B2.
2C100.2D10.B78.C.C.4BC10.2D10.3D113.8B.B.C.C$12.D4.6B3.C75.D6.11B4.B
56.4B6.25B196.C.C.2CB26.D114.6B3.C2.C$12.D.DB.6B3.2C74.D.DB2.13B.B2CB
2C52.3B5.28B195.2C.C.BCB142.4B5.2C$8.D4.2DB.11B75.2DB.16B2C.C.C.2C47.
4B.32B199.C4.C141.4B$8.3D4.11B79.20B3.C.2C45.39B200.5C142.4B$11.D4.
11B78.18B5.C46.D37B2.B2D346.4B$10.D2.B2.12B78.18B.BC.C45.B3D35B2.BD.D
196.C.2C146.4B$9.D.17B76.20B.B2C47.DBD32B8.D196.2C.C147.4B$9.2D.16B
76.2D2.18B51.D32B3.2B3.2D347.4B$12.16B.BD74.D3.17B53.2B2.2B4.21B.5B
352.4B$12.6BD10BD.D70.3D7.13B62.3B.25B353.4B$12.5B3D9B.2D70.D9.14B61.
2D2.25B$10.9BD7B85.15B61.D2.25B$10.18B85.10B.3B58.3D4.24B$9.2D18B84.
11B2.B2D56.D4.D.B4.17B.B2D$9.2DB.15B82.11B.B3.BD.D59.D.D.D5.7B.7B.BD.
D$10.B2.13B83.12B8.D59.D2.2D3.10B.4B6.D$13.12B84.12B8.2D57.2D7.9B4.2B
6.2D$14.10B6.2D77.13B75.7B$12.12B6.D79.12B76.2B.5B$12.14B.BD.D80.3D7B
83.2D$11.2D13B.B2D82.BD7B83.D$11.2D15B84.3D5B85.3D$12.B.15B84.2B2.2B
88.D$14.14B$15.11B.B2D$15.9B3.BD.D$14.8B8.D$14.7B9.2D$13.11B$13.12B$
13.12B$14.11B$12.4B.4B3DB$12.2D4.4BD2B$13.D4.2B3D2B$10.3D6.6B$10.D8.
7B$21.B.4B$24.4B$25.3B$27.B2D$27.BD.D$30.D$30.2D36$99.2D$100.D$100.D.
DB$101.2DB$103.3B$19.B83.4B$18.3D3.2D78.4B.B$18.BDB2.B2DB78.7B$17.3D
2B2.2B80.6B$17.5B3.2B79.2B3D2B$16.7B.2BCB78.2BD4B10.2C$16.9BC.C78.B3D
4B.2B6.C$17.8B.C79.13B.BC.C$17.6B4.3C.2C5.B67.13B.B2C.2C$16.6B7.C.2C
4.2B67.16B2.C.C$16.7B6.C6.3B68.14B3.C.C$11.2D4.6B4.3C5.4B62.2D7.11B2.
2C.2C$12.D4.6B3.C7.4B64.D6.11B4.B2.C$12.D.DB.6B3.2C5.4B65.D.DB2.13B.B
2CBC$13.2DB.11B4.4B67.2DB.16B2C.C.C$15.11B5.4B70.20B2.2C$16.11B3.4B
70.19B$15.18B2.B2D67.19B$13.23B2DB64.2DB.17B$D12.26B63.D2BD2.15B$3D7.
B.27B63.BDBD3.15B$3.D5.2D27B62.4BD7.13B$2.2D5.2D26B62.4B9.14B$2.4B4.B
.21B.2B62.5B9.15B$4.3B6.20B64.4B12.14B$4.4B.4B.20B62.4B4.B.19B$5.29B
61.4B.13B.9B$6.5BD22B59.21BD7B$7.2B3D20B.B2D55.D21BD6B$6.3BDBD19B2.BD
.D53.B3D18B2D6B$7.2BD21B5.D54.DBD15B2D2B2D5B$7.25B4.2D55.D15B2D3BD3B$
9.22B64.2B2.2B3.16B$11.19B75.10B3.2D$11.18B79.6B4.D$11.17B82.3B6.3D$
11.17B84.B8.D$12.4B2.9B85.2D$19.7B87.D$19.7B84.3D$19.6B85.D$19.6B$20.
5B$18.2DB.2B$17.D.DB$17.D$16.2D!
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Re: Synthesising Oscillators

Postby mniemiec » June 26th, 2016, 12:20 pm

A 1-glider reduction in the integral to test tube baby converter:
x = 50, y = 35, rule = B3/S23
28bo$28bobo$28boo$25bo$24bo$12bo11b3o$10bobo$11boo5$6bo9bo$4bobo9bo$b
oobboo9bo30boo$obo5boo12b3o21bobo$bbo6boo5bo5bo23bo$8bo6bobo5bo20boobo
$12bobobbo26bobbo$12boo3bobo22bobobbobo$18boo22boo4boo5$10boo$9bobo$
11bo$$16bo$15boo$15bobo$9bo$9boo$8bobo!
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Re: Synthesising Oscillators

Postby muzik » July 5th, 2016, 7:50 am

x = 20, y = 12, rule = B3/S23
3bo$3b2o3b3o$3bo3bo2bo$6b2ob2o$6bobo$2o5bo7b3o$2o$13bo5bo$13bo5bo$13bo
5bo2$15b3o!


Could possibly result in a synthesis for Cyclic.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
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Re: Synthesising Oscillators

Postby Goldtiger997 » July 6th, 2016, 8:16 am

Here is a 10 glider synthesis of cyclic.

x = 42, y = 42, rule = B3/S23
17bo$15b2o$16b2o$11bobo$12b2o$12bo$25bobo$25b2o$26bo3$3bo$4b2o$3b2o22b
3o$27bo$bo26bo$b2o$obo4$40bo$39b2o$39bobo2$6b2o$7b2o$6bo6b2o$13bobo$
13bo10$22b2o$21b2o$23bo!
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Re: Synthesising Oscillators

Postby Bullet51 » July 6th, 2016, 10:40 am

Final-steps for some challenging Syntheses:
#C Final step for a P7.
x = 15, y = 16, rule = LifeHistory
7.2A$7.2A$4.A$4.5A$8.A4.A$4.2A6.A$2A.A.A6.3A$2A.A$3.2A5.2E$3A4.A.E.E$
A2.6A$.2A$2.A.2A.2A$2.A2.A.A$.2A2.A.A$6.A!

#C Final step for another P7.
x = 11, y = 14, rule = B3/S23
3b2o$2bo2bob2o$3b2o3bo$3o2b3o$o2bobo$b3o$4bo$o2bobo$4bobo$6bo2bo$5b2ob
obo$6bo2bo$4bobo$4b2o!

#C Final step for a P5.
x = 19, y = 19, rule = b3s23
8bo$8b3o$11bo$10b2o4b2o$15bo2bo$bo11bo2b3o$2bo10b3o$3o13bo$6b2o2b2o3b
2o$6b2obo2bo$6b2o2b2o3b2o$16bo$13b3o$13bo2b3o$15bo2bo$10b2o4b2o$11bo$
8b3o$8bo!
Still drifting.
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Re: Synthesising Oscillators

Postby BlinkerSpawn » July 6th, 2016, 11:56 am

Bullet51 wrote:Final-steps for some challenging Syntheses:
#C Final step for a P5.
x = 19, y = 19, rule = b3s23
8bo$8b3o$11bo$10b2o4b2o$15bo2bo$bo11bo2b3o$2bo10b3o$3o13bo$6b2o2b2o3b
2o$6b2obo2bo$6b2o2b2o3b2o$16bo$13b3o$13bo2b3o$15bo2bo$10b2o4b2o$11bo$
8b3o$8bo!

Easier (I think):
x = 14, y = 19, rule = b3s23
3bo$3b3o$6bo$5b2o4b2o$10bo2bo$8bo2b3o$8b3o$11bo$b2o2b2o3b2o$b2obo2bo$
3o2b2o3b2o$11bo$8b3o$8bo2b3o$10bo2bo$5b2o4b2o$6bo$3b3o$3bo!

x = 13, y = 19, rule = b3s23
2bo$2b3o$5bo$4b2o4b2o$9bo2bo$7bo2b3o$7b3o$10bo$2o2b2o3b2o$2obo2bo$bo2b
2o3b2o$10bo$7b3o$7bo2b3o$9bo2bo$4b2o4b2o$5bo$2b3o$2bo!
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Re: Synthesising Oscillators

Postby mniemiec » July 6th, 2016, 12:10 pm

Bullet51 wrote:Final step for a P5. ...

BlinkerSpawn wrote:Easier (I think): ...

Nice. This can be further simplified. The initial beehive takes 3, the pre-beehive takes 3, and the cleanup glider takes 1 more. If you replace the pre-beehive with a house, the cleanup glider is not needed, reducing this to 5. However, if the initial beehive is created one step closer, it directly activates the mechanism, requiring only 3. Here is the completed synthesis from 37 gliders:
x = 172, y = 125, rule = B3/S23
bobo$boo$bbo140bo$141bobo$142boo$145bo$9bo135bobo$3o4boo136boo$bbo5boo
3bobo4bobo$bo11boo5boo33bo$14bo6bo6bo19bo4boo13bo5bo13bo5bo23bo5bo13bo
5bo13bo$17boo8bobobo15bobobobboo11bobobobobo11bobobobobo21bobobobobo
11bobobobobo11bobobobobo$12boo3bobo6boboboo14boboboo14bobobooboo11bobo
booboo6bo14bobobooboobo9bobobooboobo9bobobooboobo$12bobobbo8bobo17bobo
17bobo17bobo11boo14bobo7bo9bobo7bo9bobo7bo$12bo14boo18boo18boo18boo11b
obo14boo7boo9boo7boo9boo7boo$$4boo89boo$5boo87bobo6bo$4bo91bo5boo$12b
oo88bobo$11boo$13bo85b3o$101bo$100bo7$44bo$42boo$43boo8$31bobo$31boo$
32bo95bobo$34b3o91boo$34bo94bo$35bo91bo$128bo$126b3o$$158boo$18bo49bo
7bo51bo7bo22bo6bo$17bobobobobo41bobobobobobo49bobobobobobo19bobobobobo
bo$16bobobooboobo39bobobooboobobo47bobobooboobobo17bobobooboobobo$16bo
bo7bo39bobo7bobo47bobo7bobo17bobo7bobo$17boo7boo39boo7boo49boo7boo19b
oo7boo18$134bobo$135boo$135bo$137bo$55b3o78bo$55bo80b3o$56bo$128boo28b
oo5boo$10boo117bo6bo22bo5bo$9bobo115bobobobobobo19bobobobobobo$11bo
114bobobooboobobo17bobobooboobobo$59bo66bobo7bobo17bobo7bobo$58boo67b
oo7boo19boo7boo$58bobo18$130bo$bbo79bo47bobo$obo79bobo45boo$boo79boo$
127bo$125bobo$6bobo67bobo47boo7bo$bbo3boo69boo3bo52bobo$3boobbo69bobb
oo53boo$bboo77boo$7bo69bo$6bo26boo28boo13bo14boo15boo11boo15boo11boo
15boo$6b3o25bo29bo11b3o15bo15bo13bo15bo13bo15bo$34bobo27bobo27bobo11bo
bo13bobo11bobo13bobo5bo5bobo$35boo28boo28boo11boo15boo11boo15boo11boo$
158boo5boo$8boo5boo21boo5boo21boo5boo21boo5boo21boo5boo21bobb3obbo$9bo
5bo23bo5bo23bo5bo23bo5bo23bo5bo23bo5bo$7bobobobobobo19bobobobobobo19bo
bobobobobo19bobobobobobo19bobobobobobo19bobobobobobo$6bobobooboobobo
17bobobooboobobo17bobobooboobobo17bobobooboobobo17bobobooboobobo17bobo
booboobobo$6bobo7bobo17bobo7bobo17bobo7bobo17bobo7bobo17bobo7bobo17bob
o7bobo$7boo7boo19boo7boo19boo7boo19boo7boo19boo7boo19boo7boo!
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Re: Synthesising Oscillators

Postby Scorbie » July 6th, 2016, 12:39 pm

Hmm! A long shot, but that p5 could be a better alternative to a middleweight volcano in some situations.
Best wishes to you, Scorbie
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Re: Synthesising Oscillators

Postby mniemiec » July 8th, 2016, 4:15 pm

This is a partial attempt to create the core of a P4 oscillator, of which the first two instances occur at 24 bits. A natural 30-bit one popped out of a soup a while back; unfortunately, there is no way to reduce the length of the rotor.

This shows generations 0, 25, 26, 28, and 32 of various evolution stages.
The first row is the base synthesis; the two SW converters interact to produce a toxic bit at generation 25. The second row assumes the toxic bit is gone; at generation 26, the NW glider hitting the pre-block generates another bit, which becomes toxic at generation 28. The third row assumes these bits are gone, and produce the final oscillator at 28, and debris quiesces at 32. (The other related form is also shown; it can be made the same way, starting with a different still-life). I'm not sure how to create the initial still-life either, but at least this might be a start.
x = 170, y = 116, rule = B3/S23
9bo$10boo$9boo3$4bo17bo$5boo14bo24bo$4boo5bo9b3o23bo$9bobo33bo$10boo
15bo20bo$26bo18bobbo$26b3o12bo3b5o$42boboo3boo$40b3obb5o$46b3o$47bo$
50bobo$15boo28boo3boo$bo14bo29bobb3o$bbo13boboo26boboo$3o10boobobbo23b
oobobbo$12boboboo24boboboo$12bobo27bobo$11boobo14bo11boobo$14bobo10boo
15bobo$11boobboo11boo7bo3boobboo$11bo33bo$9bobo25boo4bo3bo$9boo26bo9bo
4bo$18boo17bo5bo8boo$17bobbo33bo$17bobbo18bobboo9bo$18boo19booboo3$8b
oo$3b3o3boo$5bobbo$4bo$19boo$18boo$20bo5$46bo$47bo28bo$45bo$48bo$45bo
bbo26bo$41bo3b5o27bobbo22boo5bo$42boboo3boo19bob3o5bo22b3o3bobo$40b3o
bb5o21b4o5bo22bo3bo3bo$46b3o22bo3bo3bo$47bo28b3o30bo$50bobo23bo3bo27bo
$45boo3boo23boo5bo22boo$46bobb3o24bobobbo24bo$46boboo26bobo27boboo$43b
oobobbo23boobobbo23booboboo$42boboboo24boboboo24boboboo$42bobo27bobo
27bobo$41boobo26boobo26booboo$44bobo27bobo27bo$37bo3boobboo27bobo27bob
o$45bo21boo6bo29boo$37boo8bo19boo7bo19bo$37bo9bo4bo13boo14boo13bo14boo
$37bo5bo8boo28boo13bo13bo$54bo17boo8bobo$39bobboo9bo15b5o25boobboo$39b
ooboo25b5o25bob3o$100b3o$101bo13$76bo3$75bo$77bobbo22boo5bo$70bob3o5bo
22b3o3bobo28boo$71b4o5bo22bo3bo3bo28boo$71bo3bo3bo30bo$76b3o30bo$76bo$
75boo5bo22boo28boo28boo$76bobobbo24bo29bo29bo$76bobo27boboo26boboo26bo
boo$73boobobbo23booboboo23booboboo23booboboo$72boboboo24boboboo24bobob
oo24boboboo$72bobo27bobo27bobo26bobbo$71boobo26booboo25booboo25booboo$
74bobo27bo29bo29bo$74bobo27bobo27bobo27bobo$67boo6bo29boo28boo28boo$
67boo7bo19bo$66boo14boo13bo14boo$82boo13bo13bo$72boo8bobo$69b5o25boobb
oo$69b5o25bob3o$100b3o$101bo31boo$133boo!
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Re: Synthesising Oscillators

Postby BlinkerSpawn » July 8th, 2016, 4:45 pm

I'm laughing inside.
x = 14, y = 10, rule = B3/S23
4b2o$5bo$5bob2o3bo$2b2obo2bo2bo$bobo2b2o3b3o$bobo$2ob2o3b3o$3bo4bo$3bo
bo3bo$4b2o!
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Re: Synthesising Oscillators

Postby mniemiec » July 8th, 2016, 8:48 pm

BlinkerSpawn wrote:I'm laughing inside. ...

(smashing head against wall) I had tried almost this exact approach earlier (with the frontmost glider alone) but it looked sufficiently non-viable that I didn't pursue it. Congratulations! This solves one of the two oscillators from 40 gliders. It doesn't quite solve the other one yet, but it leaves a much simpler 22-bit unsolved base still-life, which looks like it shouldn't be too difficult.
x = 288, y = 103, rule = B3/S23
130bo$129bo$125bo3b3o$126boo7bo6bo$125boo6boo5boo$69bo64boo5boo$68bo
174bo$68b3o170bobo$59bobo180boo$60boo81bo$14bo30bo14bo14bo29bo29bo7bob
o17boo28boo28boo28boo28boo$15boo27bobo27bobo27bobo27bobo6boo19bo29bo
29bo29bo29bo$14boo28bobo27bobo27bobo27bobo27boboo26boboo26boboo26boboo
26boboo$41booboo25booboo23bobooboo25booboo25booboobo21bobooboobo21bob
oobobbo21boboobobbo23boobobbo$15bo24bobo27bobo26boobo27bobo27bobo26boo
bo26boobobboo22boobobboo21bobobobboo$15boo23bobo19boo6bobo29bo27bobo
27bobo29bo29bo29bo25boobbo$14bobo24bo19bobo7bo30boo27bo14bo14bo30boo
28boo15bo12boo28boo$63bo81boo52bo40boo$145bobo50boo39boo$136b3o59bobo$
20boo116bo107boo$7boo11bobo41boo5boo64bo103b3oboo$8boo10bo44boo5boo6b
oo114b3o44bo3bo$7bo56bo6bo7boo117bo43bo$75b3o3bo115bo$77bo121b3o$76bo
122bo$200bo9$o$boo$oo$$13boo28boo28boo28boo28boo28boo28boo28boo28boo
28boo$14bo29bo29bo29bo29bo29bo29bo29bo29bo29bo$14boboo26boboo26boboo
26boboo26boboo26boboo26boboo26boboo26boboo3bobo20boboo$11boobobbo23boo
bobbo23boobobbo23boobobbo23boobobbo23boobobbo23boobobbo23boobobbo23boo
bobbo3boo18boobobbo$8bobobobboo23bobobboo23bobobboo23bobobboo23bobobb
oo23bobobboo23bobobboo23bobobboo23bobobboo5bo17bobobo$8boobbo27bobo27b
obo27bobo27bobo27bobo27bobo27bobo27bobo27bobobbo$12boo25booboo25booboo
25booboo25booboo25booboo25booboo25booboo25booboo5bo19boobo$107boo28boo
23bo29bo29bo29bo5boo22bo$77bobo26bobbo12boo12bobbo22bobo27bobo27bobo
27bobo3bobo21bobo$4bobo70boo18boo7bobbo13boobboo7bobbo23boo28boo28boo
28boo28boo$5boo59bobo9bo17bobbo7boo13bo3bobbobboo3boo$5bo61boo27bobbo
26bobboboo$67bo10boo17boo28boo4bo4bo$5b3o70bobo56boo29bo29bo$7bo58boo
10bo52boo4bobo27bobo27bobo$6bo58bobo62bobo34bobo27bobo$67bo64bo35bo29b
o$bb3o195boo$4bo195bobo$3bo196bo11$70bo$69bo$65bo3b3o$66boo7bo6bo$65b
oo6boo5boo$19bo54boo5boo$18bo$18b3o$$21boo60bo$15boo4bobo21bo29bo7bobo
17boo28boo28boo28boo28boo28boo28boo$14bobo4bo22bobo27bobo6boo19bo29bo
29bo29bo29bo29bo29bo$14bo29bobo27bobo27boboo26boboo26boboo26boboo26bob
oo26boboo3bobo20boboo$11booboo25booboo25booboo25booboobo23booboobo23b
oobobbo23boobobbo23boobobbo23boobobbo3boo18boobobbo$10bobo27bobo27bobo
27bobo27bobo27bobobboo23bobobboo9bo13bobobboo23bobobboo5bo17bobobo$9bo
bbo26bobbo26bobbo26bobbo26bobbo26bobbo26bobbo13bobo10bobbo26bobbo26bo
bbobbo$9booboo25booboo25booboo12bo12booboo25booboo25booboo21bo3booboo
12boo11booboo25booboo5bo19boobo$10bobo27bobo27bobo12boo13bobo27bobo6bo
20bobo23bo3bobo29bo29bo5boo22bo$10bobo27bobo27bobo12bobo12bobo27bobo5b
oo20bobo21b3o3bobo29bobo27bobo3bobo21bobo$11bo29bo29bo4b3o22bo29bo6bob
o20bo29bo31boo28boo28boo$78bo103boo$77bo103bobo$136b3o44bo$138bo71bo$
137bo64boo5boo$139b3o59boo6bobo$139bo48boo13bo$140bo48boo$188bo18boo$
207bobo$183boo12boo8bo$184boo10boo$183bo14bo!
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Re: Synthesising Oscillators

Postby BlinkerSpawn » July 8th, 2016, 9:47 pm

This looks pretty difficult.
x = 8, y = 11, rule = B3/S23
6bo$5bobo$5bobo$2b2ob2o$bobo$o2bo$b2o$bobobo$2obobo$2o2bo$bo4bo!

EDIT: Slightly more managable?
x = 8, y = 12, rule = B3/S23
6bo$5bobo$5bobo$2b2ob2o$bobo$o2bo$b2o$bobobo$2obobo$2obo2b2o$bo$bo!
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Re: Synthesising Oscillators

Postby mniemiec » July 8th, 2016, 10:28 pm

BlinkerSpawn wrote:This looks pretty difficult. ,,, EDIT: Slightly more managable? ...

Even if these could be made to work, they wouldn't work with the previous mechanism, as the last conversion step that makes the curl requires some clearance that isn't there once the lower bookend is in place. It can be done a different way, however:
x = 224, y = 26, rule = B3/S23
139bo$138bo$138b3o$6bobo184bo$bo4boo128bo57bo$bbo4bo3bo6bo116bo56b3o7b
o$3o7bo6bo62bo54b3o58bo4bo$10b3o4b3o55bo3bo116bobobb3o$76boob3o55bo58b
oo$75boo59boo$136bobo$82boo$81boo121bo$11bo27boo28boo12bo15boo28boo28b
ooboo25booboo9boo14boo$10bobo5bobo19bo29bo29bobboo25bobboo25bobo27bobo
10bobo14bo$10bobo5boo20boboo26boboo26bobobo25bobobo25bobo27bobo27boboo
$7booboo7bo17booboobo23booboobo23booboo25booboo25booboo25booboo25boobo
bbo$6bobo27bobo27bobo27bobo27bobo27bobo27bobo11b3o13bobobboo$5bobbo8b
3o15bobbo26bobbo26bobbo26bobbo26bobbo26bobbo11bo14bobbo$5booboo7bo17b
ooboo25booboo25booboo25booboo25booboo25booboo11bo13booboo$6bobo9bo17bo
bo29bo29bo29bo29bo29bo29bo$6bobo27bobo29bobo8boo17bobo27bobo10boo15bob
o27bobo27bobo$7bo29bo31boo8bobo17boo28boo9boo17boo28boo28boo$21boo56bo
62bo$21bobo$21bo!
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Re: Synthesising Oscillators

Postby Extrementhusiast » July 8th, 2016, 11:58 pm

BlinkerSpawn wrote:I'm laughing inside.
RLE

Same here, as I had solved all three minimal variants soon after the original oscillator showed up, but apparently forgot to post them:
x = 338, y = 170, rule = B3/S23
17bobo$11bobo4b2o$12b2o4bo$bo10bo$2bo$3o$15bo$16bo10bo$14b3o9bo$26b3o
4b2o$33bobo68bo$33bo71bo88bo$103b3o86bobo$57b2o19b2o35b2o22b2o25b2o25b
2o15b2o29b2o41b2o$50bobo5bo20bo36bo23bo26bo43bo30bo42bo$46b3o2b2o5bob
2o13b2o2bob2o16bo4b3o5b2o2bob2o20bob2o13bo9bob2o40bob2o27bob2o5bo33bob
2o$8bobo37bo2bo3b2obo2bo13bobobo2bo17b2o4bo5bobobo2bo17b2obo2bo14bo5b
2obo2bo31bo5b2obo2bo24b2obo2bo5bobo2bo25b2obo2bo$8b2o37bo7b2obobo15b2o
bobo4bo12b2o4bo8bobobo19bobobo13b3o4bobobobo26b3obobo6bobobo24bobobobo
6b2o2b2o24bobobo$9bo18bo22b2o6bo20bo5bobo24b2ob2o13bo4bobob2o21bobob2o
29bo2b2o6bob2o7bobo14bo2bob2o11bobo22bo2bo2bo$27b2o21bobo33b2o41bobo4b
2o26bo32bo10b2o10b2o15b2obo39b2obo$10b2o5b2o8bobo22bo77b2o77bo11bo18bo
42bo$11b2o5b2o119b2o25b2o41bobo28bobob2o37bobo$10bo6bo114b3o5bo26bo42b
2o29b2obobo5bo31b2o$80b2o33b2o17bo5bobo19b2o3bobo64bobo8bo5b2o$80bobo
33b2o15bo7b2o18b2o5b2o65b2o14bobo$80bo34bo3b2o37b2o3bo53b2o16bo$19b2o
55b3o40bobo35bobo14b2o41bobo$18b2o58bo40bo39bo13b2o34b2o6bo47bo$20bo
56bo97bo32bobo37b2o14b2o$210bo36b2o15bobo$160b2o8b3o39b3o24bo9bo$161b
2o7bo41bo26b2o$160bo10bo35bo5bo24bobo$207b2o$206bobo40bo$248b2o$248bob
o30$17bobo$11bobo4b2o$12b2o4bo$bo10bo$2bo$3o159bo$15bo145bo$16bo10bo
133b3o$14b3o9bo$26b3o4b2o111bobo$33bobo68bo42b2o$33bo71bo41bo$103b3o$
57b2o19b2o35b2o44b2o44b2o34b2o37b2o$50bobo5bo20bo36bo45bo45bo35bo38bo$
46b3o2b2o5bob2o13b2o2bob2o16bo4b3o5b2o2bob2o42bob2o42bob2o32bob2o5bo
29bob2o$8bobo37bo2bo3b2obo2bo13bobobo2bo17b2o4bo5bobobo2bo39b2obo2bo
39b2obo2bo29b2obo2bo5bobo2bo21b2obo2bo$8b2o37bo7b2obobo15b2obobo4bo12b
2o4bo8bobobo41bobobo39bobobobo29bobobobo6b2o2b2o20bobobo$9bo18bo22b2o
6bo20bo5bobo24b2ob2o40bobob2o40bobob2o7bobo20bobob2o11bobo19bobo2bo$
27b2o21bobo33b2o70b2o43b2obo10b2o20b2obo35b2obo$10b2o5b2o8bobo22bo153b
o11bo23bo38bo$11b2o5b2o141b2o43bobo33bobob2o33bobo$10bo6bo144bo44b2o
34b2obobo5bo27b2o$80b2o33b2o45bobo71bobo8bo5b2o$80bobo33b2o45b2o72b2o
14bobo$80bo34bo3b2o93b2o21bo$19b2o55b3o40bobo28b3o61bobo$18b2o58bo40bo
32bo53b2o6bo52bo$20bo56bo73bo53bobo42b2o14b2o$207bo41b2o15bobo$147b2o
3b2o20bo34b3o29bo9bo$146bobo2b2o20b2o34bo31b2o$148bo4bo19bobo28bo5bo
29bobo$204b2o$170b2o31bobo45bo$140bo29bobo77b2o$140b2o28bo79bobo$139bo
bo29$17bobo$11bobo4b2o$12b2o4bo$bo10bo$2bo$3o159bo$15bo145bo$16bo10bo
133b3o$14b3o9bo$26b3o4b2o111bobo$33bobo68bo42b2o47bo3bo$33bo71bo41bo
46bobo3bobo$103b3o89b2o3b2o$57b2o19b2o35b2o44b2o44b2o34b2o28b2o19b2o
37b2o$50bobo5bo20bo36bo45bo35b3o7bo28bo6bo29bo20bo38bo$46b3o2b2o5bob2o
13b2o2bob2o16bo4b3o5b2o2bob2o42bob2o34bo7bob2o23bobo6bob2o26bob2o17bob
2o5bo29bob2o$8bobo37bo2bo3b2obo2bo13bobobo2bo17b2o4bo5bobobo2bo39b2obo
2bo33bo5b2obo2bo24b2o3b2obo2bo12bo10b2obo2bo14b2obo2bo5bobo2bo21b2obo
2bo$8b2o37bo7b2obobo15b2obobo4bo12b2o4bo8bobobo41bobobo39bobobobo29bob
obobo14b2o9bobobo16bobobo6b2o2b2o22bobo$9bo18bo22b2o6bo20bo5bobo24b2ob
2o40bobob2o40bobob2o7bobo13b3o4bobob2o14b2o2b2o3bo2bob2o14bo2bob2o11bo
bo18bo2bo2bo$27b2o21bobo33b2o70b2o43b2obo10b2o16bo2bobobo20bobo2bobobo
16bobobo34bobobo$10b2o5b2o8bobo22bo153bo11bo15bo3b2o2bo22bo2b2o2bo17bo
2bo35bo2bo$11b2o5b2o141b2o43bobo33bobob2o24bobob2o15bobob2o33bobo$10bo
6bo144bo44b2o34b2obobo24b2obobo15b2obobo5bo27b2o$80b2o33b2o45bobo82bo
29bo9bobo8bo5b2o$80bobo33b2o45b2o123b2o14bobo$80bo34bo3b2o93b2o72bo$
19b2o55b3o40bobo28b3o61bobo$18b2o58bo40bo32bo53b2o6bo103bo$20bo56bo73b
o53bobo93b2o14b2o$207bo92b2o15bobo$147b2o3b2o20bo34b3o80bo9bo$146bobo
2b2o20b2o34bo82b2o$148bo4bo19bobo28bo5bo80bobo$204b2o$170b2o31bobo96bo
$140bo29bobo128b2o$140b2o28bo130bobo$139bobo!
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Re: Synthesising Oscillators

Postby mniemiec » July 11th, 2016, 9:45 pm

Well, at least my previous efforts to make the unnamed P4 weren't entirely in vain. There is a closely related 27-bit one that uses an eater, which interferes with the curl+2 glider converter. I was eventually able to fix the spurious bit in the top half, yielding this 43-glider synthesis. I'm sure there's probably a way to make the eater from fewer than 12 gliders, but given its placement, it's not obvious:
x = 172, y = 111, rule = B3/S23
70bo$68boo57bo$65bo3boo54bobo$63bobo7bo7bobo42boo$64boo7bobo5boo53bo$
20bo52boo7bo52bo$19bo109boo4b3o$12bobo4b3o61boo43bobo9bo$13boo68bobo
44bo9bobo$13bo69bo56boo$102booboo25booboo25boo$73boo6bo21boboo26boboo
6boo18bo$11bo61bo6boo21bo29bo9bobo17boboo$11bobo7bo18booboo25boobo6bob
o17boobo26boobo9bo16boobobbo$11boo6boo17bobboboo23bobboboo23bobboboo
23bobboboo4boo17bobboboo$20boo16boobo26boobo26boobo26boobo6boo18boobo$
9boo30bo29bo29bo29bo8bo20bo$8boo31boo28boo28boo28boo28boo$boo7bo127boo
$obo134bobo$bbo136bo$141boo$141bobo$5b3o133bo$7bo$6bo$9boo$8boo$10bo
22$12boo28boo28boo28boo28boo28boo$13bo29bo29bo29bo29bo29bo$13boboo26bo
boo26boboo26boboo26boboo26boboo$10boobobbo23boobobbo23boobobbo23boobo
bbo23boobobbo23boobobbo$8bobboboo23bobboboo23bobboboo23bobboboo23bobbo
boo23bobboboo$8boobo11bobo12boobo5bo20boobo5bo20boobo26boobo11bobo12b
oobo$11bo11boo16bo5bo23bo5bo23bo4boo23bo4boo5boo16bo4boo$11boo11bo16b
oo4bo23boo4bo23boo3bobo22boo3bobo5bo16boo3bo$107boo28boo30bo$21boo54b
oo68b3o18boo$20boo54bobo62boo4bo$22bo55bo62bobo4bo$137bo3bo$137boo$
136bobo6b3o23bo$145bo25bo$142bo3bo24bo$141boo$141bobo9$127bobo$128boo$
128bo$$141bobo$126bo9bo4boo$124bobo7boo6bo$125boo3bobobboo$131boo13boo
$131bo9bo3b4o$139boo3booboo$140boo3boo$$12boo28boo28boo28boo28boo28boo
$13bo29bo29bo29bo29bo29bo$13boboo26boboo26boboo26boboo26boboo26boboo$
10boobobbo23boobobbo23boobobbo23boobobbo23boobobbo23boobobbo$8bobboboo
23bobboboo23bobboboo23bobboboo23bobboboo23bobbobo$8boobo26boobo26boobo
26boobo26boobo26boobobo3bo$11bo4boo23bo4boo23bo4boo23bo4boo23bo4boo23b
o5bo$11boo3bo24boo3bo24boo3bo24boo3bo24boo3bo24boo3bo$19bo29bo29bo27b
3o27b3o27b3o$18boo28boo28boo29bo29bo29bo3$78boo$74bo3bobo$21bo52boobbo
$21bo51bobo$21bo$$22boo$22bobo$22bo!
mniemiec
 
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Re: Synthesising Oscillators

Postby Extrementhusiast » July 12th, 2016, 12:00 am

mniemiec wrote:Well, at least my previous efforts to make the unnamed P4 weren't entirely in vain. There is a closely related 27-bit one that uses an eater, which interferes with the curl+2 glider converter. I was eventually able to fix the spurious bit in the top half, yielding this 43-glider synthesis. I'm sure there's probably a way to make the eater from fewer than 12 gliders, but given its placement, it's not obvious:
RLE

It should be obvious, as there's a four-glider method right there in your list:
x = 36, y = 29, rule = B3/S23
4b2o$5bo$5bob2o$2b2obo2bo$o2bob2o$2obo$3bo16bo$3b2o14bo$19b3o$17bo$16b
2o$16bobo10$26b2o$25b2o$27bo3$33b2o$33bobo$33bo!

Additionally (if less obviously), the activation can be reduced to just three gliders:
x = 17, y = 22, rule = B3/S23
14bobo$14b2o$15bo$11bo$9bobo$10b2o2$12bo$11bo$11b3o3$4b2o$5bo$5bob2o$
2b2obo2bo$o2bob2o$2obo$3bo4b2o$3b2o3bo$9b3o$11bo!

In other news, a one-sided three-glider method of putting a beehive on a domino:
x = 23, y = 17, rule = B3/S23
obo$b2o$bo2$14bo7bo$12bobo5b2o$13b2o6b2o8$7b2o$6bo2bo$7b2o!
I Like My Heisenburps! (and others)
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Extrementhusiast
 
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Location: USA

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