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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 dvgrn » February 26th, 2018, 7:05 pm

calcyman wrote:I think this is getting somewhat off-topic, so this discussion should be migrated to either the Catagolue discussion thread, or to the old pre-Catagolue CACoin thread, or to the comments section in https://mathoverflow.net/a/277668/39521

Darn, and I had already written a long response. I guess I'll just post helpful links to

the Catagolue discussion thread

and

the old pre-Catagolue CACoin thread.

Seems like the CACoin thread is probably the better of the two places to put my long boring posting. In point of fact, calcyman posted a good shorter summary last year about how to even out the unevenness sufficiently.
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Re: Synthesising Oscillators

Postby Goldtiger997 » February 27th, 2018, 7:38 pm

Back from the very interesting but off-topic topic of LifeCoin.

Goldtiger997 wrote:As I said I would before, I will create a collection of the cheapest 16-bit oscillator synthesis (separate to the rest because there is a lot). Most of these I can easily find from mniemiec's website (though some are outdated which I will attend to later), but I may need some help finding all the ones that are marked as unsolved.


This took me longer than expected to do. I have now transferred all the syntheses marked as solved (and "X+6") into a folder. I did many obvious improvements from newer still-life syntheses and converters. There are probably several more to be done. I also created this new 16-bit oscillator synthesis in 10 gliders:

x = 68, y = 33, rule = B3/S23
45bo$44bo$44b3o2$39bo$39bobo$39b2o2$38bo$36bobo$37b2o$bo22bo19bo$2bo
20bobo17bobo$3ob2o17bo2bo16bo2bo15bo3b2o$4bobo17b2o18b2o16bo4bo$4bo56b
o2bobo2$2bo57bobo2bo$obo18b2o18b2o16bo4bo$b2ob3o13bo2bo16bo2bo15b2o3bo
$4bo16bobo17bobo$5bo16bo19bo$48b2o$48bobo$48bo2$46b2o$45bobo$47bo2$40b
3o$42bo$41bo!


So here's the folder:
oscill16-mostlyfinished.zip
97 16-bit oscillator syntheses
(33.26 KiB) Downloaded 55 times


Suspiciously, it contains 97 syntheses, when it should only contain 96 because there are still 12 more to go and 108 16-bit oscillators in total. Somehow, an extra syntheses has snuck in. Maybe I'll find it when doing the last 12 syntheses (These are the ones that are marked as synthesized). I know where to find some of those syntheses, but I may need some help finding them all.
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Re: Synthesising Oscillators

Postby mattiward » February 28th, 2018, 3:44 am

Hertz Oscillator with minimum population from 64 gliders:
x = 571, y = 243, rule = B3/S23
304bo$302b2o$153bobo147b2o$154b2o151bobo$154bo152b2o$308bo$314bo$312b
2o$313b2o2$142bobo$143b2o$143bo5$144bo154bo$145b2o152bobo$144b2o153b2o
5$149bo$147bobo146bo$148b2o117bo26b2o$265b2o28b2o$266b2o$186bo$184bobo
107bo$185b2o83bo23bobo$182bo80bo5bo24b2o$183bo79bobo3b3o$177bo3b3o79b
2o$175bobo$176b2o8bo$187b2o$186b2o11bo$190bo9bo$191b2o5b3o$190b2o4$
264bo$262b2o$263b2o4$200bo$201bo43bo$199b3o42bo$244b3o3$215bo$216b2o$
215b2o3$185bobo$186b2o$186bo55bo$242bobo$242b2o4$226bo$225bo$225b3o2$
221bo$222bo$220b3o2$212bobo$213b2o22bo$207bo5bo21b2o$208bo27b2o$206b3o
17bo$227bo$225b3o$229b2o$230b2o$229bo$240b2o$216bo22b2o3b3o$216b2o4bo
7bo10bo2bo$215bobo4b2o6b2o13bo$221bobo5bobo4$231b3o$231bo$232bo2$224b
3o$226bo$225bo3$209b2o$208bobo$210bo55bo$265b2o$265bobo3$236b2o$235b2o
$237bo3$206b3o$208bo42b3o$207bo43bo$252bo4$188b2o$189b2o$188bo4$261b2o
$252b3o5b2o$252bo9bo$253bo11b2o$264b2o$266bo8b2o$275bobo$188b2o79b3o3b
o$181b3o3bobo79bo$157b2o24bo5bo80bo$156bobo23bo83b2o$158bo107bobo$266b
o$185b2o$156b2o28b2o$157b2o26bo117b2o$156bo146bobo$303bo5$152b2o153b2o
$151bobo152b2o$153bo154bo5$309bo$308b2o$308bobo2$138b2o$139b2o$138bo$
144bo$144b2o152bo$143bobo151b2o$148b2o147bobo$149b2o$148bo32$335bo$
336bo$67bobo51bobo107bobo100b3o$68b2o52b2o108b2o104bo$14bo53bo53bo109b
o104bo$13bo323b3o$13b3o155bo$169bobo2bo219bo163bobo$9bo64bo53bo41b2o2b
obo61bo45bo50bobo52bo2bo160bo3b2o$10bo62bo53bo46b2o61bo47bo50b2o53bob
3o159b2o2bo4bo$8b3o62b3o51b3o107b3o43b3o50bo48bo3b3o162b2o6b2o$383bobo
177b2o$obo73b2o52b2o44b2o62b2o44b2o96b2o$b2o22bo38b2ob2o7bobo39b2ob2o
7bobo39b2o2bobo47b2o3b2o7bobo37b2o4bobo45b2o5b2o45b2o2bo2b2o52b2o52b2o
52b2o4bo4bobo$bo21b2o39bo3bo7bo41bo3bo7bo41bo5bo47bo2bo2bo7bo39bo2bo4b
o45bo2bobo2bo45bo2bobo2bo47b2obo2bo9bobo35b2obo2bo5bo41b2obo2bo3b2o4b
2o$24b2o39b3o51b3o51b5o49b5o49b7o47b3ob3o47b3ob3o35bobo10bob4o10b2o36b
ob4o6bobo39bob4o4bobo4bo$14bo416b2o28bo48b2o2b2o27bo$15bo51b3o51b3o51b
3o51b3o51b3o51b3o51b3o38bo12b3o51b3o12bobo27b2o7b3o3b2o$13b3o50bobobob
2o46bobobob2o46bobobob2o46bobobob2o46bobobob2o46bobobob2o46bobobob2o
46bobobob2o8bo29b2o6bobobob2o8bo28b2o7bobobobo2bo$17b2o47b2ob2ob2o46b
2ob2ob2o46b2ob2ob2o46b2ob2ob2o46b2ob2ob2o46b2ob2ob2o46b2ob2ob2o33b3o
10b2ob2ob2o7bo29bo2bo5b2ob2ob2o3b2o38bo2b2ob2obobo$18b2o43b2obo3bo46b
2obo3bo46b2obo3bo46b2obo3bo46b2obo3bo46b2obo3bo46b2obo3bo38bo7b2obo3bo
10b3o28b2o3b2obo3bo5bo2bo36bobobo3bo2bo$17bo45b2obobobo46b2obobobo46b
2obobobo46b2obobobo46b2obobobo46b2obobobo46b2obobobo37bo8b2obobobo37bo
8b2obobobo6b2o36bo2bobobobo7b2o$28b2o37b3o51b3o51b3o51b3o51b3o51b3o51b
3o51b3o12bo23bobo12b3o46b2o3b3o7b2o$4bo22b2o402bo28b2o23b2o2b2o74bo$4b
2o4bo7bo10bo39b3o51b3o49b5o49b5o47b7o47b3ob3o47b3ob3o35b2o10b4obo10bob
o26bobo6b4obo36bo4bobo4b4obo$3bobo4b2o6b2o40bo7bo3bo41bo7bo3bo47bo5bo
39bo7bo2bo2bo45bo4bo2bo45bo2bobo2bo45bo2bobo2bo33bobo9bo2bob2o41bo5bo
2bob2o36b2o4b2o3bo2bob2o$9bobo5bobo38bobo7b2ob2o39bobo7b2ob2o47bobo2b
2o37bobo7b2o3b2o45bobo4b2o45b2o5b2o45b2o2bo2b2o45b2o52b2o40bobo4bo4b2o
$59b2o52b2o60b2o42b2o60b2o116b2o$399bobo142b2o$61b3o51b3o103b3o59b3o
54bo52b3o3bo145b2o6b2o$19b3o41bo53bo59b2o44bo59bo55b2o48b3obo150bo4bo
2b2o$19bo42bo53bo59bobo2b2o39bo61bo54bobo49bo2bo154b2o3bo$20bo157bo2bo
bo206bo157bobo$181bo$12b3o322b3o$14bo53bo53bo105bo110bo$13bo53b2o52b2o
104b2o109bo$67bobo51bobo103bobo110b3o$340bo$341bo!
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Re: Synthesising Oscillators

Postby Goldtiger997 » February 28th, 2018, 8:53 am

mattiward wrote:Hertz Oscillator with minimum population from 64 gliders:
rle

That's a nice synthesis mattiward. However, an 11 glider synthesis is listed on the LifeWiki. (Edit: Not true, as pointed out by mniemiec below. I assumed that the stator variant shown on the wiki was the same as in the synthesis without properly checking it. Sorry mattiward :oops: )

I've added the syntheses of all the 16-bit oscillators, except for three which I've been unable to locate:

x = 35, y = 6, rule = B3/S23
2bobo8b3o3bo7b3ob3o$3bo2bo12bo$2obobobo6bob2o2bo7bobobo$3bo3bo5bo13bo$
bobob2o6b2o3bobo6b2o3bobo$3bo15b2o12b2o!


Could someone point me towards those syntheses...

Also, there is not a complete synthesis for another 16-bit oscillator, so this will also need to be completed (unless there is another way). It looks like it should take around 21 gliders:

x = 75, y = 46, rule = B3/S23
5$31bo$32bo$31bo$31bo$33bo$31b2ob2o$32bobo$33bo$46b2o$45bo2bo$46b2o4$
35bo$34bobo$35bo6b3o2$60bo$59bobo$59bobo$58bo$43b2o13b3o5b3o$43b2o11b
2o3bo2b2o3bo$55bo5bo6bo$59bob3ob3o$57b2obo2b4o$53bo3bo$54bo3bo$11bo43b
2obo$11b2o44bo$10bobo!
Last edited by Goldtiger997 on February 28th, 2018, 6:51 pm, edited 1 time in total.
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Re: Synthesising Oscillators

Postby mniemiec » February 28th, 2018, 9:35 am

mattiward wrote:Hertz Oscillator with minimum population from 64 gliders: ...

Goldtiger997 wrote:That's a nice synthesis mattiward. However, an 11 glider synthesis is listed on the LifeWiki.

Not true. The LifeWiki shows the minimum stator for the oscillator, but the synthesis there is David Buckingham's old synthesis for a larger (and much cheaper) stator variant. This new synthesis is for one of the 5 minimum-population stator variants (with blocks on two sides and snakes on the other two).
Goldtiger997 wrote:I've added the syntheses of all the 16-bit oscillators, except for three which I've been unable to locate: ... Could someone point me towards those syntheses... Also, there is not a complete synthesis for another 16-bit oscillator, so this will also need to be completed (unless there is another way). It looks like it should take around 21 gliders: ...

Here they the latest versions I have:
x = 270, y = 174, rule = B3/S23
3bobo121bo$4boo3bo115boo$4bobboo117boo$8boo113bo14bo$124bo13bobo$122b
3o13boo$19bo11bo19bo19bo19bo19bo19bo19bo$19bobo9bobo17bobo17bobo17bobo
17bobo17bobo17bobo$19boo8bo4bo14bo4bo14bo4bo14bo4bo14bo4bo14bo4bo7bo6b
o$3o4boo19bob5o13bob5o13bob5o13bob5o13bob5o13bob5o7bobo5b5o$bbo3boo21b
o19bo19bo19bo19bo19bo12boo5bo$bo6bo22boboo16boboo16boboo16boboo16boboo
7b3o6boboo16bobo$30booboo15booboo15booboo15booboo15boobobo8bo5boobobo
14bobbo$114bo8bo10bo4boo10boo$139bobo$71boo14boobboobboo27bo14bo$11b3o
37b3o17boo15boobooboo28boo$13bo5boo30bo35bo8bo26bobo3boo3b3o$12bo6bobo
30bo75boo4bo$19bo28b3o42boo35bo4bo$50bo41bobo$49bo44bo8$61bobo$61boo$
62bo7$3bobo$4boo$4bo$29bo$30boo$29boo6$49bo$47boo$48boo4$76b3o3bo$82bo
$77boboobbo$76bo$76boo3bobo$82boo4$57boo$57bobo$57bo$45bo$44boo$44bobo
$$53boo$52boo$54bo6boo$60boo$35bo26bo$33bobo$34boo4$47bo$46boo$42bo3bo
bo$43boo$42boo15$55bobo$bbo52boo8bobo$obo35bo17bo8boo$boo3bo29bobo27bo
$4boo17boo12boo14boo$5boo16bobo27bobo12bobo$25bo23boo4bo12boo$25boo21b
obo4boo12bo$50bo13bo$64bobo$44bo19boo$44boo46b3ob3o13b3ob3o13b3ob3o13b
3ob3o13b3ob3o13b3ob3o23b3ob3o13b3ob3o13b3ob3o$43bobo24boo$48bo20boo22b
obobo15bobobo15bobobo15bobobo15bobobo6bobo6bobobo25bobobo15bobobo15bob
obo$47boo22bo20bo5bo13bo5bo13bo5bo13bo5bo13bo5bo6boo5bo5bo9bo13bo19bo
19bo$47bobo24bo17boo3boo13boo3boo13boo3boo13boo3boo13boo3boo6bo6boo3b
oo8bo14boo3bobo12boo3bobo12boo3bobo$73boo127bo4b3o18boo18boo18boo$73bo
bo56boo18boo18b4o16b4o6bobo$113b3o16bobo17bobo6bo10bobbo11bo4bobbo6boo
$113bo19bo19bo7bobo9boo13boo3boo$59b3o52bo46boo24boo$59bo98boo44boo$
60bo96boo37bo7bobo12boo18boo$159bo35boo7bo14boobboo14boobboo$46b3o146b
obo25boo18boo$48bo191bo$47bo144b3o45boo$194bo44bobo$57b3o133bo$57bo$
58bo10$47bo$48boo$47boo$$59bo$57boo$58boo4$42bo$43bo$41b3o$5bo16bo29bo
22boo3boo32bo$4bo16bobo10boo15bobo21bo5bo22boo7bo30boo$boob3o13bobbo8b
ooboo13bobbo22bobobo21booboo6b3o26booboo$obo18boo9b4o15boo49b4o36b4o$
bbo30boo7boo17b3o12boobbo22boo7bo30boo7boo$41b4o3bo12bo16bobbo31bo37b
4o$41booboo3bo12bo17boo29b3obbo34booboo$43boobb3o66boo35boo$59boo54bob
o$36bo21boo$36boo22bo$35bobo$44boo4bo$44bobo3bobo$44bo5boo4$49b3o$51bo
$50bo!
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Re: Synthesising Oscillators

Postby Goldtiger997 » March 2nd, 2018, 9:13 pm

mniemiec wrote:
Goldtiger997 wrote:I've added the syntheses of all the 16-bit oscillators, except for three which I've been unable to locate: ... Could someone point me towards those syntheses... Also, there is not a complete synthesis for another 16-bit oscillator, so this will also need to be completed (unless there is another way). It looks like it should take around 21 gliders: ...

Here they the latest versions I have:
4 oscillator syntheses


Thanks mniemiec, I've added those. I hadn't seen those syntheses before, which suggests to me that some of the syntheses that I have are not the best known ones. Either way, here is the folder of all the cheapest 16-bit oscillator syntheses:
oscill16.zip
(38.24 KiB) Downloaded 55 times

There is still suspiciously 109 syntheses in there instead of 108.
For the sake of completeness, I'm also attaching the 3-15 bit oscillator syntheses:
oscill3-15.zip
(22.32 KiB) Downloaded 56 times

If chris_c incorporates these syntheses into the display_synth script, it will make quite a nice feature for catagolue.
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Re: Synthesising Oscillators

Postby mattiward » March 10th, 2018, 12:22 am

P-60 B-shuttle from 28 gliders:
x = 351, y = 57, rule = B3/S23
32bo$31bo$31b3o3$92b2o62b2o48b2o12b2o48b2o12b2o48b2o12b2o$36bo55b2o62b
2o48b2o12b2o48b2o12b2o48b2o12b2o$34b2o170b2o62b2o62b2o$35b2o169bo63bo
63bo$31b2o59b3o61b3o46bobo12b3o46bobo12b3o46bobo12b3o$30b2o55b2o2bob2o
56b2o2bob2o47bobob3o2b2o2bob2o41bo5bobob3o2b2o2bob2o47bobob3o2b2o2bob
2o$32bo45bo8b2o2b2o58b2o2b2o50bob4o2b2o2b2o41bobo6bob4o2b2o2b2o50bob4o
2b2o2b2o$28bo48bo13b2o34bo13bo13b2o51bo10b2o42b2o7bo10b2o51bo10b2o$19b
2o6b2o48b3o48bo11bobo$18bobo6bobo96b3o11bobo$20bo59b3o58bo$25bo54bo
259b3o$25b2o54bo57bo199bo2bo$24bobo111b2o199b2obo$138bobo$132b3o$134bo
$133bo$258bo$259bo$257b3o$123b3o$125bo$124bo107bo$231bo$231b3o$289b3o$
289bo$290bo$223bo$222bo$222b3o$216bobo$10bobo204b2o115bob2o$10b2o71bo
133bo116bo2bo$11bo72bo249b3o$16bo65b3o66bo63bo$7bobo6bobo131bobo61bobo
11b3o$8b2o6b2o67b3o62bobo61bobo11bo$8bo63b2o13bo48b2o13bo48b2o13bo13bo
34b2o10bo7b2o42b2o10bo$4bo67b2o2b2o8bo49b2o2b2o58b2o2b2o58b2o2b2o2b4ob
o6bobo41b2o2b2o2b4obo$5b2o63b2obo2b2o56b2obo2b2o56b2obo2b2o56b2obo2b2o
2b3obobo5bo41b2obo2b2o2b3obobo$4b2o64b3o61b3o61b3o61b3o12bobo46b3o12bo
bo$2o276bo63bo$b2o274b2o62b2o$o70b2o62b2o62b2o62b2o12b2o48b2o12b2o$71b
2o62b2o62b2o62b2o12b2o48b2o12b2o3$3b3o$5bo$4bo!
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Re: Synthesising Oscillators

Postby mattiward » March 17th, 2018, 5:33 pm

Jason Summers's P36 hassler from 28 gliders:
x = 228, y = 45, rule = B3/S23
115bo$113b2o$114b2o$159bo49bo$159b3o47b3o$78bo83bo49bo$76b2o37bo45b2o
48b2o$77b2o34bobo$114b2o$148bo$66bobo47bo32b2o$67b2o45b2o32b2o$67bo10b
obo34b2o$78b2o41b2o48b2o48b2o$66bo12bo43bo49bo49bo$67bo44bo7bo49bo49bo
$65b3o16bo27bobo5bo3bo45bo3bo38b3o4bo3bo$16bo45bo20bo28b2o6bo3b4o42bo
3b4o35bo2bo3bo3b4o$15bo47bo19b3o24bo11bo49bo40bob2o5bo$15b3o43b3o44bob
o49b2o$109b2o48bo2bo$81b2o77b2o$3bo64bo12bobo$b2o63bobo12bo90b2o$2b2o
9b2o52b2o54b2o46bo2bo$12b2o109bobo46b2o$bo12bo46bo49bo11bo37bo49bo5b2o
bo$b2o4b3o46b4o3bo42b4o3bo6b2o34b4o3bo42b4o3bo3bo2bo$obo6bo49bo3bo45bo
3bo5bobo37bo3bo45bo3bo4b3o$8bo2b3o49bo49bo7bo41bo49bo$11bo48bo13b2o34b
o49bo49bo$12bo48b2o11bobo34b2o48b2o48b2o$74bo42b2o$9b2o107b2o64b2o$8bo
bo106bo65b2o$10bo174bo$118b2o$118bobo$118bo52b2o48b2o$171bo49bo$172b3o
47b3o$174bo49bo$118b2o$119b2o$118bo!

Please note: This oscillator mentioned on page 3
x = 29, y = 29, rule = B3/S23
18bo$16b3o$15bo$15b2o5$12b3o$11bo3bo$14bo12b2o$9bo4bo12bo$8bo16bobo$8b
o10bo5b2o$8bob2o5b2obo$2b2o5bo10bo$bobo16bo$bo12bo4bo$2o12bo$13bo3bo$
14b3o5$12b2o$13bo$10b3o$10bo!

is actually the P18 (not the P36).
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Re: Synthesising Oscillators

Postby Entity Valkyrie » March 22nd, 2018, 6:40 am

x = 411, y = 751, rule = B3/S23
252bo13bo$251b3o11b3o$251bob2o4bo5bob2o$252b3o3b3o5b3o$252b2o3b2o2bo4b
2o$257bo3bo$257bob2o$257b2o$277bo$251bo24b3o$250b3o22b2obo$250bob2o21b
3o$251b3o21b3o$251b3o22b2o$251b3o$251b2o3b3obo$256b3obobo$257bo3bo$
257b4o2$258bo14bo$256bobo13b3o$256b2o14bob2o$273b3o$273b2o$268bo$258bo
8b4o$257bobo6bo2b2o$256bo2bo5b2o2bo$256bo9b3o$256b2o9bo$260b2o6$257b2o
$256bo2bo$257b2o6$255bo$255bo$255bo4$259b2o$259b2o4$254b2o$254b2o17bo$
170bo13bo80bo6b3o$169b3o11b3o77bo2bo5bob2o$169bob2o4bo5bob2o76bo3bo5b
3o$170b3o3b3o5b3o75bo5bo4b3o$170b2o3b2o2bo4b2o76bobo8b3o$177b3o93b2o$
263b2o3bo$266bob3o$195bo61b2o9bo$169bo8bo15b3o60b2o5bob3obo$168b3o7bo
14b2obo68bobobo$168bob2o6bo14b3o70b4o$169b3o3bobo15b3o71bo$169b3o3bobo
16b2o$169b3o3b3o$169b2o4$173bo2b3o70bo$175b5o11bo56b3o$171bo8bo9b3o55b
ob2o$170bo2bobob3o10bob2o55b3o3bo$171b2obo3bo12b3o55b3o4b2o$191b2o56b
2o4b2o$174b3o$174bo2b2o$175b2o75bo$175b5o71b3o$251bob2o$252b3o$252b3o$
252b2o7$170bo7bobo$169bobo6bo2bo$169bobo5bo3bo$170bo7bo2bo$174b2o2b3o
78b2o$173bobo83b2o$174bo2$171b2o$171b2o$176bobo$176bobo$173bo3bo$172bo
bo$173bobo$174b3o$176b2o2$191bo$190b3o$173bo16bob2o$173bo17b3o$173bo
17b3o$191b3o125bo13bo$191b2o125b3o11b3o$317b2obo5bo4b2obo$177b2o138b3o
5b3o3b3o$177b2o139b2o4bo2b2o3b2o$324bo3bo$322bo3bobo$265bo$172b2o90b3o
56b2ob2o16bo$172b2o90bob2o50bo6bo17b3o$265b3o49b3o23bob2o$265b3o48b2ob
o24b3o$265b2o49b3o25b3o$316b3o25b2o$316b3o$167bo149b2o5bo$166b3o154bob
2o$166bob2o152b2o2b3o$167b3o5b2o147bo3bo$90bo13bo62b3o5b2o148b2obo$89b
3o11b3o61b2o158bo12bo$89bob2o4bo5bob2o163bo54b2o12b3o$90b3o3b3o5b3o
162b3o66b2obo$90b2o3b2obo5b2o64bo97b2obo66b3o$169b3o96b3o12bo43bo11b2o
$169bob2o95b3o11b3o41bo$170b3o95b3o11bob2o41bo$79bo15bo74b3o96b2o12b3o
$78b3o14b3o7bo64b2o111b3o38b2o$77b2obo15bo7b3o176b3o37bo2bo$77b3o16bo
2bo4bob2o175b2o39b2o$77b3o17b3o5b3o$78b2o25b3o166b2o$105b3o165b2o$105b
2o168bo2$322bo$322bo$95b2o225bo$83bo10bo85bo$82b3o9b3o84b2o$82bob2o9bo
84b2o$83b3o10b3o227b2o$83b2o15bo225b2o55b3o11b3o$98bobo281bo2bo10bo2bo
$99bo285bo4b3o6bo$385bo4bo2bo5bo$321b2o59bobo4bo3bo2bobo$90bobo228b2o
66b4o$90bo2bo296bo$90bo2bo7b3o228b2o$90b3o10bo228b2o38b3o$89b2o7b2o2b
2o268bo2bo22b3o$90bo7bo2bo75b2o193bo16b3o5bo2bo$99b3o75b2o150bo42bo3bo
13b2o8bo$329bo3b2o37bo17b2o4bo3bo$332bo2bo37bobo14b2ob2obo3bo$249b2o
73b2o5bo3bo4bo50bobo6bo$248b2o74b2o13b3o50bo4bobo$98b2o150bo81bo2bo2b
2obo$97bo2bo228bo2bob2o2b3o$98b2o226b2obo2bobo3b3o$325b3obob3o4b3o53bo
$317b3o5b2obo10b2o35b3o15bo$327b3o45bo2bo15bo$183bo143b2o49bo$182b3o
130bo62bo$101bo80bob2o129b2o58bobo$101bo81b3o131b4o69b2o$101bo81b3o
130bob3o69b2o$183b2o3$96b2o297b2o$96b2o288bo4bo3b2o$385bo$83bo301b3o$
82b3o231bo73bo$82bob2o15b2o212b3o72bo$83b3o15b2o211b2obo$83b3o228b3o
73b2o$83b3o228b3o69bo4bo$83b2o9b2o128b2o89b2o69b3o$223b2o162bob4o$225b
o165bobo$87b2o230bo69bo3bo$86bo3b2o226b3o67bo$86bo5bo224b2obo67bo3bo$
87bo10b2o217b3o69bobo$87bo5bo4b2o217b3o70bo$92b2o224b2o69b2o$89b3o296b
o2bo$326b2o59b2ob2o2bo3bo$326b2o57b3o6b2obobo$383b2o3bo4bo5bo$383b2obo
bo6b4o$107bo279bo9bo$106b3o$106bob2o$107b3o$107b3o266b3o$107b2o266bo2b
o$378bo$374bo3bo15bobo$98bobo3bo269bo3bo14bo$98b2o3b3o272bo14b2ob2o$
99bo3bob2o268bobo16b2obo$104b3o289b3o$104b3o52bo13bo57bo13bo144b2o2b2o
$104b2o52b3o11b3o55b3o11b3o143b2o2b2o$157b2obo5bo4b2obo55bob2o4bo5bob
2o146b2ob2o$157b3o5b3o3b3o28b2o27b3o3b3o5b3o147b2o$158b2o4bo2b2o3b2o
28b2o27b2o3b2o2bo4b2o148b2o$164bo3bo67bo3bo153b3o$165b2obo67bob2o$167b
2o67b2o$184bo35bo$158bo24b3o33b3o24bo$157b3o7bo15bob2o31b2obo15bo7b3o
142b2o$156b2obo6bobo15b3o31b3o15bobo6bob2o141b2o$156b3o6bo18b3o31b3o
18bo6b3o151b3o$156b3o3bo5bo15b2o33b2o15bo5bo3b3o150bo2bo$156b3o3b3o75b
3o3b3o153bo$96b2o59b2o4b2ob2o69b2ob2o4b2o154bo$96b2o67bo73bo156bobo3bo
$396bo2bobo2$332bo$165bobo12bo43bo12bobo91b3o63b3o$164bo2b3o9b3o41b3o
9b3o2bo89b2obo62bo2bo$165bobobo8b2obo41bob2o8bobobo90b3o66bo$166bo2bo
8b3o43b3o8bo2bo91b3o62bo3bo$166bo2bo9b2o43b2o9bo2bo92b2o66bo$160bo4bo
2bo67bo2bo4bo151bobo$158bo2bo3b3o69b3o3bo2bo$158bobo4bo73bo4bobo$159bo
85bo$164b3o71b3o$160b2o3b3o69b3o3b2o$160bo2bob3o69b3obo2bo$161b2o79b2o
$337bo$336b3o3bobo$336bob2o3b2o$166b2o69b2o98b3o3bo6bo$166b2o69b2o98b
3o9b3o$91bo245b3o8b2obo$90b3o244b2o9b3o$90bob2o254b3o$91b3o67b2o79b2o
104b3o$91b3o67b2o79b2o105b2o$91b2o2$170b2o61b2o$168b3obo59bob3o$166bo
3b2o61b2o3bo$166bo2bo2b2o57b2o2bo2bo$167b2o4bobo53bobo4b2o$163b2o8b2o
55b2o8b2o$163b3o73b3o140bo$86bo75bo9bo59bo9bo138bo$85b3o85bo28b2o27bo
149b3o$84b2obo80bob2obo28b2o27bob2obo$73bo10b3o80bo2b3o59b3o2bo$72b3o
9b3o80bobobobo57bobobobo$72bob2o8b3o81b3ob3o5bo43bo5b3ob3o$73b3o9b2o
72bo9bo3b2o4b3o41b3o4b2o3bo9bo$73b3o81bobo18b2obo41bob2o18bobo$73b3o
80bob2o18b3o43b3o18b2obo141b2o$73b2o81b2o20b3o43b3o20b2o141b2o$178b3o
43b3o157b3o$161b2o16b2o43b2o16b2o139bo2bo$83bo237bo64bo$83b2o235b2o60b
o3bo$82bobo235bobo63bo$383bobo10$156bo91bo$155b3o89b3o$154b2obo89bob2o
$154b3o91b3o$154b3o91b3o$155b2o91b2o3$159bo85bo$158b3o5b2o69b2o5b3o$
157b2obo5b2o69b2o5bob2o$157b3o85b3o$108bo48b3o85b3o48bo$108b2o48b2o85b
2o48b2o$107bobo185bobo12$202b2o$202b2o10$133bo137bo$133b2o135b2o$132bo
bo135bobo10$357bo$172bo59bo123bo$171b3o57b3o122b3o$170b2obo57bob2o$
170b3o59b3o70bo13bo$170b3o59b3o69b3o11b3o$171b2o59b2o70bob2o4bo5bob2o$
179bobo41bobo79b3o3b3o5b3o$180b2o41b2o80b2o3b2o2bo4b2o$180bo43bo85bo3b
o$310bob2o$310b2o$294bo$158bo87bo46b3o24bo$158b2o85b2o45b2obo15bo7b3o$
157bobo85bobo44b3o15bobo6bob2o$292b3o18bo6b3o$293b2o15bo5bo3b3o$314b3o
3b3o$311b2ob2o4b2o$313bo4$298bo$297b3o$297bob2o7bobo$202b2o94b3o7bob2o
$19b3o11b3o166b2o94b2o9b5o$18bo2bo10bo2bo275bobo$21bo4b3o6bo276b2o$21b
o4bo2bo5bo$18bobo4bo6bobo$30bo$24bo4bo275b2o$24bo280b2obo$8b3o15bo277b
o4bo7bo$8bo2bo14b2o6b3o266b4obo6bob3o$8bo18b3o3bo2bo146bo37bo80b5o6b3o
2b2o$8bo3bo15bo7bo146b2o35b2o81bo2bo6b2o$8bo23bo3bo145bobo35bobo81b2o
6bo2bobo$9bobo20bo3bo276b2ob2o$36bo276b2ob2o$28b2o3bobo279bo$26b5o$26b
o2b2o$26b2o2b2o281b2o$312bo2bo$12b3o298b2o$11bo2bo$14bo$14bo11b2o$11bo
bo12b2o2$316bo$26bo289bo$24b4o3b2o283bo$23bo4bo2b2o$23b2o$23bo4bo$25b
3o283b2o$298bo12b2o$297b3o$23b2o272bob2o$22bo2b2o271b3o$21bo3b2o271b3o
15b2o$28bo269b3o15b2o$22bobob4o268b2o$23b2o3b2o$25b2o$25b3o4$24bobo
171b2o5b2o94bo$24bo2bo6bo57bo13bo91b2o5b2o94bo11b2o17bo$20b2obo2bo6bob
o55b3o11b3o205b2o16bo$19bo5b2o2b2o2bobo54b2obo5bo4b2obo94b2o127b3o43bo
13bo$19b2ob4o4b2o2bo55b3o5b3o3b3o95b2o172b3o11b3o$29bo61b2o4bo2b2o3b2o
269bob2o4bo5bob2o$97bo3bo275b3o3b3o5b3o$98b2obo220bo54b2o3b2o2bo4b2o$
100b2o219b3o58bo3bo$81bo239bob2o57bob2o$80b3o24bo214b3o57b2o$12b3o65bo
b2o22b3o213b3o77bo$11bo2bo66b3o21b2obo213b2o52bo24b3o$14bo66b3o21b3o
267b3o22b2obo$10bo3bo14b5obo45b2o22b3o267bob2o21b3o$10bo3bo20bo69b3o
211bo56b3o21b3o$14bo15bo67bob3o3b2o210b3o55b3o22b2o$11bobo12b2o2bo2bo
62bobob3o215bob2o54b3o$26b2o3b3o63bo3bo210bobo4b3o54b2o3b3obo$98b4o
210b2o5b3o59b3obobo$313bo5b2o61bo3bo$85bo14bo279b2ob3o$30b3o51b3o13bob
o276bobob2o$83b2obo14b2o276bo2bo15bo$83b3o293bo2bo14b3o$84b2o294bo3b2o
11bob2o$90bo290bo3bo12b3o$26b2o60b4o8bo282b2o13b2o$26b2o60b2o2bo6bobo
280bo$89bo2b2o5bo2bo277b3o$90b3o9bo$36b3o52bo9b2o$31b2o2bo2bo58b2o$31b
2o5bo$34bo3bo345b2o$38bo345b2o$35bobo273b2o$311b2o$100b2o$33b3o63bo2bo
276b2o$32bo2bo64b2o277b2o$35bo$35bo$29bobo3bo355b2o$29bo2bobo355bo2bo$
384b2o2b5o$103bo280bo3b2obo$103bo284bo$103bo2$198b2o5b2o174b2o3bob2o$
198b2o5b2o174b2o2b2obo$98b2o286bo$98b2o102b2o$202b2o184b2o$390b2o$385b
o6bo$103b2o201bo68b2o3b2o2b2o3bob2o$85bo17b2o200b3o66bo2bobo4b2obobo$
84b3o6bo211bob2o65bobo3bo4bobob2o$83b2obo5bo2bo210b3o66bo5b6o4b2o5bo$
83b3o5bo3bo210b3o72b2o9b2o3b3o$83b3o4bo5bo209b2o84b2o3bob2o$83b3o8bobo
301b3o$84b2o312b3o$90bo3b2o302b3o$88b3obo305b2o$19bo70bo9b2o$18bo69bob
3obo5b2o$18b3o68bobobo$89b4o$91bo288bo$380b3o$382bo$377bo2$307bo69bo$
26b2o278bo$26b2o81bo196b3o70bo$108b3o268b2o$107b2obo263bo4b2o$20b3o80b
o3b3o263b3o$19bo2bo78b2o4b3o263bob2o$22bo79b2o4b2o264b3o$18bo3bo351b3o
7b2o$22bo351b2o8b2o$19bobo84bo$105b3o$104b2obo269bo$104b3o269b3o$104b
3o269bob2o$105b2o270b3o$377b3o$287bobo87b2o$287b2o$15b3o270bo$15bo2bo$
15bo$2b3o10bo3bo$bo2bo10bo3bo$4bo10bo182b2o5b2o$o3bo11bobo179b2o5b2o$o
3bo93b2o$4bo93b2o102b2o$bobo198b2o13$22b3o$24bo$23bo9$93bo301bo$92b3o
301b2o$91b2obo295bo4b2o$91b3o295b3o$91b3o295bob2o$92b2o296b3o$390b3o$
386bo3b2o$386bo6$47b3o38bo$49bo37b3o$48bo38bob2o304bo$75bo12b3o303b3o$
74b3o11b3o302b2obo$73b2obo11b3o302b3o12bo$73b3o12b2o303b3o11b3o$73b3o
317b3o11bob2o$73b3o122b2o5b2o187b2o12b3o$74b2o122b2o5b2o75bo125b3o$
281bo126b3o$83b2o117b2o77b3o124b2o$84b2o116b2o$83bo12$72b3o$74bo187bob
o$73bo188b2o$263bo120b2o$383b2o$385bo6$108b2o$109b2o$108bo12$97b3o$99b
o$98bo$359b2o$358b2o$360bo3$198b2o5b2o$198b2o5b2o2$133b2o67b2o$134b2o
66b2o$133bo12$122b3o$124bo$123bo$334b2o$333b2o$335bo4$257bo$256bo$158b
2o96b3o$159b2o$158bo12$147b3o$149bo87bobo$148bo88b2o$238bo70b2o$308b2o
$310bo3$198b2o5b2o$198b2o5b2o2$183b2o17b2o$184b2o16b2o$183bo12$172b3o$
174bo$173bo$284b2o$283b2o$285bo6$208b2o$209b2o$208bo12$197b3o$199bo$
198bo$259b2o$258b2o$260bo3$198b2o5b2o$198b2o5b2o25bo$231bo$202b2o27b3o
$202b2o4$211b2o$210b3o$209b3obo$208b3obo9b2o$209b4o9b2o$210b2o4$222b3o
$224bo$223bo$234b2o$233b2o$235bo!
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Re: Synthesising Oscillators

Postby Cclee » March 22nd, 2018, 10:07 am

That is not an oscillator
^
What ever up there likely useless
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Re: Synthesising Oscillators

Postby 77topaz » March 22nd, 2018, 4:34 pm

Yeah, it's not really relevant to this thread (though there are a bunch of still life syntheses as well as oscillator syntheses in here), and you posted it in three other threads as well, anyway. :P
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Re: Synthesising Oscillators

Postby BobShemyakin » March 25th, 2018, 8:45 am

github_com_osc.rar
list of oscillator for display_synth script
(76.51 KiB) Downloaded 60 times
Goldtiger997 wrote:
mniemiec wrote:
Goldtiger997 wrote:I've added the syntheses of all the 16-bit oscillators, except for three which I've been unable to locate: ... Could someone point me towards those syntheses... Also, there is not a complete synthesis for another 16-bit oscillator, so this will also need to be completed (unless there is another way). It looks like it should take around 21 gliders: ...

Here they the latest versions I have:
4 oscillator syntheses


Thanks mniemiec, I've added those. I hadn't seen those syntheses before, which suggests to me that some of the syntheses that I have are not the best known ones. Either way, here is the folder of all the cheapest 16-bit oscillator syntheses:
The attachment oscill16.zip is no longer available

There is still suspiciously 109 syntheses in there instead of 108.
For the sake of completeness, I'm also attaching the 3-15 bit oscillator syntheses:
The attachment oscill3-15.zip is no longer available

If chris_c incorporates these syntheses into the display_synth script, it will make quite a nice feature for catagolue.


Me too, it's interesting.
I've learned to translate the link chain synthesis of rle format in the string that is used to describe this link in display_synth script.
This can be done semi-automatically via clipboard, and takes quite a long time (a few minutes link).
Much time is spent on the harmonization of the two links in the chain (the alignment position, orientation and phase oscillators , determining the optimal apgcode).
Cite this method received scripts for some oscillators (unzip and run ListOsc.html):
github_com_osc.rar
list of oscillator for display_synth script
(76.51 KiB) Downloaded 60 times

Work is still at the very beginning and is progressing slowly. In my plans to automate this process completely and get a full database of well-known chains of synthesis, to optimize it.

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Re: Synthesising Oscillators

Postby mniemiec » June 13th, 2018, 2:41 pm

The following Silver's P5 (which just happens to be the smallest basic oscillator involving two Silver's P5s on a still-life that I don't know how to synthesize) has popped up on Catagolue twice
[url=https://catagolue.appspot.com/object/xp5_4a96wstfzc8ee60gw23zy111/b3s23].
The first soup is useless, but the second could lead to a synthesis:
x = 31, y = 31, rule = B3/S23
4o2bo2bo2bo5bo2bo2bo2b4o$2o2b2ob3o11b3ob2o2b2o$obob3obobo3bobo3bobob3o
bobo$o2b2o2b2o2bob2ob2obo2b2o2b2o2bo$b3obob6ob3ob6obob3o$b2obo8b5o8bob
2o$obo3b4ob3obob3ob4o3bobo$bob2obob3obobobobob3obob2obo$b4ob2o4b3ob3o
4b2ob4o$2o2bob2obobob5obobob2obo2b2o$2bobo2bo2bo2bo3bo2bo2bo2bobo$3b2o
bo2bo2b7o2bo2bob2o$o3bob3o2b2o2bo2b2o2b3obo3bo$3bob2ob4o7b4ob2obo$2b4o
b3obo2b3o2bob3ob4o$4b3o2bob2ob3ob2obo2b3o$2b4ob3obo2b3o2bob3ob4o$3bob
2ob4o7b4ob2obo$o3bob3o2b2o2bo2b2o2b3obo3bo$3b2obo2bo2b7o2bo2bob2o$2bob
o2bo2bo2bo3bo2bo2bo2bobo$2o2bob2obobob5obobob2obo2b2o$b4ob2o4b3ob3o4b
2ob4o$bob2obob3obobobobob3obob2obo$obo3b4ob3obob3ob4o3bobo$b2obo8b5o8b
ob2o$b3obob6ob3ob6obob3o$o2b2o2b2o2bob2ob2obo2b2o2b2o2bo$obob3obobo3bo
bo3bobob3obobo$2o2b2ob3o11b3ob2o2b2o$4o2bo2bo2bo5bo2bo2bo2b4o!
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Re: Synthesising Oscillators

Postby Extrementhusiast » June 19th, 2018, 2:09 am

mniemiec wrote:The following Silver's P5 (which just happens to be the smallest basic oscillator involving two Silver's P5s on a still-life that I don't know how to synthesize) has popped up on Catagolue twice
[url=https://catagolue.appspot.com/object/xp5_4a96wstfzc8ee60gw23zy111/b3s23].
The first soup is useless, but the second could lead to a synthesis:
RLE


Done with a lot of finagling:
x = 69, y = 69, rule = B3/S23
12bo$13b2o$12b2o46bo$58b2o$59b2o4$43b2o$42b3o$42b2obo$43b3o$obo41bo$b
2o$bo39bobo$40bo12bo$40bo7bobo2bobo3bo$28bo11bo2bo4b2o3b2o3bo$26bobo
11b3o6bo8b3o6bo$27b2o37bo$66b3o$49bo$48bo$48b3o$34bo$33bobo$18bo9bo3bo
bo$19bo7bobo3bo$17b3o6bobo$27bo16b4o$44bo3bo$44bo$26bo18bo2bo$25bobo$
24bobo22b2o$25bo11b2o9b2o$36bobo11bo$35bobo$35b2o2$15b4o39b2o$14bo3bo
39bobo$9b2o7bo39bo$8b4o2bo2bo$8b2ob2o16b3o$10b2o17bo2bo$29bo$29bo$16b
2o4b2o6bobo2bo$17b2o2bobo10b2o$16bo6bo10bobo3$15b3o$17bo$16bo3$3bo13b
2o21b3o$3b2o11bobo21bo$2bobo13bo22bo6$19b2o$18bobo$20bo!


I highly suspect that there's a better, more direct way based on this (or something similar):
x = 39, y = 55, rule = B3/S23
33bo$32bo$8bobo21b3o$9b2o$9bo2$25bo$25bobo$25b2o10$36bo$36bobo$36b2o3$
8bob2o$8b2obo10$10b3o$12bo$11bo12b2o$23b2o$25bo7b3o$28b3o2bo$28bo5bo$
29bo4$b3o$3bo$2bo2$28b2o$27b2o$29bo$2o$b2o$o!


(Say, anything else in particular on the Most-Wanted List?)
I Like My Heisenburps! (and others)
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Re: Synthesising Oscillators

Postby mniemiec » June 19th, 2018, 6:06 am

Extrementhusiast wrote:Done with a lot of finagling: ... (Say, anything else in particular on the Most-Wanted List?)

Nice! This also trivially solves the related 30-bit one with a pond instead of a loaf.

This is my current wish list of unsolved small object syntheses:
Not shown: still-lifes (because there are thousands of 19-bit ones).
Rows 1-4: The remaining 14/199 17-bit and 26/484 18-bit P2 oscillators (9 of which are trivial pole-extensions of the 17s).
Row 5: the 2/216 P3s up to 21 bits and the 7 non-trivial P4s up to 25 bits.
Row 6: the 4 Elkies' P5s up to 28 bits; the other non-trivial P5s up to 30 bits,
mold on mold (the only remaining non-trivial pseudo-P4 up to 32 bits);
blocker and two clocks (the smallest non-trivial P8).
Row 7: the 9 non-trivial pseudo-P3s up to 28 bits.
Row 8: the 7 spaceships up to 32 bits.
x = 174, y = 132, rule = B3/S23
oo4bo8boobboo9boobboo10bobb3o8boo13boobb3o8b3o12b3o12boo13boobb3o$obob
obboo6bobbobo9bobobbo10bo13bobobo10bo36boo6bobbobo9bo$4bo11bo17bo10bo
bbobboo11bobo9bobobboo8boboob3o7boboobobo8bobbobo8bobobboo$bbo3bo12bo
11bo30bo5bo21bo14bo21bo$bo13bobo12bobbobo9bobobobbo8bo6bo8bobbobbo6boo
3bobo7boo3bobbo7boo4bo9bo3bo$boob3o8bobobboo8boo4bo8boo3bo10boobobobo
9bo3bo15bo13bo11boo13bo$15bo3bo15boo13bo15bo11bo3bo14boo13bo9boo11boo
bbo$124bo12bo8$3bo11boo14boo13boo12boo4boo7boo3bobo8bo3bo9boo13boobboo
10bo3bo$3boboboo6bobo13bobo12bobo11bobo4bo7bo4bo10bobobboo7bobobboo8bo
bobbo10bo3bobo$bo6bo41bo13bobo9bobo4boo6bobo15bobo12bo10bobbo$7bo7bobb
oob3o7bobboo10bo3bo11bo19bo12bo11bo13bo21boo$oo14bo19bo14bo13bo10bo3bo
11bo17bo9bobbobo10boo$6bobo7bo3bobo7boo13boo14bobobbo8bobbobo13bobo9bo
bo11boo21bo$bbobobboo14bo12bobo12bobo7boobboo8boo13boobbobo9boobbobo
12bobo7b3obobo$4bo17boo8bobobboo8bobobboo38bo3bo14boo13boo13bo$34bo14b
o7$oo13boo13boo4bo8boo3bo10bo3bo9boo17bo11boo12boo4bo10boo$obo5bo6bo7b
oo5bo5bo8bo4bobo8bo3bobo7bobo14bobo11bobo11bo5bo11bo$4bobobo7bobo3bobo
6bobobobbo7bobo11bobbo15bobo8bo5bobo11bo10bobobobbo8bo3bo$bbo3bobo44b
oo13boo7bo3bo8bo7bobo5bobbobo27bobobo$15b3oboobo10bo3boo8bo13boo20bo6b
obo7bo10bo11bo3boo6boo6bo$bbobobbo38bo6bo13bobbo6bobo4boo6bobo5bo4boo
35bobo$bboobbo14b3o9b3ob3o6boobobo11bobo3bo7boobbo14bobo12bobo8bobobo
9bo5bo$6bo44bo13bo3bo11bobo12bo10bobobboo8bobo13bobo$109bo12bo15bo7$bo
14boo12b3o12boo13boo13boo3bo9boo3bo11bobo12bobo12bobo$bo14bobo26bobo
12bobo12bo4bobo7bo4bobo11bo14bo14bo$obbo16bobo8boboob3o37bobo12bobo11b
oo4bo8boo4bo8boo4bo$8boo6bo3bo9bo14bobboo3bo6bobboob3o14boo13boo7bo4b
oo8bo4boo8bo$oboboobobo13boo5boo3bobo8bo6bo7bo16bo14bo30bo16boo$oo13b
oo5bo23bo3boobbo6bo3bobo11bo3bo10boobbo9boo4bo9bo4bo8boo$6bobbo11bobo
13bobo39bo30bo4boo8bo4boo11bo$8bo8bobo18boo12bobo12bobo11bobo12bobo13b
o14bo11bo4boo$8bo10bo33boo13boo12boo13boo13bobo12bobo11bo$141bobo6$oo
13boo13boo8boo4bo16boo10b3obobbobo12bo18boo17boo$o14bo14bobo4boobbo3bo
boo12bobo3boo7bobobobobbo10bobo10boo6boboo4bo10bobboo$bobo12bobo12b3ob
o12boobboo6bo3bobobo16bo20boobo5bo7bobbo3boo4bobobbo$10bo22bo3b3o6bobo
bobbo7bo3bo12bo16bobboobobo7bo3boobboboboboboobbo5bobboo$bbobo3b3o6bob
o17bo13boo25bobbobobobo7boo3bobbobobobboo8bo24bo$bbo4bo9bo4boo10bobo
11bobbo11b4obbo9bobobbob3o12bo4bo21bobo10boobb3o$4bobobo10bobobo12bo
14boo17bo58bo9boboobbo$3boobboo9boobbo24bobo17bobo69bobo$23b3o21boo17b
oo71bo$25bo113bo6$bo14bo14bo14bo15boo11boo13boo14boo7boo4bo$obb3o9bobb
3o9bobb3o9bobb3o11bo4boo6bo14bo14bobbo5bobbo4boo$bbo14bo14bo14bo15bo3b
obo7boo13boo11bobobbobobbobobboo4boo$3bobobbo9bobobbo9bobobbo9bobobbo
9boo5bo35bo9bo5bo3boo$bboob4o8boob4o8boob4o8boob4o7bobbo6bo6bobo12bobo
11booboboboo$4bo4boo5bobbo11bobbo11bobbo10bo9boo37bo3bo12bo$4bobobbo7b
obobo10bobobo10bobboboo6boo18bobo12bobo27bobo$5bobobo8bobobo10bobobo
10boo3bo71bobbo$6bobo10bobbo11bobbo15bobo12boo12bobo12bobo26bobbo$7bo
12boo15boo15boo13boobo11bo14bo$71boo13bo14bo24bo4bo$66bobo16boo13boo
24boo4boo$66boo19boo13boo26boo$87bo14bo29bo$89boo13bo$104bobo$90bobo$
106bobo$92bobo$108bobo$94bobo$96bo13boo$98bo14bo$97boo13boo7$b3o5b3o
10b3o16bo19b3o5b3o9boo18b3o17bo20b3o16boo$5bobo12bo20bo23bobo12bobbo
21bob3o11bo24bob3o9bobbo$o4bobo4bo7bo4bo15bo18bo4bobo4bo7bobobbo4b3o7b
o4boboo12bo19bo4boboo10bobobbo$4bo3bo12bo19boo21bo3bobbobo7bo4bobo15bo
3boo11boo17bobobbo3boo10bo4bob3o$boo7boo11boo3bo15bo4b3o9boo7bobbo12bo
bo4bo7boo5bo15bo15bobbo5bo16boboo$bo9bo12bo3bo11bo4bobo13bo9boo9b3o4bo
11bo9boo7bo4bob3o11boo9boo8b3o4boo$bo9bo12bo3bo16bobo4bo8bo29boo8bo6b
oobo13boboo20boobo16bo$bo9bo12bo3boo11b3o4bo12bo30bo8bo7bo11b3o4boo20b
o21boo$31bo18boo40bo16bo18bo21bo18boobo$27bo4bo18bo40bo38boo37bo$32bo
18bo76boobo38bo$28b3o20bo77bo$129bo$$24boo$4boo20bo$3bo19boobo37bo$bo
bb5obo14bo36boobo$o7bo15boobo92bobbo$3o5bobbo13bobo15booboo12bo6bo47bo
bbobboo22bobbo$8bo23bo8bo8bobo7boboboo3bo20bo23bo3booboo17bobbobboo$
25b3obobo8bo4bobobo11bo3bo4bo18bobbobo21b3o20bo3booboo$9boo13b3o4boo7b
o3bobobbo3bo7bo4bo3bo9bobbo7bo3bo20bo13bobbo7b3o$10boo12bo4b3o8bo3bo4b
o3bo6bo3bo5bo10boobbo5b4o11boo3bobbo16boobbo5bo$8bo13bo17bo8bo10bo6bo
bbo10booboo3bo3bo11bo6boo17booboo3bo$7bo12boo18bobbo5bobbo7bobbo4b3o
14b4o17b3ob3o22b4o$7b3o11boo17b3o6b3o8b3o24bo22bo26bo!

I'm sure many of the P2s can be solved by combining pieces that have been used to construct some other P2s by brute force. The two P3s should also be possible. I have no idea how to even approach the P4s.
The Elkies' P5s are probably not too difficult. The dual Silver's P5 on canoe looks like it might be possible adding one side at a time, using your new 11-glider component with some modifications (although after messing with it for about an hour, I wasn't able to get all the pieces to come together nicely). I have no idea how one would go about gluing a pseudo-barber-pole onto something else.
The dual mold looks tantalyzingly close to being doable. The P8 needs a way to edge-shoot a clock, which might also benefit some other syntheses that need clocks as rocks. The pseudo-P3s need better ways to edge-shoot caterers and jams.
Some of the P3 spaceships might be not too difficult, as they are made of similar components
to some of the smaller P3 spaceships.

As for which of these I would personally like to see solve first, my choice would probably be the two 20-bit P3s (and the 21-bit P4) for completeness (i.e. that would solve everything 21 bits or less with period above 2), and the mold-on-mold because it's so close.
(These are all pretty academic; about the only "useful" object in the entire lot would probably be the 25-bit T-nosed P4).

Also, if anyone cares:
rows 1-5: the 45/70637 remaining 20-bit pseudo-still-lifes (plus 2 trivial ones derived from these)
rows 6-8: the 25/972040 remaining 19-bit quasi-still-lifes (plus 3 trivial ones derived from these)
x = 145, y = 114, rule = B3/S23
ooboobo8booboobo8booboboo8booboobo8booboobboo7booboo10booboo9boo13boob
oo10booboobo$obooboo8booboboo8bobooboo8bobooboo9bobobbobo6bobobo10bobo
bobo8bobbooboo8bobobboo8boboboo$60bo3bobo8bo4b3o7bo6bo8bobo3bo7bo3bobo
9bo$obooboo8booboboo9booboobo8booboobo7booboobbo8bo5bo8bo3b3o7boobbobo
8booboobbo9bo$ooboboo8bobooboo9booboboo8bobooboo13boo9bobobo10bobo12bo
boboo12bobo10boboboo$76booboo10booboo11boo16boo10booboobo10$oo3boo9boo
boo10booboo10booboo9bobooboo8boo13boo13boo13boobbo10boobboo$o5bo10bobo
bo10bobobo8bobobo10boobobo10bo14bobbo10bo4boo8bo3b3o8bo3bo$bbobo11bo5b
o8bo4bo8bo4bo16bo7bo5boo7bo3b3o10bobbobo8bo5bo8bo3bo$booboo9bo4boo8bo
5boo8bo4bo14boo7b4obobo7boo5bo8boo4bo7boo4bo8boo4bo$bo3bo9bobobbo9bobo
4bo9bo4bo9boobo12bobo10bo4bo8bo5bo8bo4bo9bo6bo$bbobo11boo3bo9boobbo12b
obobo8bobboo11bo3bo9bobobo10bobobo11bobo12bob3o$booboo14boo13boo10boob
oo9boo14booboo10booboo10booboo9booboo10boobo9$oobboo9boobo11boobobboo
7booboo12booboo9boboo11boobbo10booboo9boboobo9boboobo$obobbo9boboo11bo
boo3bo7boobo14bobo10boobo10bobobb3o9bobobo8boobob3o7boobob3o$bbobo16b
oo11b3o11bobboo9bo3bo15boo6bo7bo7bo5bo15bo14bo$bobb4o7boboo3bo8boobo
13boobbo8bo5bo7boboo4bo7bo5bo7bo7bo13boo10booboo$boo4bo7boobobbo10bo
16bobo8bo7bo6boobbobbo9bo3bo8bobo3bobo9boobbo11bo$6bo11bobo11bobo13bo
bboo8b3ob3o10bobbo11bobo10boobbobo10bobobo9bobo$6boo10boo13boo13boo13b
obo13boo11booboo14bo14bo10boo9$obooboo8bobooboo8boobboo9booboo10booboo
10booboo11booboo10booboo10booboo9boo$oobobo9boobobobo7bobbobo10bobo12b
oboo10bo3bo12bobo12bobo12bobobbo8bo4boo$6bo16bo8boo11bo3bo10bo6boo7bob
o3boo7bo3bo9bo4bo10bo4boo8boboobbo$7bo13boo10bobo9booboobbo7booboo3bo
6booboo3bo6bo5bo8boo4bo8bo16boboo$bboo4bo8boobbo10bobb3o11bobobo10bobb
o11bobbo7bobo4bo8bo5bo8b3o$bbobb3o9bobobo10boo4bo10bobbo11bobo12bobo9b
obobboo8bobobboo10b3o11boboo$4boo14bo16boo9boo15bo14bo12bo13bobo16bo
10boobbo$93boo13bo16boo13boo8$oo13booboo11booboo9bo14boo15boobo11boobo
$obo3boo7bo3bo12bobo10b3o4boo6bobo12bobbob3o7bobbob3o$bbo3bo9bobo3bo8b
o3b3o10bo4bo8bo3boo7boo6bo6boo6bo$bboo3bo7boob5o7bo7bo8bobb3o9boobbo
15boo10booboo$6boo22boo5bo9boobo17bo9boobbo11bo$bboobbo13bo15bo11bo13b
oo3boo9bobobo9bobo$bbobobo12bobo11bobo12bobo11bobobo14bo10boo$5bo14bo
12boo14boo14boo8$bobboo10bobboo9boo3boobo6boboo3boo6boobboo10bo13boo
13boo15bo14boobbo$obobbo9bobobbo9bobobboboo6boobobbobbo6bo3bo9bobo12bo
4boo8bobo5bo7bobobboo9bo3b3o$bo3boboo7bo3boboo8bo18boboo5bo3bo11bobboo
11bo3bo11bobb3o6bobo4bo10bo5bo$4boobbo10boobo9boo16boo8boo3b3o12bo10b
oobbo10boobbo9bo5bo8b3o5bo$bbobbobo9bobbobo11boboo10bobbo9bo5bo9bobbob
oo6bo5b3o7bo4bo9bo5b3o5bo6bo$bboobbo10boobbo12boobo10boo11bobo12bobobo
bbo7bobo4bo8bobboo10bobo4bo9bobo$62boo13booboo10boo12boo15boo14boo9$ob
ooboo8booboo12boobo10boo13boobo12boo13boo13boo12bo13boo$oobobobo8bobob
o10bobboo10bobboobo8boboo12bobobo9bobbo11bobbo10bobo12bo$4bo3bo7bobbo
bboo6bobo3boo10booboo12boo13boo9bobo3boo6bobobobboo7bobbooboo7bo3bo$9b
o7boo4bo7bo4bo28bobo8bo5boo6booboo3bo7bobo4bo11boboo8bobb3o$5bobboo12b
o14bo7boo13boo4bo8bobo4bo14bo9bo4bo9bobbo9bobo5bo$4bobo16b3o7bobboo8bo
bboo9bobo13bo3bobo13bo14bo9bobobo9boo5bo$5bo19bo6bobo11bobobo12bobo13b
obo11bobo12bobo11bobo14bobo$33bo13bo16boo14bo12boo13boo13bo15boo8$oob
oo10bo14boo13boo13boo14boo3boo9booboo8boo$oobo11b3o4bo7bo14bo8bo6bo13b
obbobbobbo5bobbobobo8bo$3bo3boo9bobbobo7b3o12b3o3b3o6boboo10boobo4boo
5boobbo3bo7boboo$3boo3bo8bo4bobo8bobboo10bobbo10bobo13boo19bo7bobo$7bo
9boo5bo12bo14bo25bobbo13bobboo$6bo16bo9bobbo11bobboo12bo14boo12bobo13b
obboo$3bobo14bobo9bobobb3o7bobo14boboboo25bo13bobobbo$3boo15boo11bo5bo
8bo14bobboobo38bobboo$63boo43boo!
mniemiec
 
Posts: 905
Joined: June 1st, 2013, 12:00 am

Re: Synthesising Oscillators

Postby Extrementhusiast » June 20th, 2018, 8:35 pm

(Really? No components in the wish list? Or are you of the mentality that whatever components appear during solving appear? Or have I just done everything already?)

Component to make a pseudobarberpole from two end eaters and an extra block:
x = 45, y = 24, rule = B3/S23
21bo$19b2o$20b2o4$19bo$8bo7bo2bobo$9b2o3bobo2b2o$8b2o5b2o3$22b2o19b2o$
23bo20bo$8bo11b3o18b2o$9bo10bo$7b3o6b2o21bobo$16b2o$37bobo$bo4b3o$b2o
5bo5b2o19bobo$obo4bo6bo20bo$12bobo18bo$12b2o19b2o!


(Speaking of components, you never got me that list of components used in the expert system....)



On an entirely different note, have 475 different three-glider bookend syntheses:
x = 6245, y = 4717, rule = B3/S23
6240bo$6239bo$348bo5030bo859b3o$348bobo2217bobo2809b2o$348b2o2219b2o
503bobo91bobo1442bo765b2o$1112bobo1454bo505b2o91b2o1444b2o856bo$346bo
765b2o1961bo93bo509bo933b2o857bobo163bo347bo$345bo263bo412bobo88bo
1031bo253bo508bo513bobo254bobo164bo1370bo254b2o162bobo347bobo$345b3o
259b2o161bo252b2o519bo249bo348b2o254bobo504b2o514b2o255b2o163bobo1025b
o342b2o161bobo256b2o4bo342b2o$517bo90b2o158bobo252bo259bo85bo172bobo
247bobo257bo91b2o253b2o420bo85b2o514bo164bobo254b2o3bobo1020b2o341b2o
161b2o260bobo$518b2o249b2o510bobo84bo174b2o248b2o258b2o250bo513bobo
767b2o260b2o1019b2o505bo262b2o249bo$95bo421b2o763b2o84b3o681b2o252b2o
507bo4b2o767bo261bo2039bobo$9bo84bo2210b2o509b2o1284bo1789b2o$10bo83b
3o754bobo1961b2o1286bo$8b3o840b2o782bo2465b3o$769bobo80bo781bo$770b2o
862b3o$770bo71$4442b2o$2567b2o1872b2o$350b2o2214bobo84b2o1698b3o87bo$
350bobo1522bo692bo84bobo1699bo$350bo1523b2o777bo1700bo$1793bo80bobo
4268b2o$1793b2o4349bobo$1112b3o169b2o506bobo1371b3o1019b2o253bo677bo
1024bo90b3o$1112bo170bobo1880bo936b2o83bobo251b2o677b2o515b2o343bo253b
o$1113bo171bo1112bo768bo936b2o82bo253bobo258b2o415bobo516b2o341b2o254b
o$89bo1455b2o850b2o1024b2o165b3o510bo599bobo163b3o87bo252b2o424bo343bo
bo$88b2o1454bobo503b3o344bobo1023bobo166bo256b2o852bo167bo86b2o252bobo
$88bobo1455bo505bo1279b2o89bo167bo256bobo759b2o258bo87bobo251bo$519b3o
1529bo1281b2o515bo760b2o$521bo2810bo1277bo$520bo152$3584bo$1632bo164bo
1787b2o$1630b2o166b2o1784b2o1889bo$1631b2o164b2o1875bo512bo1285b2o$
3673bo513bobo1284b2o$3673b3o511b2o933bo$5123b2o$607bo1449bo248bo348bo
1960bobo503b2o255bobo857bo$607bobo1445bobo249b2o346bobo418bobo1538b2o
761b2o346bo510bobo$607b2o1447b2o248b2o347b2o420b2o1538bo594bo167bo347b
obo508b2o$94bo2982bo2134bobo513b2o$94bobo5115b2o$94b2o3832bo$3415bo
510b2o2312bobo$519bo2893b2o512b2o1964bo346b2o$517bobo88bo2805b2o1530bo
bo945b2o345bo$518b2o87bo4338b2o945b2o$607b3o4337bo16$1044bo255bo1535bo
1535bo$280bo764bo6bobo246bo5bo1529bo68bo1466bo64bobo$281b2o760b3o7b2o
244b3o6b2o1525b3o67bo1465b3o64b2o$280b2o771bo253b2o1596b3o1531bo42$
2057b3o$2059bo$2058bo71bo$2129b2o$2129bobo6$3843bo$3331b2o510b2o$3332b
2o76b3o429bobo$3331bo78bo512b3o$3411bo511bo267bo$863b3o3058bo265b2o$
772b2o89bo673b2o254b2o514b3o1878bobo$771bobo90bo671bobo253bobo516bo
1276bo1883b3o$773bo277b2o256bo228bo90b3o162bo90b3o422bo592bo684b2o851b
3o1028bo$1052b2o255b2o318bo255bo509b2o505b2o683bobo513b2o336bo168b3o
257bo602bo$1051bo256bobo319bo255bo507b2o506bobo1199b2o336bo169bo89b2o
166b2o339b2o684bo$99b3o172bo2121bo1706bo507bo89b2o166bobo80b3o255b2o
424b2o259b2o$8b2o89bo174b2o6bo490b2o2302b3o1623bo248bo259bo422bobo253b
2o3bobo$7bobo90bo172bobo6b2o490b2o1789b3o511bo1873bo683bo252bobo$9bo
271bobo489bo1793bo510bo2813bo344b2o$2566bo600b2o2555b3o509b2o$2655b2o
509b2o2556bo513bo$2654b2o512bo2556bo$2656bo155$346bo167bo2048bobo1116b
o933bobo$344b2o169b2o1544bo502b2o1114b2o935b2o$345b2o167b2o1546b2o500b
o1116b2o934bo$769bobo87bo1201b2o2898bo$90bo679b2o86bo4100b2o$90bobo
677bo87b3o1533bo174bo1362bo166bobo858b2o752bo$90b2o2301bo173bobo1361bo
168b2o1534bobo74bo$1292bobo1098b3o172b2o1361b3o166bo1536b2o74b3o$1293b
2o2039bo259bo852bo169bo1019bo$1293bo2041b2o258b2o848b2o171b2o77bo$
3334b2o258b2o850b2o169b2o78bobo429bo$4697b2o431b2o$5129b2o$3089bo3073b
obo$524bobo1020bo1542bo78bo2994b2o$525b2o1021bo76bo1462b3o76b2o245bo
2749bo$525bo1020b3o74b2o1543b2o242b2o$1358bobo263b2o1787b2o951bo$1358b
2o3007b2o1034bo550bo$1359bo3006b2o1033bobo550bobo$5144bo257b2o550b2o$
1040bo4104b2o$1041bo4102b2o$1039b3o46$5954b2o$5953b2o$5955bo6$5402b2o$
5403b2o$5144b2o256bo$5143bobo$1032bo4112bo744b2o$1032b2o1026b3o3828b2o
$1031bobo1028bo3827bo272b3o$1040b2o840b2o177bo1789b3o71bo2239bo$1041b
2o314b3o442b3o76b2o1970bo70b2o174b3o2061bo$342bo697bo316bo446bo78bo
165bo519bo1282bo71bobo175bo$341b2o1015bo436bo7bo245b2o518b2o249b3o77bo
1200bo85bo$341bobo1451b2o251bobo517bobo251bo76b2o1285b2o$1794bobo598bo
425bo77bobo1284bobo1448b2o$2b2o521b3o1100b3o763b2o3240bobo$bobo342b2o
179bo1100bo765bobo2556bo684bo$3bo89b3o249b2o179bo1102bo1281b2o499b2o
953b2o499b2o82b2o512b3o$93bo253bo419b2o2142bobo164bo333bobo180b2o769bo
bo498bobo82bobo511bo$94bo671bobo1535b2o605bo166b2o332bo181bobo771bo
500bo597bo$768bo1534bobo771bobo516bo$2305bo3846b2o$6151bobo$6153bo152$
1374bo4518bo$1372b2o3076bo1443b2o$1373b2o3073b2o1443b2o$1028bo3420b2o$
1026bobo$1027b2o3$95bo5378bo$95bobo3498bobo1873b2o$95b2o3500b2o1874b2o
$1539bo2057bo1011bobo$1540b2o327bo2740b2o$521bo253bobo761b2o326b2o
2059bo681bo$519bobo254b2o1090b2o2056b2o$520b2o254bo3150b2o2$2129bo256b
o2825bo$2127b2o255b2o962bobo1607bobo249b2o$2128b2o255b2o962b2o1607b2o
168bo71bo10b2o$3349bo1609bo169bo68b2o$5127b3o69b2o$19bobo$20b2o1084bo
1782bo198bo$20bo1019bobo62bo1783bobo197bo$1041b2o62b3o190bo61bo1208bo
60bobo256b2o196b3o1280bo61bo1473bo61bo$536bo255bo248bo257b2o58bo1207bo
bo60b2o1468bobo268b2o58bo1475b2o58bo$537b2o254b2o503b2o59b3o1206b2o61b
o1469b2o267b2o59b3o1472b2o59b3o$536b2o254b2o3307bo538bo755bo$4164bobo
474bo755bo56bobo$4164b2o473b3o753b3o56b2o$315bo3849bo1289bo$314bo1281b
o$314b3o1277b2o2267bo$1595b2o2267bo$3862b3o1029bobo$4895b2o$4895bo23$
315b2o$314b2o$316bo2$3613b2o36b2o$3614b2o35bobo$3613bo37bo7$6219bo$
6167b3o48b2o$6169bo48bobo$6168bo2$5710bo$1595b2o4057b3o52b2o$1595bobo
1291b2o2765bo52bobo$1595bo1292b2o1274b3o472b2o1014bo$2890bo1273bo475b
2o$1868b2o1479b2o814bo473bo254b3o$279b2o1587bobo1216b2o259bobo1545bo$
278bobo255b2o254b2o1074bo1219b2o260bo1544bo$280bo254bobo253bobo1334b2o
255b2o700bo774b2o$537bo255bo1334bobo254bobo1475b2o$2128bo256bo1476bo2$
19b3o$21bo$20bo2$3144b2o$2145b2o996b2o$2145bobo997bo$2145bo509bo$2654b
2o$1882b2o770bobo247b2o425b2o$1882bobo1018b2o425bobo2820b3o$1882bo
1022bo426bo2822bo$2307bo3846bo$2307b2o3419b2o$2306bobo3418b2o$5729bo
154$3934bobo$3934b2o$3935bo1264bo$772bo1277bo1372bo1776bobo521bo255bo$
773bo1277b2o1025bo343bo679bobo508bo586b2o522bobo253bobo$771b3o1276b2o
1024bobo343b3o678b2o509b2o1108b2o254b2o159bo$96bo255bo2303bo420b2o597b
obo424bo509b2o1524bobo$94b2o254b2o2302b2o1020b2o2462b2o$95b2o254b2o
1531bo770b2o1020bo$1883bo2229bobo$1883b3o2228b2o$1375bo1703bo1034bo
2038bo75bo$1373b2o1705b2o508bo2560bobo73b2o$1374b2o1703b2o510bo2560b2o
74b2o$3338bo250b3o1805bobo$3336bobo2059b2o$3337b2o2059bo3$2899bo2503bo
$2898bo2505bo64bobo$2898b3o2501b3o64b2o$4378bo1091bo$4379bo$4377b3o4$
4419bo$2080bo2336b2o$2078bobo757bo57bo1521b2o$2079b2o758b2o54bo$1313bo
1524b2o55b3o$1314bo3623bo$1053bo37bo220b3o3621b2o$1051bobo35b2o3846b2o
$1052b2o36b2o3$4901bo$4902b2o$4901b2o13$538b2o31b3o$539b2o30bo$538bo
33bo6$4378bo$4378b2o$4377bobo5$1822b2o40b2o$1823b2o39bobo$1822bo41bo
2757b3o63b2o$794b2o49bo713b2o46b2o3015bo62b2o$793bobo48b2o714b2o45bobo
3013bo65bo$795bo48bobo712bo47bo471b2o2820b3o$2080b2o2821bo$1313bo765bo
2822bo$1313b2o3886bo$1312bobo3885b2o$5200bobo3$592b3o$592bo3520b3o$
593bo3521bo$4114bo3$5725bo255bo$5724b2o254b2o$5724bobo253bobo$1035bo$
1035b2o2897b3o$1034bobo2897bo1189b3o$3676b3o256bo1190bo$1631b2o765b2o
1276bo1448bo$1631bobo764bobo1276bo165bo$1631bo766bo1444b2o$3842bobo$
94b3o253b3o2301b3o3074bo$94bo255bo1959b2o83b3o256bo424b3o2648b2o254b2o
$95bo255bo1959b2o82bo166b2o91bo425bo255b2o2391bobo253bobo$2310bo85bo
164bobo516bo257b2o2646bo$6b2o253b2o2300bo773bo$5bobo254b2o$7bo253bo
149$3677bo$3675b2o258bo$3676b2o255b2o760bo$3934b2o758bo1545bo$2567bo
87bo2038b3o1542bo$1372bo255bo255bo680bobo85b2o670bo2913b3o$1028bo343bo
bo253bobo253bobo158bo520b2o86b2o670bo$1029bo342b2o254b2o254b2o157bobo
1121bo156b3o$352bo674b3o1014b2o1121bobo2974bo$350b2o173bo1794bo85bo
760b2o2973bobo$82bo268b2o173b2o1793b2o82bo2204bo1532b2o$4bobo74bo443b
2o1793b2o83b3o2200bobo1282bo$5b2o74b3o4525b2o1283b2o$5bo2051bo75bo
1203bo75bo2479b2o$1034bo1020bobo73b2o942bo87bo171bobo73b2o$1035b2o
1019b2o74b2o942bo84b2o173b2o74b2o2303bo$1034b2o2038b3o85b2o2551b2o$
5716b2o2$4437bo$4437bobo$4437b2o434bobo$4874b2o$4874bo4$4172bo$789bo
3382bobo$787bobo3382b2o1030bobo$788b2o4414b2o$5205bo$5653bobo$5654b2o$
5654bo3$5154bo39bo$5152bobo37b2o$5153b2o38b2o21$4883bo$4883b2o28b3o$
4882bobo28bo$4914bo11$2840bo51b2o$2840b2o50bobo$2839bobo50bo1280bo$
4172b2o$4172bobo6$525b2o$524bobo4168b2o$526bo4167b2o$4696bo$5391b2o73b
3o$4358b2o1032b2o72bo187b2o$1373bo255bo255bo2233b2o236bobo1031bo75bo
185bobo$1034b2o336b2o254b2o254b2o2232bobo238bo1295bo$1033bobo336bobo
253bobo253bobo2233bo$1035bo$83b2o4352b2o$83bobo702b2o1772b3o1018b2o88b
2o164b2o88b2o505b2o$83bo705b2o1773bo336b2o681b2o87bobo164b2o87bobo506b
o$788bo1774bo336b2o681bo89bo165bo89bo1530b2o$2397b3o502bo2556b2o528bo
247b2o$2397bo3063bo526b2o247bobo$1380bo1017bo3589bobo246bo$350b3o1026b
2o511bo$257b2o91bo250b3o166b2o607bobo253b2o254b2o4000b3o$256bobo92bo
249bo167bobo862b2o255bobo4001bo$258bo343bo168bo864bo4257bo154$2140bobo
$2140b2o2297bo$262bo1878bo2295b2o779bo761bo$255bobo2bobo1788bo766bo
1619b2o778bobo759bobo167bo$256b2o3b2o1789b2o256bo508b2o859bo763bo512bo
bo258b2o250bobo507b2o166bobo$256bo1121bo672b2o258bo345bo160b2o349bo
247bo169bo91bo255bo161bo346bobo510b2o418bo92b2o162bo514b2o$2bo94bo
1280bobo928b3o343b2o511bo247bo171bo90b3o253bobo160b2o3bo340b2o259bo
252bo162bobo254b2o91bo163bo87bo170bo342bo$obo92b2o939bo341b2o504bobo
769b2o416bobo91b3o241bo3b3o167b3o346b2o160b2o5bo598b2o417b2o253b2o254b
3o87bobo166bobo340b2o$b2o93b2o939b2o845b2o1189b2o333b2o528bo161b3o503b
obo93b2o416bo600b2o168b2o341b2o$525bo510b2o847bo936bo252bo335b2o525b2o
669b2o$526bo1362bo930bobo1116b2o668bo$524b3o1360b2o673bo258b2o$519bobo
512bo507bo345b2o670bobo$520b2o513b2o506b2o1016b2o$520bo513b2o506b2o2$
1547bobo$1548b2o$784bo763bo$785bo$783b3o71$346bo2052b3o1789b3o$345b2o
2052bo1791bo160b2o$345bobo2052bo1791bo160b2o511b2o768bo512bo$604bo252b
3o255b2o3235bo512bobo514b2o252b2o511b2o$603b2o176b2o74bo256b2o171b2o
851b2o761b2o424b2o1536bo513bobo251bobo343b3o164bobo$603bobo176b2o74bo
257bo169bobo339bo510b2o255b2o505bobo424b2o1794b2o255bo597bo$92b2o687bo
506bo338b2o168bo343bo254bobo504bo258bo166bo1370b2o253b3o169b2o853bo$
92bobo1282b2o248bobo167b2o597bo255b2o507b2o512b3o1022bobo252bo170bo$
92bo1283b2o418bobo853bobo506bobo511bo169b2o853bo255bo$1378bo1273bo
1023bo169b2o$3845bo155$5211bo$5209b2o$355bo4600bo253b2o$354bo1523bo
3076bo$354b3o507bo1013bobo174bo344bo927bo92bobo416bo92bobo1019b3o935bo
$769bo92b2o1014b2o176b2o341bo929b2o90b2o418b2o90b2o1959b2o$257bobo349b
o160b2o91b2o1190b2o250bo91b3o163bo91bo509bo160b2o92bo417b2o92bo257bo
931bo768b2o$6bo251b2o253bo93b2o160b2o259bo511bo762bobo255bobo90bo508b
2o1023b2o933b2o$7bo250bo255b2o92b2o418bobo253bo255bobo763b2o256b2o90b
3o507b2o1023b2o682bobo246b2o1037bo$5b3o505b2o514b2o254b2o254b2o341bo
936bobo853bobo420bobo773b2o503bobo771bo5bobo$1284b2o598bobo935b2o853b
2o422b2o773bo505b2o258bo510bobo6b2o$1884b2o936bo255bo599bo422bo1280bo
260b2o509b2o$3076bobo1534bo4bo1023b2o$3077b2o1532bobo2bobo1105bobo$
4612b2o3b2o85bo1019b2o$4703bo1021bo$4703b3o70$4439b2o$4439bobo$4439bo$
4353b3o$4355bo1808b3o$4354bo772bo1038bo$1120b2o510b2o161bo2646b2o434b
2o247b2o341b2o693bo$1119b2o510b2o162b2o254bo2390bobo434b2o245bobo340b
2o$774b2o345bo511bo160bobo254b2o94b2o2293bo435bo592bo$773bobo248b2o
350b3o671bobo94bobo761b2o675b2o604bo$262b2o511bo249b2o349bo160bo609bo
762b2o677b2o602b2o1787b2o$263b2o339b2o418bo352bo159b2o1373bo506bo168bo
604bobo1188b2o596bobo$92bo3b2o164bo341bobo929bobo1879b2o510b3o1452b2o
595bo$91b2o3bobo505bo676b2o1114b2o167b2o850bobo509bo1453bo505b3o$91bob
o2bo1185b2o1112b2o169b2o1362bo1960bo$1281bo1116bo167bo252b3o341b3o421b
3o2045b3o253bo$2821bo341bo425bo2047bo$2820bo343bo423bo2047bo152$1790bo
bo$1791b2o$1791bo90bo$1881bo$1881b3o1279bo1705bo$856bo2305bo1707b2o$
855bo258bo2047b3o518bo420bo600bo163b2o$351bo253bo249b3o254b2o7bo2468bo
90b2o422b2o596b2o253bobo$349b2o253bo508b2o4b2o1443bo764bobo256bobo91b
2o159bo260b2o598b2o252b2o$350b2o252b3o513b2o1440bobo344bobo418b2o257b
2o253b2o1113bo$520bo1787bobo252b2o94bobo247b2o165bobo251bo512b2o1023bo
bo593bobo$90bo427bobo1109bo678b2o90bo257b2o249bo166b2o1790b2o593b2o
428bobo$88b2o429b2o853bobo253bobo676bo91bobo256bo416bo1791bo595bo429b
2o$89b2o1283b2o254b2o769b2o1519bobo1970bo$6bobo1366bo771bo760bo1013b2o
$7b2o2136b2o760bo1015bo$7bo255bo1287bo594b2o759b3o$264bo1287bo3832bobo
$262b3o1285b3o3833b2o$5386bo11$5657bobo$5658b2o$5140bo517bo$5141bo$
5139b3o31$5699b3o$5653b3o43bo$5655bo44bo$5654bo22$1290b2o1791bo3073b3o
$1289bobo1023b2o766b2o334b2o932b2o1804bo$1291bo764bo5b3o251b2o764bobo
333b2o932bobo1803bo$2056b2o6bo250bo1104bo933bo1026b3o$768b3o1025bo258b
obo5bo505b2o2812bo846b3o$770bo1025b2o770bobo1354b2o510b2o765b2o176bo
507b3o337bo$769bo89b3o933bobo772bo840b3o510b2o172b2o337bobo764bobo685b
o96bo241bo$515bo343bo167b3o257b3o2121bo273b2o239bo172b2o336bo766bo686b
o96b2o$515b2o343bo168bo259bo1528b2o592bo271b2o412bo92bo158b3o258bo
1376bobo168b2o$265b2o247bobo511bo259bo338b2o1190b2o865bo503b2o160bo
258b2o537bo1009b2o$264bobo1359b2o1190bo1371bobo158bo258bobo537b2o1007b
o$266bo1361bo3075b2o443bobo$3b3o4697b2o$5bo4699bo$4bo153$1287bo$1288b
2o$1110bo176b2o339bo$1108b2o516b2o4008bobo$1109b2o262bo253b2o3583bo
424b2o$1372bo1026bo255bo1440bo88bobo1024bobo422bo$514bobo517bo337b3o
930bo93bobo253bobo1439bo87b2o1025b2o766bo$511bo3b2o518bo760bo506bobo
93b2o254b2o1273bo164b3o88bo170bo513bobo1106bobo$509bobo3bo517b3o761bo
506b2o1624bobo425bo513b2o1106b2o$510b2o331bo951b3o861bo1270b2o424b3o
507bobo3bo$842bo1816bobo157bo2047b2o603bo$842b3o1295bo518b2o156bobo
1027bo505bo513bo602b2o$2135bobo2bobo675b2o1025bobo506b2o1115b2o$273bo
1861b2o3b2o1704b2o505b2o$274bo1604bobo254bo$272b3o1604b2o$1880bo2$
3348bo255bo$772bo2573bobo253bobo$773bo2573b2o254b2o$771b3o2577bobo253b
o$3352b2o254b2o$3352bo254b2o6$3104bo$3105b2o$3104b2o5$43bo$42bo6129bo$
42b3o6128b2o$6172b2o16$43b3o$43bo$44bo2$26b2o$27b2o$26bo15$3147b3o$
3147bo$3148bo2$3669b2o$3104b3o562bobo$3106bo562bo$3105bo304b3o2754b3o$
3410bo2758bo$3411bo2756bo50bo$1116b2o5100b2o$1116bobo3835b2o1262bobo$
268b2o236bo609bo505b3o3328b2o$269b2o235b2o268bo845bo3332bo$268bo236bob
o268b2o845bo259b3o$261b2o512bobo502b2o601bo3839b2o$260bobo1018b2o264b
2o335bo3837b2o$262bo1017bo267b2o3148b2o932bo91bo$1547bo2379bo769b2o
425b3o253bo251b2o256b3o$3926b2o170b3o347bo159b3o88bo426bo253b2o249bobo
258bo$2911b2o1013bobo171bo346b2o161bo514bo253bobo509bo$2910b2o1187bo
347bobo159bo$2054b2o856bo1781b3o519b2o167bo598b2o$2055b2o253b3o342b2o
2037bo521bobo166b2o597bobo$2054bo257bo341b2o166b2o1871bo520bo167bobo
597bo$2311bo344bo164bobo$2823bo156$2566bo1109bo172bo597bo933bo344bo$
2140bo426b2o338bobo765bo174bo594b2o165bobo767bo342bo$2138b2o426b2o339b
2o766b3o170b3o595b2o165b2o765b3o342b3o508bo$1628bo510b2o767bo1704bo
1277bo93bo248b2o$1628bobo3587bo673b2o89b2o250b2o$1628b2o1705bo507bo
1283bo88b2o417bo255b2o91b2o$7bobo2294bobo863bo162bobo505bobo1281bobo
89b2o414bobo$8b2o250bo2044b2o861b2o164b2o506b2o1282b2o506b2o$8bo252bo
509bo1105bobo425bo863b2o509bobo1789bobo$259b3o510bo1104b2o1801b2o1790b
2o$770b3o519bobo583bo1802bo1791bo$347bobo943b2o$347b2o944bo$348bo$
1368bo$1367bo$1367b3o68$3bo$3b2o$2bobo1361bo$83b3o1279b2o$83bo1281bobo
4863bo$84bo1798bo4346b2o$519b2o254b2o762b2o341b2o161b3o1885b2o1790b2o
503bobo$520b2o254b2o760bobo334b2o5bobo162bo1377b2o505b2o1790b2o510b3o$
519bo85b2o168bo85b2o169b2o506bo85bo248bobo168bo90b2o514b2o166b3o254b2o
344b2o163b2o343bo510b2o166b3o254b2o509b2o343bo509bo$515b2o88bobo253bob
o167bobo591b2o248bo260b2o258b3o254bobo167bo253bobo346bo163b2o505bo90b
3o254bobo167bo253bobo89b2o419b2o853bo$514bobo88bo255bo171bo81bo509bobo
510bo257bo256bo168bo256bo509bo507b2o89bo256bo168bo256bo88b2o419bo$349b
3o164bo597b2o1281bo1698bobo90bo772bo$349bo764bobo1283b2o254b2o766b2o
766b2o254b2o766b2o768b3o$350bo768b2o1279bobo253bobo164bo255bo344bobo
765bobo253bobo164bo255bo344bobo767bo$1119bobo1278bo255bo166b2o254b2o
343bo767bo255bo166b2o254b2o343bo770bo$1119bo1702bobo253bobo1533bobo
253bobo154$2817bobo343bobo419bobo343bobo$2818b2o343b2o421b2o343b2o$
2818bo345bo421bo345bo4$8bo4950bo$9b2o509bo3151bo255bo1030bobo762bo$8b
2o511b2o3148bo255bo175bobo248bobo258bobo89bo251b2o761b2o$520b2o2386bo
255bo506b3o253b3o174b2o249b2o259b2o89bobo1013b2o$2908bobo253bobo937bo
250bo260bo90b2o254bobo$2908b2o254b2o1797b2o$605bobo1257bo3098bo673bobo
$605b2o1257bo6bo3767b2o$606bo1012bo244b3o3bo703bobo3062bo587bo$1619bob
o248b3o702b2o3650bobo$1619b2o954bo762bo2888b2o$1797bo1541b2o$1795bobo
1540b2o$1796b2o591bo$2387b2o2800bo$2388b2o2797b2o975bobo$1352bobo197bo
3635b2o975b2o$1352b2o199b2o4610bo$1353bo198b2o$842bo$841bo1479bo$841b
3o1475bobo$2320b2o44$1100bo1023bo3288bo511bo$1099b2o1022b2o3288b2o510b
2o$1099bobo1021bobo3286bobo509bobo3$1062b2o1022b2o3361b2o510b2o$1063b
2o1022b2o3359b2o510b2o$1062bo1023bo3363bo511bo3$846b2o4345bo$846bobo
4343b2o$846bo1723b2o2620bobo965b2o$1348b2o1221b2o770bo2817b2o$1057bo
289b2o208bo570bo441bo772b2o2111bo464bo238bo$850bo206b2o290bo8bo198b2o
568b2o195b3o1015bobo1853bo256b2o464b2o$849b2o205bobo298b2o197bobo568bo
bo196bo2870b2o256bobo462bobo$849bobo505bobo965bo2871bobo2$3676b2o254b
2o$2650bo767bo257bobo253bobo$4bo2644b2o766b2o257bo255bo$4b2o2643bobo
251b3o253b3o255bobo$3bobo2897bo255bo939b2o94b2o414b2o$101bo249b2o2551b
o255bo939b2o93bobo161b2o90b2o159b2o$100b2o249bobo3745bo95bo164b2o88b2o
159bo$100bobo248bo4007bo92bo2$261b2o4696b2o$260bobo4695b2o$262bo4697bo
$516bo5119bo$516b2o5118b2o$347b3o165bobo5117bobo$347bo$348bo154$2393bo
768bo2054bo$1885bo506bo769bobo2051bo510bo$1885bobo504b3o4bo762b2o2052b
3o508bobo$1541bo252bobo88b2o511bo3328b2o$1539bobo253b2o601b3o$1540b2o
253bo340bobo509bobo3080bo$90bo2045b2o510b2o3080bo$89bo2047bo511bo8bobo
1193bobo1873b3o$89b3o1034bobo1529b2o1195b2o$1126b2o1531bo679bobo513bo
1529bo$764bo362bo2212b2o2044b2o$12bo752bo2574bo2044b2o$13b2o748b3o$12b
2o$597bo4283bo1091bo255bo$595b2o4285bo1088b2o254b2o$596b2o4282b3o1089b
2o254b2o3$533bo$534bo5371bo$532b3o2347bobo3022bo$2882b2o3021b3o$2883bo
10$3638bo$3637bo$3637b3o2$1333bobo$1334b2o$1334bo$1336bo$1336b2o$1335b
obo6$1334b2o$1333bobo$1335bo21$1056bo3071bo$1056b2o3070b2o$1055bobo57b
o3011bobo57bo$1114b2o2523b3o544b2o$1114bobo2522bo546bobo$3640bo2$2885b
o$528b2o2354b2o$527bobo2354bobo1554b3o$529bo238b2o3429bo241bo$767bobo
2829b2o256bo340b2o160b3o79bo1528b2o191b3o$274b3o492bo2131b3o694bobo
256b2o339bobo161bo519b3o1085b2o194bo$276bo2624bo698bo255bobo502bo522bo
1087bo192bo64bo$275bo2626bo257b2o685b2o849b2o183bo1345b2o$3160bobo683b
obo848b2o1530bobo$349b2o489b2o2318bo687bo763b2o85bo253b3o$269b3o77bobo
487b2o3772b2o338bo$8bo262bo77bo491bo1552b3o2215bo341bo170b2o341b3o$8b
2o260bo2123bo947bo83bo934b2o763b2o340bo$7bobo2385bo946b2o81b2o935b2o
761bo343bo$1797bo341bo511bo689bobo81bobo933bo853bo249bo$1633b2o162b2o
339b2o510b2o425b2o2135b2o248b2o$1632b2o162bobo339bobo509bobo425b2o
2134bobo247bobo$1541b2o91bo1442bo1623b2o934b2o$1542b2o602b2o2552b2o
936b2o$1541bo604bobo2553bo934bo$2146bo156$3842bobo1277bobo$3843b2o
1278b2o$3843bo1279bo$98bo1276bo421bo775bo593bobo$98bobo161bo1112bobo
417bobo91bo163bo520b2o591b2o1002bobo1209bobo$4bo93b2o163bo1111b2o419b
2o90bo162bobo338bo180b2o329bo263bo1002b2o1211b2o$2bobo256b3o1624b3o
161b2o338bobo509bobo937bo327bo1037bo173bo$3b2o2387b2o510b2o939b2o1361b
2o762bo266bo$3844b2o1020bo342b2o761bobo262b2o$1287bo3579bo1104b2o264b
2o$1288bo3576b3o1277bobo$1286b3o4857b2o5bo$6146bo4bobo$2312bobo589bobo
3245b2o$2313b2o589b2o$2313bo591bo$597bo258bo254bobo510bo3065bo1023bo$
595b2o257b2o255b2o509b2o3064b2o1022b2o$596b2o257b2o255bo510b2o3064b2o
1022b2o$850bo767bobo3060bo$529bo247bo72bobo692bo72b2o3059b2o$530bo247b
2o70b2o694b2o71bo3060b2o973bobo$528b3o246b2o766b2o4109b2o$5656bo$4437b
obo$4437b2o$4438bo2$3346bobo11bobo239bobo$3347b2o12b2o240b2o62bo$3347b
o13bo241bo61b2o$3666b2o32$4632bo$4632b2o$4631bobo1070b2o$5703b2o$5705b
o6$3410b2o$3409b2o206bo$3411bo205b2o$3616bobo$4102b2o1349b2o$4103b2o
1347b2o$4102bo1351bo5$532b3o$534bo3565b2o1278b2o$533bo3565bobo1277bobo
507b3o$4101bo846b2o431bo509bo$2658b3o2287bobo939bo$2658bo2289bo$2659bo
$2653b3o2299b2o1022b2o$2653bo2301bobo1021bobo$7b2o2645bo419b2o852bo
1026bo170bo852bo$6bobo248b3o2133b2o429b2o247bobo851b2o1197b2o$8bo250bo
2133bobo427bobo249bo851bobo1195bobo$258bo851b2o3b2o936b3o337bo431bo$
1110bobo2bobo681bo255bo90b2o1021b2o$348b3o759bo4bo683b2o253bo91bobo
1020bobo1271bo$348bo1449bobo345bo1022bo1272b2o$349bo936b2o3154bobo$
1285bobo$1287bo3075b2o$4364b2o$4363bo152$4866bobo1277bobo$4867b2o1278b
2o$4867bo1279bo$5383bo$1631bo1445bo511bo1794b2o$1631bobo1441bobo509bob
o1793b2o$1366bobo262b2o1443b2o510b2o$1366b2o4086bo439bo$595bo771bo174b
obo1619bobo509bobo166bo1606b2o438bobo$594bo948b2o1619b2o168bobo339b2o
168b2o1278bo326b2o438b2o$594b3o946bo1621bo169b2o340bo167b2o82bo1197b2o
$3335bo591b2o1197b2o$3928b2o4$338bo2559bo2815bo$336b2o2558b2o2814b2o$
330bo6b2o2558b2o2814b2o$330bobo$330b2o5323bo$1801bo1084bobo2767b2o$
1802bo1083b2o2767b2o$1800b3o1084bo2$1877bo$31bo1843b2o$32bo1843b2o$18b
obo9b3o2033bobo2045bobo253bobo57bobo$19b2o2046b2o13bo2032b2o61bobo190b
2o57b2o$19bo2047bo15b2o2030bo62b2o191bo59bo$2082b2o2095bo32$327bo$326b
2o$326bobo5330b2o$2890b2o2768b2o$2890bobo2766bo$2890bo5$34b2o4399bo$
35b2o4138bo258b2o$34bo2345bo187bo1605b2o258bobo$2078b3o298b2o187b2o
1604bobo$2080bo298bobo185bobo$2079bo$2309b2o327b2o$2308bobo327bobo$
2310bo327bo4$2308b2o254b2o2814b2o$856bo179bo325b3o942bobo253bobo2813bo
bo507b2o$855b2o179b2o324bo946bo255bo1275b2o1538bo506bobo$599bo255bobo
177bobo325bo2478b2o2046bo$598b2o3241bo$598bobo176b2o335b2o3837b2o1193b
2o$603b2o171bobo335bobo254b2o2050b2o1527b2o1025b2o168b2o$603bobo172bo
335bo256bobo2048b2o1530bo1024bobo166bo$603bo767bo2052bo1278b2o505b2o
767bo$4703bobo163b2o339bobo1019b2o$777b2o254b2o3668bo166b2o338bo1020b
2o$778b2o254b2o2295b2o1536bo1363bo$777bo255bo601b2o1534b2o157bobo350bo
929b2o515b2o$1634b2o247bo1286b2o160bo349b2o928bobo514bobo$1636bo245b2o
1288bo509bobo929bo516bo$1882bobo$4702b2o$4702bobo$4702bo153$2572bo
1279bo$2573bo1279bo$2571b3o1277b3o2045bo$77bo1297bo4524b2o$75b2o1298bo
bo4521b2o$76b2o1297b2o$2654bo$6bo1366bo1278b2o3251bobo$7b2o761bo601bo
1202bo77b2o3251b2o73bo170bo$6b2o760bobo601b3o1201bo3329bo73bo169bobo$
769b2o1289bobo511b3o3403b3o168b2o$2061b2o$2061bo$2136bo768bo511bo$
2135bo768bo173bo337bo948bo765bo$2135b3o766b3o172b2o335b3o947bo765b2o$
338bo1720bobo1016b2o79bo1028bo175b3o583bo180b2o$336b2o1722b2o1096bo
1027b2o760b2o$337b2o1210bo510bo1097b3o946bo79b2o685bo74b2o$283bo1266b
2o2556bo763bobo259bobo$284b2o1263b2o75bo2479b3o764b2o260b2o71bo$283b2o
1340bo3509bo71bo$1625b3o1789bobo1787b3o$3417b2o$3345bo72bo$3343bobo$
3344b2o38$279b2o$280b2o$279bo14$3931b3o$3931bo$3853b2o77bo$3854b2o$
3853bo$4b2o$3bobo$5bo767b2o$518b2o252bobo$517bobo254bo$519bo1279b3o
1102b2o692b3o762bo82b2o510b2o$859b2o940bo1102bobo693bo762b2o80b2o510b
2o$514b2o82b2o259bobo938bo79b2o511b3o435bo72bo694bo75b2o685bobo82bo
165b2o344bo418b3o253b3o$515b2o81bobo258bo1019b2o512bo437b2o841b2o938b
2o764bo89bo165bo89bo$514bo83bo519b2o761bo431b2o79bo435bobo843bo936bo
86b3o676bo89b2o164bo89b2o$1117b2o767bo427b2o850bo1533bo768bobo253bobo
425bo$1119bo765b2o426bo851b2o1534bo4b3o1444b2o87b3o$1123b2o760bobo
1277bobo1538bo767bo255b2o420bobo87bo$1030b2o90b2o3583bo765b2o254b2o
512bo$1031b2o91bo250b2o4096bobo255bo$1030bo343b2o171b2o759b2o1285b2o
503b2o$1376bo169bobo760b2o1283bobo504b2o$1548bo759bo1287bo503bo154$
4701bo$4700bo$11bo4688b3o$12b2o$11b2o5619bo$89bo955bo2638bo256bo1691bo
$89bobo954bo2636bo255b2o997bo531bobo158b3o$89b2o953b3o497bo2138b3o254b
2o498bo496bo532b2o$1545b2o586bo2306bobo494b3o531bo$1544b2o587bobo1984b
obo317b2o$2133b2o434bo1551b2o$516bo74bo256bobo1719b2o1549bo$514bobo74b
obo254b2o1719b2o3591bo$515b2o74b2o256bo190bobo5120bo$1041b2o5118b3o$
1041bo5179bobo$6221b2o$6222bo$783bobo2051bo$784b2o2052bo$784bo2051b3o$
3596bo255bo766bo512bo523bo$3597bo73bo181bo73bo689bobo68bo444bo73bo449b
o$3595b3o72bo180b3o72bo691b2o68bobo440b3o72bo448b3o$1875bo1794b3o253b
3o434bobo322b2o516b3o$1873b2o2489b2o60bobo955bo$1874b2o453bo2034bo61b
2o957b2o66bo$2327bobo2097bo956b2o65b2o$2328b2o3122b2o6$1344bobo$1344b
2o$1345bo25$2896b3o$2847b3o46bo$2849bo47bo$2848bo4$6221bo$1308b2o4910b
2o$1309b2o4909bobo$1308bo3$3341bo$3341b2o73bo$3340bobo72b2o705bo$3415b
obo704b2o$2639bo1481bobo$2638b2o$91b2o2545bobo$90b2o756b2o4086b3o$92bo
754b2o1209b3o2875bo964bo$259b2o74b2o512bo1210bo1097b3o1776bo963b2o59bo
$258bobo74bobo1721bo1021b3o74bo2741bobo58b2o$260bo74bo2049b3o695bo75bo
2801bobo$1811bo325b2o246bo259b3o434bo2571b3o$1811b2o324bobo246bo258bo
3010bo$1810bobo324bo508bo1449b2o1557bo$1802b2o2293b2o$1119b2o680bobo
2292bo$1118b2o683bo$337b2o254b2o525bo4843bo$337bobo253bobo2735bo1627bo
1003b2o$337bo255bo693b2o2042b2o1625b2o260b2o741bobo$1288b2o342bo1697bo
bo1625bobo258b2o$1287bo343b2o3588bo$1626b2o3bobo$1626bobo696b2o$1626bo
697bobo$2326bo837b3o$3164bo$3165bo155$1627bo$94bo932bo504bobo90b2o$92b
2o674bo259b2o503b2o91b2o4519bo$93b2o674b2o256b2o504bo603bobo4008b2o$
768b2o1367b2o4008b2o$2138bo4019bo$607bo5551b2o$606bo748bobo759bo4040b
2o$606b3o183bobo560b2o758b2o2583bobo$12bo780b2o561bo759b2o1217bo255bo
1021bo86b2o169bo$13b2o778bo2542bo255bo1021bo86bo170bo269bobo$12b2o
3320b3o253b3o1019b3o255b3o270b2o$5143bo$1817bo$1818bo2292bo255bo1337bo
255bo$1816b3o2293bo255bo1335bo255bo$4110b3o253b3o1335b3o253b3o6$2324bo
$2322bobo$2323b2o5$2580bo1279bo$2581b2o1278b2o$2580b2o1278b2o6$5460bo$
5459bo$5459b3o32$2328bo$2328b2o43bo$2327bobo42b2o$2372bobo$794bo4855b
2o254b2o$794b2o559bo761b2o3530bobo253bobo$793bobo245b3o310b2o760b2o
712b3o64b2o187b3o64b2o1022b2o254b2o1216bo255bo$1043bo72b3o235bobo13b2o
746bo713bo63b2o190bo63b2o1022b2o254b2o771b2o$344b2o696bo73bo252b2o
1460bo66bo188bo66bo1023bo255bo769b2o$266b2o75b2o772bo253bo3834bo$267b
2o76bo$266bo$5142b3o$5144bo$5143bo3$1815b3o$1817bo753bo344bo934bo344bo
1190bo344bo$1816bo754b2o342b2o254b3o677b2o342b2o254b3o933b2o342b2o254b
3o$1625b2o943bobo342bobo253bo678bobo342bobo253bo934bobo342bobo253bo$
11b2o1611b2o1546bo1279bo1535bo251bo$12b2o1612bo3771b2o839b2o$11bo5385b
obo839bobo$261b3o343b3o4007b3o779bo$263bo343bo1187b2o2822bo$262bo345bo
1185bobo783b3o1340b3o692bo$1796bo785bo752bo255bo331bo1032bo$519b3o
2059bo748bo4b2o248b2o4b2o331bo940b2o88b2o$521bo2808b2o2bobo247bobo3bob
o1271bobo88bobo$520bo2808bobo254bo1279bo151$4697bo$4696bo$4696b3o$
3423bo$3423bobo764bo$2658bo764b2o765bobo$2658bobo1014bo514b2o$83bobo
2572b2o674bo340bobo$83b2o3247bobo340b2o170bo258bo247bo90bobo418bo$84bo
507bo256bo1967bo515b2o513bo258bo247bo89b2o420b2o$592bobo254bobo1966bo
602bo424b3o256b3o245b3o90bo419b2o1105bo$592b2o255b2o1965b3o600b2o1269b
obo1279bo$1030bobo253bobo253bobo253bobo253bobo253bobo1107b2o506bobo
759b2o692bobo503bo81b3o$1031b2o254b2o254b2o254b2o254b2o254b2o584bo
1030b2o761bo693b2o504b2o$1031bo255bo255bo255bo255bo255bo253bo330bo269b
o762bo1455bo504b2o$2566b2o328b3o265b2o2557bo$2565b2o598b2o2554b2o$845b
obo4874b2o$845b2o4803bo$846bo4278bo525bo$5126bo522b3o$5124b3o$6176bo$
6174bobo$6175b2o7$6179bo$6180b2o$6179b2o$339bobo5880bo$339b2o5880bo$
340bo5880b3o50$4869b3o$769b2o4100bo$279b2o489b2o4098bo$7b2o271b2o487bo
2057b2o$8b2o269bo2546bobo1864b3o432bo847b2o$7bo2820bo841b2o1021bo434b
2o845b2o$3669b2o431b2o590bo177b3o252bobo847bo$514b3o3154bo264b2o165b2o
252bo516bo$275bo240bo87b2o513b2o254b2o254b2o254b2o254b2o254b2o690bo
491b2o351bobo163bo254b2o514bo856bo$3bo271b2o238bo87b2o513b2o254b2o254b
2o254b2o254b2o254b2o691b2o489bobo351bo419bobo1370b2o$3b2o269bobo328bo
514bo255bo255bo255bo255bo255bo253bo435bobo491bo2144bobo$2bobo2648b2o
2726b3o$2653bobo502b3o2222bo$3158bo2223bo$3159bo2314b3o$1115b2o166b2o
256bo510bo254bo3166bo$1115bobo164bobo256b2o343b2o164b2o253b2o3166bo$
1115bo168bo255bobo342b2o164bobo252bobo$1887bo2$5200b3o$5200bo$5201bo!
I Like My Heisenburps! (and others)
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Extrementhusiast
 
Posts: 1696
Joined: June 16th, 2009, 11:24 pm
Location: USA

Re: Synthesising Oscillators

Postby mniemiec » June 20th, 2018, 8:58 pm

Extrementhusiast wrote:(Really? No components in the wish list? Or are you of the mentality
#C that whatever components appear during solving appear? Or have I just done everything already?)

You haven't quite done everything, but you've provided enough components to keep me backlogged in updating things for years. :)
Seriously though, yes, I do tend to look at the targets, and those do sometimes suggest desired components that would simplify them (and often, as a side-effect, many others as well). A few that suggested themselves from my previous post: extruding a pseudo-barberpole (now solved! Thanks!), and edge-shooting clocks, caterers, jams, and molds.
Extrementhusiast wrote:Component to make a pseudobarberpole from two end eaters and an extra block: ...

Splendid! This fills in a very-much-needed gap in the tool set, and it's cheaper and much more useful than any previous pseudo-barberpole synthesis (and also brings it in at below 1 glider/bit), which will remove all of the remaining >1-glider-per bit P5s, pseudo-P5s, P10s (except 24P10.1) and likely all of the pseudo-P10s as wl.
Extrementhusiast wrote:(Speaking of components, you never got me that list of components used in the expert system....)

Oops! I will try to zip up the current state of it and email it to you. (It only includes recipes that grow things or make them more complicated, to avoid infinite recursion).
Extrementhusiast wrote:On an entirely different note, have 475 different three-glider bookend syntheses: ...

(head explodes)
Wow! I have less than ten, and often can't find a suitable one.
Come to think of it, what might be useful is collections of 3-glider syntheses of various common still-lifes, oscillators, methuselahs, and sparks. On my web site, I include several, but those lists are fairly small, and likely to only be a drop in the bucket.
At one point, I started to try to find all the ways of making constellations of two objects out of collisions of 3 gliders, but I didn't get too far - and still have about a thousand different ones that I haven't had time to sort and make presentable!
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