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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 gmc_nxtman » July 27th, 2017, 5:25 pm

P3 billiard table in 11 gliders:

x = 27, y = 34, rule = B3/S23
24bo$24bobo$24b2o4$2bo$obo$b2o$9bo$8bo$8b3o2$7bo$8bo9bo$6b3o8bo$17b3o$
21b3o$21bo$12bo9bo$12bo$12bo$8bo$9bo$7b3o4$21b2o$20b2o$22bo$9b2o$8bobo
$10bo!


EDIT:

Bullet51 wrote:Eater 2 variant from dr...


The base still-life can be made in 7 gliders, allowing a suitably edgy eater synthesis to make this much cheaper:

x = 51, y = 38, rule = B3/S23
25bo$23b2o$24b2o4$2bo$obo$b2o5$46b2o$47bo$16bo30bob2o$14b2o28b2obo2bo$
15b2o26bo2bob2o$43b2obo$46bo$46b2o$17bo$16b2o$16bobo2$12bo$11b2o$7b2o
2bobo$8b2o$7bo6$17b3o$17bo$18bo!
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Re: Synthesising Oscillators

Postby BlinkerSpawn » July 27th, 2017, 5:54 pm

Bullet51 wrote:Eater 2 variant from dr:
x = 17, y = 11, rule = B3/S23
10bo$8b3o4bo$3b2o2bo6bo$3bo3b2o5b3o$2obo$o2bobo$b2obobo$4bobo$4bo2b2o$
3b2o4bob2o$9b2obo!

This reaction could also work:
x = 10, y = 11, rule = B3/S23
7b2o$6b3o$2bo3b2o$3o4bo$2bo$4b2o$3bobo$2bo2bob2o$3b2obo2bo$6bobo$6b2o!
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Re: Synthesising Oscillators

Postby mniemiec » July 28th, 2017, 12:03 am

gmc_nxtman wrote:Here's an upper bound for some scaffolding: ...

Nice! Unfortunately, it recedes a bit on the right, making it difficult to add the other spark;
none of the ways I know to make it fit there. (Now obviated by Extrementhusiast's nice synthesis).
gmc_nxtman wrote:A p2 in 6 gliders: ...

Adding an extra glider to reduce the beacon to a block makes 20.4763 from 7 gliders.
gmc_nxtman wrote:Alternate 6-glider jam synthesis, that can probably be reduced with a suitable 3-glider synthesis of the right object: ...

The existing 6-glider synthesis is edgy with respect to the point-spark; this is edgy with respect to the loaf at a 90 degree angle to the previous one, which reduces the cost of at least 24 pseudo-objects in my collection.
gmc_nxtman wrote:Probably trivial p2 synthesis: ...

BlinkerSpawn found a 9-glider synthesis of this on 2016-08-24; however, his appears to be from a soup, while yours is more synthetic, so it's more likely adaptible to other similar syntheses.
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Re: Synthesising Oscillators

Postby gmc_nxtman » July 28th, 2017, 11:33 am

The penny lane synthesis can be slightly reduced (from 33 to 28):

x = 379, y = 29, rule = B3/S23
224bo$223bo$80bo142b3o$81bo3bo30b2o30b2o$79b3ob2o30bo2bo24bo3bo2bo144b
o$84b2o29bo2bo22bobo3bo2bo142b2o$116b2o24b2o4b2o144b2o37bo4bobo4bo$
331bobo2bobobobo2bobo$332b2o3b2ob2o3b2o$223bo66bo$17bo161bo31bo10bo20b
o31bo14bobo14bo31bo$16bo29bo31bo11bobo17bo31bo31bo3bobo25bo3bobo9b3o
13bo3bobo25bo3bobo13b2o10bo3bobo3bo21bo3bobo3bo22b2o5b2o$16b3o26bobo
29bobo10b2o17bobo29bobo29bobo3bo25bobo3bo25bobo3bo3b2o20bobo3bo3b2o5b
3o12bobo3bo3bobo19bobo3bo3bobo21bo7bo$11bo33bobo29bobo11bo17bobo29bobo
29bobo29bobo13bo15bobo7bo21bobo7bo6bo14bobo7bobo19bobo7bobo18b2obo7bob
2o$9bobo32b2obobo26b2obobo26b2obob2o25b2obob2o8bo16b2obob5o22b2obob5o
6b2o14b2obob5obo20b2obob5obo7bo12b2obob5obob2o17b2obob5obob2o17b2obob
5obob2o$10b2ob2o33b2o30b2o5bobo22bo2bo28bo2bo7bobo18bo5bo25bo5bo5bobo
17bo5bo25bo5bo25bo5bo25bo5bo25bo2bo2bo$13bobo71b2o24b2o30b2o8b2o20b5o
27b5o27b5o27b5o27b5o27b5o27b5o$13bo74bo202b2o$152b3o24bo31bo31bo31bo
14b2o15bo31bo31bo$b2o83b2o64bo25bobo29bobo29bobo29bobo15bo13bobo29bobo
29bobo$obo82b2o66bo25bo31bo31bo31bo31bo31bo31bo$2bo84bo134b2o$221b2o$
223bo$116b2o24b2o4b2o$84b2o29bo2bo22bobo3bo2bo152b2o$79b3ob2o30bo2bo
24bo3bo2bo152bobo$81bo3bo30b2o30b2o153bo$80bo!
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Re: Synthesising Oscillators

Postby BobShemyakin » July 28th, 2017, 1:17 pm

gmc_nxtman wrote:The penny lane synthesis can be slightly reduced (from 33 to 28):

x = 379, y = 29, rule = B3/S23
224bo$223bo$80bo142b3o$81bo3bo30b2o30b2o$79b3ob2o30bo2bo24bo3bo2bo144b
o$84b2o29bo2bo22bobo3bo2bo142b2o$116b2o24b2o4b2o144b2o37bo4bobo4bo$
331bobo2bobobobo2bobo$332b2o3b2ob2o3b2o$223bo66bo$17bo161bo31bo10bo20b
o31bo14bobo14bo31bo$16bo29bo31bo11bobo17bo31bo31bo3bobo25bo3bobo9b3o
13bo3bobo25bo3bobo13b2o10bo3bobo3bo21bo3bobo3bo22b2o5b2o$16b3o26bobo
29bobo10b2o17bobo29bobo29bobo3bo25bobo3bo25bobo3bo3b2o20bobo3bo3b2o5b
3o12bobo3bo3bobo19bobo3bo3bobo21bo7bo$11bo33bobo29bobo11bo17bobo29bobo
29bobo29bobo13bo15bobo7bo21bobo7bo6bo14bobo7bobo19bobo7bobo18b2obo7bob
2o$9bobo32b2obobo26b2obobo26b2obob2o25b2obob2o8bo16b2obob5o22b2obob5o
6b2o14b2obob5obo20b2obob5obo7bo12b2obob5obob2o17b2obob5obob2o17b2obob
5obob2o$10b2ob2o33b2o30b2o5bobo22bo2bo28bo2bo7bobo18bo5bo25bo5bo5bobo
17bo5bo25bo5bo25bo5bo25bo5bo25bo2bo2bo$13bobo71b2o24b2o30b2o8b2o20b5o
27b5o27b5o27b5o27b5o27b5o27b5o$13bo74bo202b2o$152b3o24bo31bo31bo31bo
14b2o15bo31bo31bo$b2o83b2o64bo25bobo29bobo29bobo29bobo15bo13bobo29bobo
29bobo$obo82b2o66bo25bo31bo31bo31bo31bo31bo31bo$2bo84bo134b2o$221b2o$
223bo$116b2o24b2o4b2o$84b2o29bo2bo22bobo3bo2bo152b2o$79b3ob2o30bo2bo
24bo3bo2bo152bobo$81bo3bo30b2o30b2o153bo$80bo!

And from 28 to 27:
x = 379, y = 32, rule = B3/S23
207bo$205bobo$206b2o3$80bo$81bo3bo30b2o30b2o$79b3ob2o30bo2bo24bo3bo2bo
144bo$84b2o29bo2bo22bobo3bo2bo142b2o$116b2o24b2o4b2o144b2o37bo4bobo4bo
$331bobo2bobobobo2bobo$332b2o3b2ob2o3b2o$225bo64bo$17bo161bo31bo14bo
16bo31bo14bobo14bo31bo$16bo29bo31bo11bobo17bo31bo31bo3bobo25bo3bobo11b
3o11bo3bobo25bo3bobo13b2o10bo3bobo3bo21bo3bobo3bo22b2o5b2o$16b3o26bobo
29bobo10b2o17bobo29bobo29bobo3bo25bobo3bo25bobo3bo3b2o20bobo3bo3b2o5b
3o12bobo3bo3bobo19bobo3bo3bobo21bo7bo$11bo33bobo29bobo11bo17bobo29bobo
29bobo29bobo29bobo7bo21bobo7bo6bo14bobo7bobo19bobo7bobo18b2obo7bob2o$
9bobo32b2obobo26b2obobo26b2obob2o25b2obob2o8bo16b2obob5o22b2obob5o9b3o
10b2obob5obo20b2obob5obo7bo12b2obob5obob2o17b2obob5obob2o17b2obob5obob
2o$10b2ob2o33b2o30b2o5bobo22bo2bo28bo2bo7bobo18bo5bo25bo5bo10bo14bo5bo
25bo5bo25bo5bo25bo5bo25bo2bo2bo$13bobo71b2o24b2o30b2o8b2o20b5o27b5o10b
o16b5o27b5o27b5o27b5o27b5o$13bo74bo202b2o$152b3o24bo31bo31bo31bo14b2o
15bo31bo31bo$b2o83b2o64bo25bobo29bobo29bobo29bobo15bo13bobo29bobo29bob
o$obo82b2o66bo25bo31bo31bo31bo31bo31bo31bo$2bo84bo3$116b2o24b2o4b2o$
84b2o29bo2bo22bobo3bo2bo152b2o$79b3ob2o30bo2bo24bo3bo2bo152bobo$81bo3b
o30b2o30b2o153bo$80bo!

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Re: Synthesising Oscillators

Postby gmc_nxtman » July 28th, 2017, 1:20 pm

Nice! I forgot about the 3G tail-adder. In other news, 28.003 reduced from 8 to 6 gliders (probably unnecessary but posting for completeness):

x = 50, y = 34, rule = B3/S23
41bo$42bo$40b3o$18bobo$18b2o25bo$19bo23bobo$44b2o$8bobo$9b2o$9bo30bobo
$40b2o$2bo18b3o17bo$obo$b2o36b3o$41bo$3b3o34bo$5bo$4bo43b2o$47bobo$19b
o29bo$18b2o$18bobo5$35b2o$36b2o$35bo3$2b2o$3b2o$2bo!


EDIT: Squid in 5 gliders:

x = 18, y = 12, rule = B3/S23
2b2o$b2o$3bo2$b2o3b3o$obo3bo$2bo4bo$16b2o$15b2o$2b2o13bo$3b2o$2bo!


EDIT2: All possible mirror-and-block still lifes in 8-12 gliders:

x = 51, y = 120, rule = B3/S23
42bo$40b2o$41b2o$33bo$34b2o$33b2o4$38bo6bo$39bo4bo$37b3o4b3o$33b3o$35b
o$34bo5b3o$42bo$41bo2$32b3o$34bo$33bo$39b3o$39bo$40bo9$41bo$39b2o$40b
2o$32bo$33b2o$32b2o4$37bo6bo$38bo4bo$36b3o4b3o$32b3o$34bo$33bo5b3o$41b
o$40bo2$33b3o$35bo$34bo$40b3o$40bo$41bo6$40bo$40bobo$40b2o$45bo$44bo$
29bo14b3o$bo28bo$2b2o24b3o$b2o$26b2o8bo$25bobo7bobo$27bo7b2o$6bo6bo$7b
o4bo22b4o$5b3o4b3o19bo4bo9bo$b3o30bobo2bo8b2o$3bo31b4o9bobo$2bo5b3o$
10bo24b2o$9bo25b2o2$3o$2bo$bo$7b3o$7bo$8bo6$40bo$40bobo$40b2o$45bo$44b
o$29bo14b3o$o29bo$b2o25b3o$2o$26b2o8bo$25bobo7bobo$27bo7b2o$5bo6bo$6bo
4bo23b4o$4b3o4b3o20bo4bo9bo$3o31bobo2bo8b2o$2bo32b4o9bobo$bo5b3o$9bo
27b2o$8bo28b2o2$b3o$3bo$2bo$8b3o$8bo$9bo!
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Re: Synthesising Oscillators

Postby mniemiec » August 1st, 2017, 12:02 pm

gmc_nxtman wrote:Boat to shillelagh in 3G: ... Is this known? There's a 3G version in Extrementhusiast's component collection, but it has different clearance.

Nice! This was certainly new to me. The previous 3-glider one was mine, a slight improvement over Dave Buckingham's original 4-glider one. One problem that all the previous ones had was that they required a glider to come in from above. In yours, they all come from behind, which allows for several situations where a shillelagh is sideways and close to something else. This solves several still-lifes and pseudo-still-lifes 20 bits and up (including one of the ones on the unsolved pseudo-still-life list), and also, surprisingly, reducing one of the two non-trivial 21-bit P2 pseudo-oscillators from a convoluted 88 glider synthesis to a trivial 14 glider one:
x = 254, y = 215, rule = B3/S23
92bo$92bobo$92boo$128bo5bo$91bo4bo32bo5boo$92boobo31b3o4boo3bo$91boobb
3o41bobo$58bo80boo14boo18boo18booboo15booboo25booboo$51bo6bobo51boo18b
oo22bo19bobboo15bobobo15bobobo25bobobo$52bo5boo13boo18boo17bobo17bobo
18bo19bo5bobo11bo5bo13bo5bo23bo6bo$50b3o20boo18boo18boo18boo18boo18boo
4bo13boo18boo8bobo17boo4bo$46b3o174boo24boo$48bo24boo18boo18boo18boo
18boo18boo18boo18boo9bo5bo12boo$47bo25bobobo15bobobo15bobobo15bobobo
15bobobo15bobobo15bobobo15bobobo8bo3bobo10bobobo$76boo18boo18boo18boo
18boo18boo18boo18boo7boo3boo14boo$59boo164bobo$59bobo$59bo3$152bo$152b
obo$152boo9$190bobo$144bobo43boo$144boo45bo$145bo18bobbo16bobbo16bo19b
o19bo$162b6o14b6o4boo8b3o17b3o7bo9b3o$123boo18boo16bo19bo9boo8bo19bo
10bobo6bo$102bobo17bobbo16bobbo15bobboo15bobboo7bo7bobb3o14bobb3o5boo
7bobb3oboo$103boo17bobbo12boobbobbo14boobobo14boobobo14boobobbo13boobo
bbobboo9boobobboboo$103bo19boo14boobboo16boboo16boboo18bo19bo5bobo11bo
$138bo22bo19bo21boo18boo4bo13boo$102boo56boo18boo$101bobo$103bo$177boo
$178boobbo$126b3o48bo3boo$128bo52bobo$127bo19$234bo$234bobo$230bo3boo$
231boo19boo$230boo19bobo$102bobo43bo102bo$52bo50boo3bo37boo19bo19bo19b
o19bo19bobboo$44bo8bo20bo19bo8bobboo16bo19bobboo15bobobo15bobobo15bobo
bo15bobobo15bobobo$42b3o6b3o18b3o17b3o12boo13b3o17b3o17b3oboo14b3oboo
14b3oboo14b3oboo14b3oboo$41bo13boo14bo19bo29bo19bo19bo19bo19bo19bo19bo
$41bobb3oboo6boo13bobb3oboboo9bobb3oboboo19bobb3oboboo9bobb3oboboo9bo
bb3oboboo9bobb3oboboo9bobb3oboboo9bobb3oboboo9bobb3oboboo$40boobobbob
oo5bo14boobobboboobo8boobobboboobo18boobobboboobbo7boobobboboobbo7boob
obboboobbo7boobobboboobbo7boobobboboobbo7boobobboboobbo7boobobboboobbo
$43bo29bo19bo29bo7boo10bo7boo10bo7boo10bo7boo10bo7boo10bo7boo10bo7boo$
43boo14b3o11boo18boo8bo19boo18boo18boo18boo10bo7boo18boo18boo$59bo43b
oo3bo85bo16boo18boo18boo$60bo41bobo3bobo83b3o13bobo17bobo17bobo$108boo
79b3o19bo19bo19bo$191bo$49boo139bobboo$48bobo142bobo$50bo142bo12$31bo
20bobo$29bobo20boo$30boo21bo3$99bo130bo$97bobo77boo52bo$98boo73bo3bobo
49b3o$171bobo3bo$80boo18boo36bo33boo58bobo$57bo22boo18boo34bobo29b3o
61boo$42boo13bobo77boo31bo62bo$41bobo13boo84bo25bo$41bo36bo19bo19bo19b
o3bo107bo$37bobboo9bobo23bobo17bobo17bobo17bobobb3o13boo18boo29boo18b
oo4b3o11bobo$34bobobo12boo21bobobbo14bobobbo14bobobbo14bobobbo14bobobb
o14bobobbo24bobo3bo13bobo3bo4bo8bobo3bo$32b3oboo14bo19b3ob3o13b3ob3o
13b3ob3o13b3ob3o13b3ob3o13b3ob3o23b3ob4o12b3ob4o6bo5b3ob4o$31bo39bo19b
o19bo19bo19bo19bo29bo19bo19bo$31bobb3oboboo8b3o18bobb3o14bobb3o14bobb
3o14bobb3o14bobb3o14bobb3o24bobb3oboo11bobb3oboo11bobb3oboo$30boobobbo
boobbo7bo19boobobbo13boobobbo13boobobbo13boobobbo13boobobbo13boobobbo
23boobobbobobo9boobobbobobo9boobobbobobo$33bo7boo8bo21bo19bo19bo19bo
19bo19bo29bo5bo13bo5bo13bo5bo$33boo38boo18boo18boo18boo18boo18boo28boo
18boo18boo$41boo$40bobo$41bo5$188b3o$188bo$29bo159bo$29boo$23b3obbobo
9boo$25bo13boo$24bo8bo7bo$33boo14b3o$32bobo14bo$50bo9$11bo$10bo$7bobb
3o$8bo$6b3o$$10bo$9bobo$4bobo3bo13bobobbo14bobobbo24bobobbo14bobobbo
14bobobbo14bobobbo14bobobbo14bobobbo24bobobbo14bobobbo14bobobbo$bb3ob
4o12b3ob4o12b3ob4o22b3ob4o12b3ob4o12b3ob4o12b3ob4o12b3ob4o12b3ob4o22b
3ob4o12b3ob4o12b3ob4o$bo19bo19bo29bo19bo19bo19bo19bo19bo29bo19bo19bo$b
obb3oboo11bobb3oboo11bobb3oboo21bobb3oboo11bobb3oboo11bobb3oboo11bobb
3oboo11bobb3oboo11bobb3oboo21bobb3oboo11bobb3oboo11bobb3oboo$oobobbobo
bo9boobobbobobo9boobobbobobo19boobobbobobo9boobobbobobo9boobobbobobo9b
oobobbobobo9boobobbobobo9boobobbobobo19boobobbobobo9boobobbobobo9boobo
bbobobo$3bo5bo13bo5bo13bo5bo9bo13bo6bo12bo6bo12bo6bo12bo6bo12bo6bo12bo
6bo22bo6bo12bo6bo12bo6bo$3boo18boo18boo13bo14boo4bo13boo4bo13boo4bo13b
oo4bo13boo4bo13boo4bo20booboo4bo10booboo4bo10booboo4bo$51boo5b3o18boo
18boo18boo18boo18boo18boo18bobobo5boo8bobobo5boo9boobo5boo$52boo59boo
18boo18boo18boo25bo3bo15bo3bo19bo$51bo3b3o36b3o16boo18boo18boo18boo30b
obo8b3o6bobo17bobo$55bo38bo111boo10bo7boo18boo$56bo38bo61boo5boo11boo
38bobboo$91b3o63bobo5boo10bobo40bobo$93bo64bo5bo13bo13b4o24bo$92bo98b
6o$184boo4boob4o$148bo35bobo4boo$147bo28boo6bo$147b3o17boo6boo$143b3o
22boo7bo$136b3o4bo23bo3b3o$138bo5bo26bo$137bo34bo8$135bo$134bo50bo$
134b3o47bo8bo$184b3o4boo$133bo58boo$13bo120bo$13bobo38bo6bo30bo10bo28b
3o$13boo40bo4bo32bo8bo75bo$9bo43b3o4b3o12boobboo10b3oboobboob3o25bo23b
oo23bo4boo$7bobo66bobbo16bobbo15boobboo9boo3boobboo13bobobboo16b3o4bob
obboo26bo$bbo5boo4bobobbo16bobbo16bobbo15bo4bo14bo4bo14bo4bo8bobo3bo4b
o14bo4bo24bo4bo27bo$3bo8b3ob4o16b4o16b4o16b4o16b4o16b4o16b4o16b4o13bob
o10b4o26b3o$b3o7bo162boo24boo18boo$5boo4bobb3oboo14b3oboo14b3oboo14b3o
boo14b3oboo14b3oboo14b3oboo14b3oboo14bo9b3oboo6boobboo3booboo10boo3boo
boo15booboo$6boobboobobbobobo12bobbobobo12bobbobobo12bobbobobo12bobbob
obo12bobbobobo12bobbobobo12bobbobobo22bobbobobo4boo9bobobo15bobobo15bo
bobo$5bo7bo6bo12bo6bo12bo6bo12bo6bo12bo6bo12bo6bo12bo6bo12bo6bo22bo6bo
6bo5bo6bo12bo6bo12bo6bo$10booboo4bo10booboo4bo10booboo4bo10booboo4bo
10booboo4bo10booboo4bo10booboo4bo10booboo4bo20booboo4bo13boo4bo13boo4b
o13boo4bo$10boobo5boo9boobo5boo9boobo5boo9boobo5boo9boobo5boo9boobo5b
oo9boobo5boo9boobo5boo19boobo5boo18boo18boo18boo$14bo19bo19bo19bo19bo
19bo19bo19bo29bo18boo18boo18boo$3o12bobo17bobo17bobo17bobo17bobo17bobo
17bobo17bobo19bo7bobo15bobobo15bobobo15bobobo$bbo13boo18boo18boo18boo
18boo18boo18boo18boo20boo6boo18boo18boo18boo$bo175boo3$179bo$179boo$
178bobo6boo$187bobo$172b3o12bo$174bo$173bo!
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Re: Synthesising Oscillators

Postby gmc_nxtman » August 4th, 2017, 10:52 am

From now on I'll be posting these here. I assume the three 18-bitters from the unsure discoveries thread have already been noted.

17.1010 (xs17_8k4r2qrzw1) in 7 gliders:
x = 107, y = 12, rule = B3/S23
9bo$7bobo8bobo$8b2o8b2o$12bo6bo43bo$12bobo49bo$12b2o25bo22b3o6bo31bo$
38bobo29bobo29bobo$33b2o2bo2bo24b2o2bo2bo28bo2bo$3o2b2o7bo18b2o3b2ob2o
22b2o3b2ob2o27b2ob2o$2bob2o7b2o26bo31bo31bo$bo4bo6bobo22b2obo28b2obo
28b2obo$38b2ob2o27b2ob2o27b2ob2o!


17.3192 (xs17_4aab94ozx321) in 14 gliders:

x = 117, y = 24, rule = B3/S23
10bo$9bo$9b3o4$101bo$102b2o$101b2o3bobo$4bo68bo32b2o$5bo65b2o34bo$3b3o
66b2o$20bo15bo15bo15bo15bo15bo13bo$5b3o10b3o13b3o13b3o13b3o4bo8b3o13b
3o7bo5bobo$5bo11bo15bo15bo15bo6b2o7bo15bo8b2o6b2o$6bo11b3o13b3o13b3o
13b3o3bobo7b5o11b5o4b2o2b2o$b2o18bo15bo15bo15bo16bo15bo8bobo$obo17b2o
14b2o3bo10bobo13bobo13bo15bo10bo$2bo37bo11b2o14b2o6b3o5b2o14b2o$40b3o
33bo$77bo$38b3o$40bo$39bo!


By the way, does anyone know of a loaf-to-beehive (or wing-to-bun) component? That might allow 16.736 to be reduced somewhat.

EDIT: Niemiec's component below solves this, reducing 16.375 (xs16_2ege93z321) to 8 gliders and allows for an alternate 10-glider synthesis of 16.736 (xs16_2ege96z321):

x = 75, y = 17, rule = B3/S23
37bo3b2o10bo15bo3b2o$7b2o28b3o2bo26b3o2bo$6bobo31b2o11bo18b2o$2b2o4bo
28b3o29b3o$3b2o8b2o21bo2bo13bo14bo2bo$2bo10bobo15b3o2bobo29b2o$13bo19b
o3bo15bo$32bo31b2o$37b2o14bo9bobo$5b2o30bobo25bo$4bobo2b2o26bo15bo13b
3o$6bo2bobo55bo$9bo43bo14bo$bo$b2o50bo$obo$53bo!
Last edited by gmc_nxtman on August 4th, 2017, 4:41 pm, edited 3 times in total.
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Re: Synthesising Oscillators

Postby mniemiec » August 4th, 2017, 1:57 pm

gmc_nxtman wrote:By the way, does anyone know of a loaf-to-beehive (or wing-to-bun) component? That might allow 16.736 to be reduced somewhat.

Not directly, but how about wing-to-bookend and then bookend-to-bun?
x = 185, y = 40, rule = B3/S23
oobo16boobo16boobo16boobo16boobo16boobo$oboo16boboo16boboo16boboo16bob
oo16boboo$$b3o17b3o17b3o17b3o17b3o17b3o$bobbo16bobbo16bobbo16bobbo16bo
bbo16bobbo$bbobobb3o13boo17bobo18boo11bo5bobo18boo$3bo3bo35bo33bo5bo$
8bo66b3o$bboo75boo$bobo34boobboo34boo$3bo35boobobo35bo$38bo3bo9$oobo
16boobo16boobo16boobo16boobo16boobo16boobo16boobo16boobo16boobo$oboo
16boboo16boboo16boboo16boboo16boboo16boboo16boboo16boboo16boboo$$b3o
17b3o17b3o17b3o17b3o17b3o17b3o17b3o17b3o17b3o$bobbo16bobbo16bobbo16bo
bbo16bobbo16bobbo16bobbo16bobbo16bobbo16bobbo$3boo17boo19boo17boo19boo
17boo19boo17boo19boo17boo$$7boo39bobo$7bobo34boobboo$7bo36boo3bo115boo
$3b3o45boo37bo30boo43boo$5bo45bobo29boo4boo31boo41bo3boo$4bo46bo22boo
6boo5bobo29bo3boo41boo$75boo7bo39boo35boo7bo$74bo3b3o45bo35boo$78bo82b
o$79bo$125boo$125bobo$125bo!
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Re: Synthesising Oscillators

Postby gmc_nxtman » August 4th, 2017, 5:07 pm

17.1317 (xs17_69bkk8z253) in nine gliders, one-sided:

x = 118, y = 31, rule = B3/S23
26b2o$25b2o$17bo3b3o3bo$17b2o4bo$16bobo3bo$47b2o3bo26b2o3bo26b2o3bo$
46bo2bobobo24bo2bobobo24bo2bobobo$46b2obob2o25b2obob2o25b2obob2o$48bob
o29bobo29bobo$48bobo29bobo29bobo$49bo31bo31bo$32bo21bo31bo$31b2o20bobo
29bobo$31bobo18bo2bo28bo2bo$53b2o30b2o2b2o$89bobo$89bo$3o18b2o$2bo18bo
bo$bo19bo6$4b2o$3bobo$5bo$28b2o$28bobo$28bo!


EDIT: 17.3522 (xs17_j96o8a6z121) in ten gliders, very messy:

x = 156, y = 75, rule = B3/S23
15bo$16bo$14b3o29$86b2o30b2o30b2o$86bobo29bobo29bobo$55bo32bo31bo31bo$
53b2o33b2o30b2o30b2o$54b2o30b2o2bo27b2o2bo27b2o2bo$85bo2bo2bo25bo2bo2b
o25bo2bo2bo$85b2o2b2o26b2o2b2o26b2o2b2o$15bobo76b2o30b2o$16b2o76b2o30b
2o$16bo$128b3o$128bo$129bo5$47bo$45b2o$46b2o$51b3o$37bo13bo$37bobob3o
8bo$37b2o2bo$42bo5$19bo$19b2o$18bobo10$3o$2bo$bo!


EDIT2: 17.3639 (xs17_c8ad1e8z33) in eight gliders:

x = 48, y = 23, rule = B3/S23
25bo$10bo12b2o$11bo12b2o$9b3o2$17bo$16bo$16b3o2$7bo$b2o5bo$2b2o2b3o35b
o$bo40b3o$8bo32bo$7b2o32bob2o$7bobo32bobo$3o41bob2o$2bo40b2ob2o$bo2$
25b2o$25bobo$25bo!


EDIT3: 17.1247 (xs17_4aajkcz253) in eight gliders:

x = 117, y = 31, rule = B3/S23
17bo$17bobo$17b2o2$77bo$76bo$16bo59b3o$14b2o$15b2o25b2o30b2o$42b2o30b
2o2$bo46bo31bo31bo$2bo16b2o26bobo29bobo29bobo$3o15b2o28b2o30b2o30b2o$
20bo29b2o30b2o30b2o$48b2o2bo27b2o2bo27b2o2bo$47bo3b2o26bo3b2o26bo3b2o$
17bo30b3o29b3o29b3o$15bobo32bo31bo31bo$16b2o$22b3o$22bo$23bo6$25b3o$
25bo$26bo!


EDIT4: 17.3178 (xs17_4aabaiczx32) in eight gliders, almost cetainly reducible by constellations:

x = 55, y = 15, rule = B3/S23
34bo$32b2o$5bo27b2o$3bobo15b2o14b2o$4b2o15b2o7bo6b2o$b2o28b2o19bo$obo
10bo10bo5b2o8bo10bobo$2bo5b2o2b2o10bo15bo10bobo$9b2obobo9bo9bobo3bo7b
2obob2o$8bo26b2o11bo2bobo$35bo14bo2bo$51b2o$34b2o$33bobo$35bo!


EDIT5: 17.1068 (xs17_ci6o8brzw1) in nine gliders:

x = 122, y = 29, rule = B3/S23
9bo$10bo10bo$8b3o8bobo$20b2o$92bo$93bo$8bo82b3o$9b2o52b2o30b2o$8b2o52b
o2bo28bo2bo$63bobo29bobo$19bo44bo31bo$17bobo$18b2o6b3o24bo31bo31bo$26b
o25bobo2bo26bobo2bo26bobo2bo$27bo23bo2b4o25bo2b4o25bo2b4o$51bobo29bobo
29bobo$52b2o2b2o26b2o2b2o26b2o2b2o$56b2o30b2o30b2o4$5b2o$6b2o$bo3bo$b
2o$obo$21b2o$20bobo$22bo!
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Re: Synthesising Oscillators

Postby yootaa » August 10th, 2017, 3:50 am

I tried to get synthesis of pseudo-mold, but I couldn't complete this.
x = 34, y = 23, rule = B3/S23
2bo24b2o$2bo24bobo$2bo$3o$3bo20b3o$o2bo20bo2b2o$b3o20bo$24bo4bo$25bo3b
o2b2o$26b3o2bo$30bo$30bo$30bo$26b3o2bo$25bo3bo2b2o$24bo4bo$b3o20bo$o2b
o20bo2b2o$3bo20b3o$3o$2bo$2bo24bobo$2bo24b2o!
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Re: Synthesising Oscillators

Postby BlinkerSpawn » August 10th, 2017, 12:45 pm

yootaa wrote:I tried to get synthesis of pseudo-mold, but I couldn't complete this.
x = 34, y = 23, rule = B3/S23
2bo24b2o$2bo24bobo$2bo$3o$3bo20b3o$o2bo20bo2b2o$b3o20bo$24bo4bo$25bo3b
o2b2o$26b3o2bo$30bo$30bo$30bo$26b3o2bo$25bo3bo2b2o$24bo4bo$b3o20bo$o2b
o20bo2b2o$3bo20b3o$3o$2bo$2bo24bobo$2bo24b2o!

The middle part is easy; how do you make the sides?
x = 28, y = 23, rule = B3/S23
16bo$16bo$16bo$14b3o$17bo$14bo2bo$15b3o3$5bo17bo$4bo17b3o$4b3o14bo3b3o
$3o18bobo$o21bo$bo2$15b3o$14bo2bo$17bo$14b3o$16bo$16bo$16bo!
Last edited by BlinkerSpawn on August 10th, 2017, 6:30 pm, edited 1 time in total.
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Re: Synthesising Oscillators

Postby AbhpzTa » August 10th, 2017, 3:44 pm

gmc_nxtman wrote:EDIT2: 17.3639 (xs17_c8ad1e8z33) in eight gliders:

x = 48, y = 23, rule = B3/S23
25bo$10bo12b2o$11bo12b2o$9b3o2$17bo$16bo$16b3o2$7bo$b2o5bo$2b2o2b3o35b
o$bo40b3o$8bo32bo$7b2o32bob2o$7bobo32bobo$3o41bob2o$2bo40b2ob2o$bo2$
25b2o$25bobo$25bo!

Reduced to 6:
x = 18, y = 26, rule = B3/S23
9bo$10bo$8b3o2$5bo$6bo$4b3o2$7bo$7bobo5bobo$7b2o6b2o$16bo3$12bo$11b2o$
11bobo7$b2o$obo$2bo!
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 » August 10th, 2017, 6:24 pm

AbhpzTa wrote:Reduced to 6...


Nice! Here's 17.1247 (xs17_4aajkcz253) reduced to seven gliders:

x = 105, y = 34, rule = B3/S23
5bo$5bobo$5b2o2$65bo$64bo$4bo59b3o$2b2o$3b2o25b2o30b2o$30b2o30b2o2$36b
o31bo31bo$7b2o26bobo29bobo29bobo$6b2o28b2o30b2o30b2o$8bo29b2o30b2o30b
2o$36b2o2bo27b2o2bo27b2o2bo$35bo3b2o26bo3b2o26bo3b2o$5bo30b3o29b3o29b
3o$3bobo32bo31bo31bo$4b2o$10b3o$10bo$11bo9$2o$b2o$o!


EDIT: One can also make 17.3639 (xs17_c8ad1e8z33) + a canoe in 6 gliders:

x = 21, y = 26, rule = B3/S23
12bo$13bo$11b3o2$8bo$9bo$7b3o2$10bo$10bobo5bobo$10b2o6b2o$19bo3$15bo$
14b2o$14bobo7$b2o$obo$2bo!
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Re: Synthesising Oscillators

Postby Goldtiger997 » August 12th, 2017, 9:20 am

Goldtiger997 wrote:
mniemiec wrote:I already had that step; what is missing is the underlying still-lifes.
In fact, syntheses of these should give them all:
x = 86, y = 9, rule = B3/S23
3boo13boo13boo13boo13boo13boo$bbobbo11bobbo11bobbo11bobbo11bobbo11bobb
o$3bobobbo9bobobbo9bobobbo9bobobbo9bobobbo9bobobbo$bboob4o8boob4o8boob
4o8boob4o8boob4o8boob4o$bobbo11bobbo11bobbo14bo4boo5bobbo11bobbo$obo3b
o9boobboo9boobboo12bobobbo7bobobo10bobboboo$bo3boo14bo14bo13bobobo8bob
obo10boo3bo$20bo15bobo12bobo10bobbo15bobo$20boo15boo13bo12boo17boo!


Sorry for that misconception. To make up for it, here is a final step for the second still-life above:...
I wasn't able to make a full synthesis from that, but this is how I was planning on doing it:...
Can anyone complete it?...


Got much closer after noticing a converter I hadn't noticed before in Extrementhusiast's collection. Now only one step is missing:

x = 644, y = 46, rule = B3/S23
17bobo581bobo$17b2o482bo100b2o19bo$18bo482bobo98bo18b2o$501b2o44bo74b
2o$12bo473bo18bo42b2o44bobo$11bo475b2o16bobo39b2o46b2o$11b3o472b2o17b
2o88bo$7bobo305bo237bo$8b2o303bobo220bo14b2o$8bo305b2o126bo94bo10bo3b
2o40bo$438bo2b2o92b3o11b2o41bobo$bo317bo116bobo2bobo96bo7b2o43b2o3bo$
2bo315bo118b2o102b2o53b2o$3o315b3o146b2o28b2o41b2o55b2o40bo$368bo31bo
29bo29bo5bobo21bo5bobo79b2o28b2o26b4o$39bo29bo29bo29bo29bo29bo29bo29bo
5bo3bo19bo29bo29bo5b2o19bo3bo28bobo3b2o22bobo3b2o2b3o17bobo3bo23bobo3b
o23bo16bo12bo27bo2bo26bo2bo26bo2bo$35b2obobo24b2obobo24b2obobo24b2obob
o24b2obobo24b2obobo24b2obobo24b2obobo5b2obobo13b2obobob2o21b2obobob2o
3b3o2bobo10b2obobobobobo48b2obobobobobo18b2obobobobobo2bo15b2obobobobo
20b2obobobobo20b2obobo2bo13b2o6b2obobo2bo24bobo2bo24bobo2bo24bobo2bo$
35bob2obo24bob2obo24bob2obo24bob2obo24bob2obo24bob2obo24bob2obo24bob2o
bo4b2o2b2o14bob2obob2o21bob2obob2o3bo4b2o11bob2obob2o21bo5bo23bob2obob
2o21bob2obob2o6bo14bob2obob2o21bob2obob2o21bob2ob4o12b2o7bob2ob4o23b2o
b4o23b2ob4o23b2ob4o$39bo29bo29bo29bo29bo29bo29bo29bo29bo29bo8bo4bo15bo
59bo29bo29bo29bo29bo29bo26bo2bo26bo2bo26bo2bo$36b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o32bo25b2o28b2o28b2o28b2o28b2o2b2o24b2o
2b2o24b2o2b2o24b2o2b2o24b2o2b2o$36bo29bo29bo29bo29bo29bo10bo18bo29bo
29bo29bo29bo59bo29bo29bo29bo29bo4bo18b2o4bo4bo29bo29bo29bo$38bo29bo28b
o29bo29bo29bo9bobo17bo2b3o24bo2b3o24bo2b3o24bo2b3o10bo13bo2b3o25bo28bo
2b3o24bo2b3o24bo2b3o24bo2b3o7bo16bo2bo20b2o4bo2bo29bo29bo29bo$37b2o28b
2o27b2o28b2o27bobo27bobo9b2o16bobo27bobo27bobo27bobo14b2o11bobo57bobo
27bobo27bobo27bobo12bobo12bobo2b2o18bo4bobo2b2o28b2o28b2o28b2o$15bo
106bo9bo22b2o28b2o28b2o28b2o28b2o28b2o15bobo10b2o31bo26b2o28b2o28b2o
28b2o13b2o13b2o28b2o$14bo108b2o5b2o62b3o$14b3o105b2o7b2o61bo302b3o$11b
o183bo172bo128bo44bo$b2o6bobo50bo67bo367bo43b2o$2b2o6b2o3b3o44b2o11bo
53b2o410bobo$bo13bo45bobo10b2o45b3o5bobo$16bo48b3o6bobo44bo$65bo56bo
152b3o204bo$66bo208bo206b2o16b2o$3o273bo204bobo15b2o$2bo498bo$bo66bo
416bo$67b2o416b2o$67bobo414bobo$15b2o$14b2o$16bo3$20b2o$19b2o$21bo!
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Re: Synthesising Oscillators

Postby A for awesome » August 12th, 2017, 11:53 am

Goldtiger997 wrote:Got much closer after noticing a converter I hadn't noticed before in Extrementhusiast's collection. Now only one step is missing:

rle

In all honesty, I'm not sure if that step is physically possible. Can anyone figure out a way to back these up further?
x = 35, y = 15, rule = B3/S23
27bo$6b3o18bo$7bo17bobo4b2o$7bo22b2o$4bob3o17bob2o$27b2o$4bo5b2o16bo4b
2o$2obobobobobo11b2obobobobobo$ob2obob2o14bob2obob2o$4bo22bo$b2o21b2o$
bo22bo$2bo2b3o17bo2b3o$obo20bobo$2o21b2o!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Synthesising Oscillators

Postby gmc_nxtman » August 12th, 2017, 12:33 pm

Alternate 6-glider unix synthesis that doesn't seem useful either:

x = 41, y = 41, rule = B3/S23
28bo$26b2o11bo$27b2o9bo$38b3o7$15bo$16bo$14b3o2$13bo$13b2o$12bobo10$bo
$b2o$obo10$2b2o$bobo$3bo!


EDIT: Unix + Glider in 6 gliders:

x = 22, y = 27, rule = B3/S23
o$b2o$2o13$5b2o$5bobo$b2o2bo$2b2o$bo$11bo$10b2o$10bobo$4b2o$5b2o12b2o$
4bo14bobo$19bo!
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Re: Synthesising Oscillators

Postby Extrementhusiast » August 12th, 2017, 10:17 pm

I actually did that problem step very differently:
x = 186, y = 39, rule = B3/S23
25bo$23bobo$24b2o2$26bo$26bobo$26b2o78bo$37bo66bobo$22bo13bo68b2o11bob
o$23bo12b3o79b2o$21b3o95bo$143bo$144bo2bo$34bo107b3obo$34bobo109b3o$
34b2o$142b2o19bo$18b2obob2o32b2obob2obo37b2obob2obo24b2obobo2bo14b2obo
bo2bo$18bob3o2bo31bob2obob2o37bob2obob2o24bob2ob4o14bob2ob4o$obobo19bo
bo34bo45bo32bo22bo17bobobo$19b2o4bo32b2o44b2o31b2o2b2o17b2o2b2o$19bo
38bo45bo32bo4bo17bo4bo$20bo7bo30bo45bo2b3o7bo19bo2bo19bo2bo$18bobo6bob
o27bobo43bobo12bobo15bobo2b2o16bobo2b2o$18b2o7bobo27b2o14b2o28b2o13b2o
16b2o21b2o$28bo43bobo2b2o$74bob2o37b3o$78bo36bo$34b3o79bo$34bo46b2o$
35bo45bobo$81bo$100bo$100b2o16b2o$99bobo15b2o$119bo$103bo$103b2o$102bo
bo!
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Re: Synthesising Oscillators

Postby Goldtiger997 » August 12th, 2017, 11:24 pm

Goldtiger997 wrote:Got much closer after noticing a converter I hadn't noticed before in Extrementhusiast's collection. Now only one step is missing:,,,

A for awesome wrote:In all honesty, I'm not sure if that step is physically possible. Can anyone figure out a way to back these up further?

Extrementhusiast wrote:I actually did that problem step very differently:...


Great work, I hadn't thought of doing it that way. Here is the complete synthesis in 58 gliders:

x = 515, y = 274, rule = B3/S23
141bo$139bobo228bo$140b2o227bo$369b3o$134bo$132bobo$133b2o3$131bo$132b
2o$131b2o212bo$344bo$344b3o3$159bo$160bo$158b3o2$347bo$346bo$146bobo
11bo185b3o$147b2o12bo$147bo4bo6b3o$153bo10bo$151b3o11b2o183bo$164b2o
182b2o$148bo200b2o$149bo20bo$147b3o21bo$169b3o173bo$343b2o$344b2o12$
344bo$343bo$343b3o2$200bo$201bo$199b3o2$311bo$310bo$310b3o2$321bo$198b
o122bobo$196bobo122b2o$197b2o2$319bo$318bo$318b3o4$318bo$317bo$209bobo
105b3o$210b2o95bo$210bo94b2o$306b2o32$222bo55bo$223b2o18bo32b2o$222b2o
20b2o31b2o$243b2o3$255bo$229bo23b2o$227bobo24b2o$228b2o2$247bo$248bo
20bo$237bo8b3o13bo4b2o$238b2o2bo7bo9b2o6b2o$237b2o4b2o5b2o9b2o$242b2o
5bobo4$257b3o4bo$259bo3b2o$258bo4bobo$245b3o$247bo$246bo$254b3o$254bo$
255bo4$243bo$243b2o$242bobo9$233b3o$235bo$234bo5$276bo$275b2o$267b3o5b
obo$267bo$268bo2$226bo$226b2o$225bobo75bo$302b2o$302bobo5$213b3o$215bo
$214bo5$210b2o$211b2o$210bo5$314b3o$314bo$315bo3b2o$319bobo$319bo3$
201b3o127bo$203bo126b2o$202bo127bobo3$334b3o$334bo$335bo12$341b2o$341b
obo$341bo5$151b3o10b2o178bo$153bo11b2o176b2o$152bo11bo178bobo2$167b2o$
168b2o$153b2o12bo$152bobo$154bo10$213bo$211bobo238bobo$bo152bo57b2o
239b2o19bo$2b2o151b2o296bo18b2o$b2o151b2o21bobo34bo193bo64b2o$177b2o
35bobo192b2o34bobo$178bo35b2o93bo98b2o36b2o$13bo211bo81bobo136bo$11b2o
197bo13bo83b2o11bobo90bo$12b2o197bo12b3o94b2o74bo14b2o$209b3o110bo75bo
10bo3b2o30bo$363bo32b3o11b2o31bobo$5bo358bo2bo33bo7b2o33b2o3bo$6bo215b
o139b3obo35b2o43b2o$4b3o13bo201bobo141b3o32b2o45b2o60bo$o7bo9b2o202b2o
235b2o46b4o$b2o5b2o9b2o341b2o33bo12bo47bo2bo46bo2bo$2o5bobo46b2obob2o
43b2obob2o43b2obob2o43b2obob2o43b2obob2obo41b2obob2obo41b2obobo2bo33b
2o6b2obobo2bo44bobo2bo44bobo2bo$47bo8bob3obo43bob3obo43bob3obo43bob3o
2bo42bob2obob2o41bob2obob2o41bob2ob4o32b2o7bob2ob4o43b2ob4o43b2ob4o$
48bo163bobo6bo38bo49bo49bo49bo46bo2bo46bo2bo$46b3o8b2o48b2o48b2o48b2o
4bo7bobo33b2o48b2o48b2o2b2o44b2o2b2o44b2o2b2o44b2o2b2o$15b3o4bo34b2o
48bo49bo12b2o35bo13b2o34bo49bo49bo4bo38b2o4bo4bo49bo49bo$17bo3b2o85bo
49bo12b2o35bo49bo49bo2b3o7bo36bo2bo40b2o4bo2bo49bo49bo$16bo4bobo37b2o
44b2o47bobo11bo3b2o30bobo47bobo47bobo12bobo32bobo2b2o38bo4bobo2b2o48b
2o48b2o$3b3o56b2obobo35bo9bo42b2o15b2o31b2o48b2o14b2o32b2o13b2o33b2o
48b2o$5bo49bobo3bo3b2o37b2o5b2o62bo42b2o51bobo2b2o$4bo51b2o8bo36b2o7b
2o104bobo52bob2o41b3o$12b3o41bo161bo58bo40bo84bo$12bo98bo110b3o94bo83b
2o$13bo96b2o46b2o62bo57b2o120bobo$102b3o5bobo44bobo63bo56bobo$102bo56b
o120bo$103bo199bo$52b2o249b2o16b2o$51bobo248bobo15b2o$53bo268bo$155bo
150bo$155b2o149b2o$154bobo148bobo!


Are there any converters that will convert the above Elkies' P5 variant into either of these?:
x = 28, y = 10, rule = B3/S23
3bo19bo$4o16b4o$bo2bo16bo2bo$2bobo2bo14bobo2bo$b2ob4o13b2ob4o$o2bo16bo
2bo$2o2b2o14b2o3bo$5bo18b2o$5bobo$6b2o!
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Re: Synthesising Oscillators

Postby gmc_nxtman » August 12th, 2017, 11:29 pm

57 gliders:

x = 746, y = 57, rule = B3/S23
39bobo$40b2o$40bo45bo$85bo$85b3o7$392bo$390bobo308bobo$391b2o309b2o19b
o$702bo18b2o$393bo249bo78b2o$393bobo248b2o48bobo$393b2o121bo126b2o50b
2o$404bo109bobo178bo$389bo13bo111b2o11bobo118bo$390bo12b3o122b2o102bo
14b2o$388b3o138bo103bo10bo3b2o44bo$8bo575bo46b3o11b2o45bobo$7bo577bo2b
o47bo7b2o47b2o3bo$7b3o391bo181b3obo49b2o57b2o$401bobo183b3o46b2o59b2o
42bo$bo4bo58bo335b2o273b2o30b2o28b4o$b2o4bo55bobo485b2o30b2o28bo18bo
12bo29bo2bo28bo2bo28bo2bo$obo2b3o28bob2o24b2o2bob2o25b2obob2o25b2obob
2o25b2obob2o25b2obob2o25b2obob2o14bobo8b2obob2o25b2obob2o25b2obob2o25b
2obob2o25b2obob2o25b2obob2obo23b2obob2obo23b2obob2obo23b2obob2obo23b2o
bobo2bo23b2obobo2bo23b2obobo2bo15b2o6b2obobo2bo26bobo2bo26bobo2bo26bob
o2bo$36b2o2bo20b2o5b2o2bo24bob3o2bo24bob3o2bo24bob3o2bo24bob3o2bo24bob
3o2bo14b2o8bob3o2bo24bob3o2bo24bob3o2bo24bob3o2bo24bob3o2bo24bob2obob
2o23bob2obob2o23bob2obob2o23bob2obob2o23bob2ob4o23bob2ob4o23bob2ob4o
14b2o7bob2ob4o25b2ob4o25b2ob4o25b2ob4o$4bo34bobo18bobo8bobo29bobo29bob
o29bobo29bobo29bobo13bo15bobo29bobo29bobo29bobo29bobo27bo31bo31bo31bo
31bo31bo31bo31bo28bo2bo28bo2bo28bo2bo$3b2o35bo21bo9bo25b2o4bo25b2o4bo
25b2o4bo25b2o4bo25b2o4bo25b2o4bo25b2o4bo25b2o4bo6bo18b2o4bo25b2o4bo25b
2o30b2o30b2o30b2o30b2o2b2o26b2o2b2o26b2o2b2o26b2o2b2o26b2o2b2o26b2o2b
2o26b2o2b2o$3bobo92b2o30b2o30bo31bo31bo31bo31bo31bo11bo19bo31bo31bo31b
o31bo31bo31bo4bo26bo4bo26bo4bo20b2o4bo4bo31bo31bo31bo$164bo31bo30bo31b
o31bo31bo10b3o18bo7bo23bo7bo23bo31bo31bo2b3o26bo2b3o7bo18bo2bo28bo2bo
28bo2bo22b2o4bo2bo31bo31bo31bo$65bobo95b2o30b2o29b2o30b2o29bobo29bobo
29bobo6bobo20bobo6bobo20bobo29bobo29bobo29bobo12bobo14bobo2b2o25bobo2b
2o25bobo2b2o20bo4bobo2b2o30b2o30b2o30b2o$66b2o221b2o30b2o8b3o19b2o7bob
o20b2o7bobo20b2o30b2o14b2o14b2o30b2o13b2o15b2o30b2o30b2o30b2o$66bo204b
o59bo31bo31bo68bobo2b2o$271bobo58bo133bob2o55b3o$65b3o73bo125bo3b2o
197bo54bo112bo$67bo71b2o49bo75bo134b3o122bo111b2o$66bo66bobo4b2o48b2o
11bo62b3o132bo71b2o162bobo$133b2o54bobo10b2o198bo70bobo$134bo58b3o6bob
o62bo205bo$193bo72b2o242bo$132b2o60bo71bobo241b2o16b2o$131b2o376bobo
15b2o$133bo395bo$196bo316bo$195b2o64b2o250b2o$195bobo63bobo248bobo$
261bo$145b2o$144b2o$146bo$81b2o$81bobo$81bo!
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Re: Synthesising Oscillators

Postby Goldtiger997 » August 13th, 2017, 2:38 am

Can this method used by Extrementhusiast here be used to solve another of the Elkies' P5 variants?:

x = 43, y = 54, rule = B3/S23
5$16bo$17bo$15b3o2$12bo$13b2o$12b2o7$15bo9b2o$16bo8bo2b2o$14b3o9b2o2bo
$22bo5bobo2bo$12b2o8bo5bob4o$11bobo8bo6bo$13bo16b2o$26b2o3bo$26bobo2bo
bo$27bo4b2o6$14b3o$16bo$15bo2$25bo7b2o$24b2o7bobo$24bobo6bo3$15b3o$17b
o$16bo2$26bo$25b2o$25bobo!
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Re: Synthesising Oscillators

Postby mniemiec » August 13th, 2017, 3:42 am

Goldtiger997 wrote:Got much closer after noticing a converter I hadn't noticed before in Extrementhusiast's collection. Now only one step is missing: ...

Extrementhusiast wrote:I actually did that problem step very differently: ...

Goldtiger997 wrote:Great work, I hadn't thought of doing it that way. Here is the complete synthesis in 58 gliders: ...

gmc_nxtman wrote:57 gliders: ...

Good work guys! The block can be turned into a snake directly, saving one glider, for 56:
x = 92, y = 51, rule = B3/S23
44bo$45boo$44boo6$3booboboo13booboboo33booboboo13booboboo$3bob3obbo12b
ob3obbo32bob3obbo12bob3obbo$9bobo17bobo37bobo17bobo$4boo4bo13boo4bo33b
oo4bo13boo4bo$4boo18boo38boo18bo$85bo$51bo32boo$49bobo$50boo$$22boo38b
oo$boo18bobbo36bobbo$obo19boo38boo$bbo$4boo54boo$4bobo52bobo$4bo56bo4$
47boo$48boo$47bo18$74b3o$74bo$75bo!

Goldtiger997 wrote:Are there any converters that will convert the above Elkies' P5 variant into either of these?

Unfortunately, Extrementhusiast's snake-to-eater converter doesn't work as shown, as the hook gets in the way. He had previously posted an 82-glider synthesis of the version with the pre-block on 2015-08-02, although if it can be converted from a snake or carrier, this new synthesis would reduce that.
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Re: Synthesising Oscillators

Postby gmc_nxtman » August 13th, 2017, 2:04 pm

Can anyone figure out how to make this work, preferably with an edgier 3-glider synthesis of those two blocks?

x = 100, y = 42, rule = B3/S23
44bo$45bo$43b3o2$86bo11bo$39bo31bo12bobo10bo$40bo31bo12b2o10b3o$38b3o
29b3o4$52b2o30b2o$48b3o2bo26b3o2bo$48b3o29b3o$14b3o16b3o13bo31bo$16bo
16bo$15bo18bo$48b2o30b2o$15b2o15b2o14b2o30b2o$15bobo13bobo18b2o30b2o$
3b3o9bo17bo18b2o30b2o$3bo$4bo$b2o$obo$2bo12bo17bo18b2o30b2o$15bobo13bo
bo18b2o30b2o$15b2o15b2o14b2o30b2o$2b2o44b2o30b2o$b2o12bo18bo$3bo12bo
16bo$14b3o16b3o13bo31bo$48b3o29b3o$48b3o2bo26b3o2bo$52b2o30b2o4$38b3o
29b3o$40bo31bo12b2o10b3o$39bo31bo12bobo10bo$86bo11bo!
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Re: Synthesising Oscillators

Postby mniemiec » August 13th, 2017, 8:28 pm

gmc_nxtman wrote:Can anyone figure out how to make this work, preferably with an edgier 3-glider synthesis of those two blocks? ...

Here is a 27 glider solution with a bug: 2 gliders pass through each other, although I am pretty sure that should be fairly easy to remedy. There are probably also many suitable 3-glider bullet syntheses; unfortunately, the most common predecessor (parenthesis) is unsuitable; T tetrominos work, but they appear to be much more rare. Using half a pulsar predecessor is probably overkill.
x = 207, y = 39, rule = B3/S23
80bo38bo$81bo36bo$79b3o36b3o4$88bo$89boo28bo$88boo27boo$83bo15bo18boo$
bbo81bo12boo$obo79b3o13boo$boo133boo4boo22boo4boo22boo4boo$91bo19bo24b
o6bo22bo6bo22bo6bo$4bo19boo18boo18boo23boo13boo4bo18boobboobobobbobob
oobboo8boobboobobobboboboobboo12boobobobboboboo$3bo20boo18boo18boo19b
3obboo12boo4b3obboo12boobbobbobobbobobbobboo8boobbobbobobbobobbobboo
12bobbobobbobobbo$3b3o79bo28boo19bobbobbobbo10b3o7bobbobbobbo7b3o10bo
bbobbobbo$36bo49bo29bo19boo4boo13bo8boo4boo8bo13boo4boo$bbo19boo10bobo
5boo12boo4boo32boo4boo52bo26bo$boo19boo11boo5boo12boo4boo32boo4boo3b3o
$bobo28boo45boo28bo$31bobo46boo26bo$33bo45bo4boo28boo$85boo26boo$84bo
30bo$93boo10boo$92boo12boo$94bo10bo$85boo26boo$86boo24boo$85bo28bo6$
75b3o44b3o$77bo44bo$76bo46bo!

EDIT:
gmc_nxtman wrote:EDIT: Unix + Glider in 6 gliders: ...

This is edgy, unlike any of the other unix syntheses I know. 2 gliders to edgy block plus 5 glider block to unix = 7 glider edgy unix, so this costs the same. Of course, this is edgy along both block surfaces, so it would be useful when creating something where a unix is sandwiched between two other difficult-to-add objects.
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Re: Synthesising Oscillators

Postby gmc_nxtman » August 14th, 2017, 10:35 am

mniemiec wrote:
gmc_nxtman wrote:EDIT: Unix + Glider in 6 gliders: ...

This is edgy, unlike any of the other unix syntheses I know. 2 gliders to edgy block plus 5 glider block to unix = 7 glider edgy unix, so this costs the same. Of course, this is edgy along both block surfaces, so it would be useful when creating something where a unix is sandwiched between two other difficult-to-add objects.


It turns out that it's possible to synthesise it cleanly with just 6 gliders:

x = 45, y = 26, rule = LifeHistory
.BA$ABAB$.2A2B11.2B$2.4B9.4B$3.4B8.5B$4.4B5.8B$5.4B.BA9B$6.3BABA8B$7.
3B2A8B.BA$7.13B2AB$8.13B2A$10.12B$9.13B$9.10BA4B$8.9BABA6B$7.5B2.4B2A
6B$6.4B5.12B$5.4B6.13B12.B2AB$4.2A2B8.13B10.B4A$3.ABAB8.2A5B.6B10.A2B
ABA$4.BA8.ABA6B.5B8.BA.A.B2A$15.BA7B2.2B8.BABA3.B$17.7B12.2AB$19.6B
11.3AB$20.5B11.BABAB$21.3B14.2A!


The use of a prepond in the first version released an extra clean glider, but I didn't look to see if it could be replaced by a single glider. Also, the base reaction can be simplified, allowing a more edgy, three-quadrant synthesis.

Also, is this useful? Four gliders add stabilizing bookends to a twin bees shuttle:

x = 39, y = 47, rule = B3/S23
37bo$36bo$36b3o2$15bo$16bo$14b3o12$10b2o$2o7bobo$2o7bo$9b3o4$9b3o$9bo$
9bobo$10b2o12$14b3o$16bo$15bo2$36b3o$36bo$37bo!
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