## Synthesising Oscillators

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

### Re: Synthesising Oscillators

P3 billiard table in 11 gliders:

x = 27, y = 34, rule = B3/S2324bo$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/S2325bo$23b2o$24b2o4$2bo$obo$b2o5$46b2o$47bo$16bo30bob2o$14b2o28b2obo2bo$15b2o26bo2bob2o$43b2obo$46bo$46b2o$17bo$16b2o$16bobo2$12bo$11b2o$7b2o2bobo$8b2o$7bo6$17b3o$17bo$18bo!

gmc_nxtman

Posts: 1094
Joined: May 26th, 2015, 7:20 pm

### Re: Synthesising Oscillators

Bullet51 wrote:Eater 2 variant from dr:
x = 17, y = 11, rule = B3/S2310bo$8b3o4bo$3b2o2bo6bo$3bo3b2o5b3o$2obo$o2bobo$b2obobo$4bobo$4bo2b2o$3b2o4bob2o$9b2obo!

This reaction could also work:
x = 10, y = 11, rule = B3/S237b2o$6b3o$2bo3b2o$3o4bo$2bo$4b2o$3bobo$2bo2bob2o$3b2obo2bo$6bobo$6b2o!
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### Re: Synthesising Oscillators

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.
mniemiec

Posts: 878
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

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

x = 379, y = 29, rule = B3/S23224bo$223bo$80bo142b3o$81bo3bo30b2o30b2o$79b3ob2o30bo2bo24bo3bo2bo144bo$84b2o29bo2bo22bobo3bo2bo142b2o$116b2o24b2o4b2o144b2o37bo4bobo4bo$331bobo2bobobobo2bobo$332b2o3b2ob2o3b2o$223bo66bo$17bo161bo31bo10bo20bo31bo14bobo14bo31bo$16bo29bo31bo11bobo17bo31bo31bo3bobo25bo3bobo9b3o13bo3bobo25bo3bobo13b2o10bo3bobo3bo21bo3bobo3bo22b2o5b2o$16b3o26bobo29bobo10b2o17bobo29bobo29bobo3bo25bobo3bo25bobo3bo3b2o20bobo3bo3b2o5b3o12bobo3bo3bobo19bobo3bo3bobo21bo7bo$11bo33bobo29bobo11bo17bobo29bobo29bobo29bobo13bo15bobo7bo21bobo7bo6bo14bobo7bobo19bobo7bobo18b2obo7bob2o$9bobo32b2obobo26b2obobo26b2obob2o25b2obob2o8bo16b2obob5o22b2obob5o6b2o14b2obob5obo20b2obob5obo7bo12b2obob5obob2o17b2obob5obob2o17b2obob5obob2o$10b2ob2o33b2o30b2o5bobo22bo2bo28bo2bo7bobo18bo5bo25bo5bo5bobo17bo5bo25bo5bo25bo5bo25bo5bo25bo2bo2bo$13bobo71b2o24b2o30b2o8b2o20b5o27b5o27b5o27b5o27b5o27b5o27b5o$13bo74bo202b2o$152b3o24bo31bo31bo31bo14b2o15bo31bo31bo$b2o83b2o64bo25bobo29bobo29bobo29bobo15bo13bobo29bobo29bobo$obo82b2o66bo25bo31bo31bo31bo31bo31bo31bo$2bo84bo134b2o$221b2o$223bo$116b2o24b2o4b2o$84b2o29bo2bo22bobo3bo2bo152b2o$79b3ob2o30bo2bo24bo3bo2bo152bobo$81bo3bo30b2o30b2o153bo$80bo!

gmc_nxtman

Posts: 1094
Joined: May 26th, 2015, 7:20 pm

### Re: Synthesising Oscillators

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

x = 379, y = 29, rule = B3/S23224bo$223bo$80bo142b3o$81bo3bo30b2o30b2o$79b3ob2o30bo2bo24bo3bo2bo144bo$84b2o29bo2bo22bobo3bo2bo142b2o$116b2o24b2o4b2o144b2o37bo4bobo4bo$331bobo2bobobobo2bobo$332b2o3b2ob2o3b2o$223bo66bo$17bo161bo31bo10bo20bo31bo14bobo14bo31bo$16bo29bo31bo11bobo17bo31bo31bo3bobo25bo3bobo9b3o13bo3bobo25bo3bobo13b2o10bo3bobo3bo21bo3bobo3bo22b2o5b2o$16b3o26bobo29bobo10b2o17bobo29bobo29bobo3bo25bobo3bo25bobo3bo3b2o20bobo3bo3b2o5b3o12bobo3bo3bobo19bobo3bo3bobo21bo7bo$11bo33bobo29bobo11bo17bobo29bobo29bobo29bobo13bo15bobo7bo21bobo7bo6bo14bobo7bobo19bobo7bobo18b2obo7bob2o$9bobo32b2obobo26b2obobo26b2obob2o25b2obob2o8bo16b2obob5o22b2obob5o6b2o14b2obob5obo20b2obob5obo7bo12b2obob5obob2o17b2obob5obob2o17b2obob5obob2o$10b2ob2o33b2o30b2o5bobo22bo2bo28bo2bo7bobo18bo5bo25bo5bo5bobo17bo5bo25bo5bo25bo5bo25bo5bo25bo2bo2bo$13bobo71b2o24b2o30b2o8b2o20b5o27b5o27b5o27b5o27b5o27b5o27b5o$13bo74bo202b2o$152b3o24bo31bo31bo31bo14b2o15bo31bo31bo$b2o83b2o64bo25bobo29bobo29bobo29bobo15bo13bobo29bobo29bobo$obo82b2o66bo25bo31bo31bo31bo31bo31bo31bo$2bo84bo134b2o$221b2o$223bo$116b2o24b2o4b2o$84b2o29bo2bo22bobo3bo2bo152b2o$79b3ob2o30bo2bo24bo3bo2bo152bobo$81bo3bo30b2o30b2o153bo$80bo!

And from 28 to 27:
x = 379, y = 32, rule = B3/S23207bo$205bobo$206b2o3$80bo$81bo3bo30b2o30b2o$79b3ob2o30bo2bo24bo3bo2bo144bo$84b2o29bo2bo22bobo3bo2bo142b2o$116b2o24b2o4b2o144b2o37bo4bobo4bo$331bobo2bobobobo2bobo$332b2o3b2ob2o3b2o$225bo64bo$17bo161bo31bo14bo16bo31bo14bobo14bo31bo$16bo29bo31bo11bobo17bo31bo31bo3bobo25bo3bobo11b3o11bo3bobo25bo3bobo13b2o10bo3bobo3bo21bo3bobo3bo22b2o5b2o$16b3o26bobo29bobo10b2o17bobo29bobo29bobo3bo25bobo3bo25bobo3bo3b2o20bobo3bo3b2o5b3o12bobo3bo3bobo19bobo3bo3bobo21bo7bo$11bo33bobo29bobo11bo17bobo29bobo29bobo29bobo29bobo7bo21bobo7bo6bo14bobo7bobo19bobo7bobo18b2obo7bob2o$9bobo32b2obobo26b2obobo26b2obob2o25b2obob2o8bo16b2obob5o22b2obob5o9b3o10b2obob5obo20b2obob5obo7bo12b2obob5obob2o17b2obob5obob2o17b2obob5obob2o$10b2ob2o33b2o30b2o5bobo22bo2bo28bo2bo7bobo18bo5bo25bo5bo10bo14bo5bo25bo5bo25bo5bo25bo5bo25bo2bo2bo$13bobo71b2o24b2o30b2o8b2o20b5o27b5o10bo16b5o27b5o27b5o27b5o27b5o$13bo74bo202b2o$152b3o24bo31bo31bo31bo14b2o15bo31bo31bo$b2o83b2o64bo25bobo29bobo29bobo29bobo15bo13bobo29bobo29bobo$obo82b2o66bo25bo31bo31bo31bo31bo31bo31bo$2bo84bo3$116b2o24b2o4b2o$84b2o29bo2bo22bobo3bo2bo152b2o$79b3ob2o30bo2bo24bo3bo2bo152bobo$81bo3bo30b2o30b2o153bo$80bo! Bob Shemyakin BobShemyakin Posts: 205 Joined: June 15th, 2014, 6:24 am ### Re: Synthesising Oscillators 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/S2341bo$42bo$40b3o$18bobo$18b2o25bo$19bo23bobo$44b2o$8bobo$9b2o$9bo30bobo$40b2o$2bo18b3o17bo$obo$b2o36b3o$41bo$3b3o34bo$5bo$4bo43b2o$47bobo$19bo29bo$18b2o$18bobo5$35b2o$36b2o$35bo3$2b2o$3b2o$2bo!

EDIT: Squid in 5 gliders:

x = 18, y = 12, rule = B3/S232b2o$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/S2342bo$40b2o$41b2o$33bo$34b2o$33b2o4$38bo6bo$39bo4bo$37b3o4b3o$33b3o$35bo$34bo5b3o$42bo$41bo2$32b3o$34bo$33bo$39b3o$39bo$40bo9$41bo$39b2o$40b2o$32bo$33b2o$32b2o4$37bo6bo$38bo4bo$36b3o4b3o$32b3o$34bo$33bo5b3o$41bo$40bo2$33b3o$35bo$34bo$40b3o$40bo$41bo6$40bo$40bobo$40b2o$45bo$44bo$29bo14b3o$bo28bo$2b2o24b3o$b2o$26b2o8bo$25bobo7bobo$27bo7b2o$6bo6bo$7bo4bo22b4o$5b3o4b3o19bo4bo9bo$b3o30bobo2bo8b2o$3bo31b4o9bobo$2bo5b3o$10bo24b2o$9bo25b2o2$3o$2bo$bo$7b3o$7bo$8bo6$40bo$40bobo$40b2o$45bo$44bo$29bo14b3o$o29bo$b2o25b3o$2o$26b2o8bo$25bobo7bobo$27bo7b2o$5bo6bo$6bo4bo23b4o$4b3o4b3o20bo4bo9bo$3o31bobo2bo8b2o$2bo32b4o9bobo$bo5b3o$9bo27b2o$8bo28b2o2$b3o$3bo$2bo$8b3o$8bo$9bo! gmc_nxtman Posts: 1094 Joined: May 26th, 2015, 7:20 pm ### Re: Synthesising Oscillators 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/S2392bo$92bobo$92boo$128bo5bo$91bo4bo32bo5boo$92boobo31b3o4boo3bo$91boobb3o41bobo$58bo80boo14boo18boo18booboo15booboo25booboo$51bo6bobo51boo18boo22bo19bobboo15bobobo15bobobo25bobobo$52bo5boo13boo18boo17bobo17bobo18bo19bo5bobo11bo5bo13bo5bo23bo6bo$50b3o20boo18boo18boo18boo18boo18boo4bo13boo18boo8bobo17boo4bo$46b3o174boo24boo$48bo24boo18boo18boo18boo18boo18boo18boo18boo9bo5bo12boo$47bo25bobobo15bobobo15bobobo15bobobo15bobobo15bobobo15bobobo15bobobo8bo3bobo10bobobo$76boo18boo18boo18boo18boo18boo18boo18boo7boo3boo14boo$59boo164bobo$59bobo$59bo3$152bo$152bobo$152boo9$190bobo$144bobo43boo$144boo45bo$145bo18bobbo16bobbo16bo19bo19bo$162b6o14b6o4boo8b3o17b3o7bo9b3o$123boo18boo16bo19bo9boo8bo19bo10bobo6bo$102bobo17bobbo16bobbo15bobboo15bobboo7bo7bobb3o14bobb3o5boo7bobb3oboo$103boo17bobbo12boobbobbo14boobobo14boobobo14boobobbo13boobobbobboo9boobobboboo$103bo19boo14boobboo16boboo16boboo18bo19bo5bobo11bo$138bo22bo19bo21boo18boo4bo13boo$102boo56boo18boo$101bobo$103bo$177boo$178boobbo$126b3o48bo3boo$128bo52bobo$127bo19$234bo$234bobo$230bo3boo$231boo19boo$230boo19bobo$102bobo43bo102bo$52bo50boo3bo37boo19bo19bo19bo19bo19bobboo$44bo8bo20bo19bo8bobboo16bo19bobboo15bobobo15bobobo15bobobo15bobobo15bobobo$42b3o6b3o18b3o17b3o12boo13b3o17b3o17b3oboo14b3oboo14b3oboo14b3oboo14b3oboo$41bo13boo14bo19bo29bo19bo19bo19bo19bo19bo19bo$41bobb3oboo6boo13bobb3oboboo9bobb3oboboo19bobb3oboboo9bobb3oboboo9bobb3oboboo9bobb3oboboo9bobb3oboboo9bobb3oboboo9bobb3oboboo$40boobobboboo5bo14boobobboboobo8boobobboboobo18boobobboboobbo7boobobboboobbo7boobobboboobbo7boobobboboobbo7boobobboboobbo7boobobboboobbo7boobobboboobbo$43bo29bo19bo29bo7boo10bo7boo10bo7boo10bo7boo10bo7boo10bo7boo10bo7boo$43boo14b3o11boo18boo8bo19boo18boo18boo18boo10bo7boo18boo18boo$59bo43boo3bo85bo16boo18boo18boo$60bo41bobo3bobo83b3o13bobo17bobo17bobo$108boo79b3o19bo19bo19bo$191bo$49boo139bobboo$48bobo142bobo$50bo142bo12$31bo20bobo$29bobo20boo$30boo21bo3$99bo130bo$97bobo77boo52bo$98boo73bo3bobo49b3o$171bobo3bo$80boo18boo36bo33boo58bobo$57bo22boo18boo34bobo29b3o61boo$42boo13bobo77boo31bo62bo$41bobo13boo84bo25bo$41bo36bo19bo19bo19bo3bo107bo$37bobboo9bobo23bobo17bobo17bobo17bobobb3o13boo18boo29boo18boo4b3o11bobo$34bobobo12boo21bobobbo14bobobbo14bobobbo14bobobbo14bobobbo14bobobbo24bobo3bo13bobo3bo4bo8bobo3bo$32b3oboo14bo19b3ob3o13b3ob3o13b3ob3o13b3ob3o13b3ob3o13b3ob3o23b3ob4o12b3ob4o6bo5b3ob4o$31bo39bo19bo19bo19bo19bo19bo29bo19bo19bo$31bobb3oboboo8b3o18bobb3o14bobb3o14bobb3o14bobb3o14bobb3o14bobb3o24bobb3oboo11bobb3oboo11bobb3oboo$30boobobboboobbo7bo19boobobbo13boobobbo13boobobbo13boobobbo13boobobbo13boobobbo23boobobbobobo9boobobbobobo9boobobbobobo$33bo7boo8bo21bo19bo19bo19bo19bo19bo29bo5bo13bo5bo13bo5bo$33boo38boo18boo18boo18boo18boo18boo28boo18boo18boo$41boo$40bobo$41bo5$188b3o$188bo$29bo159bo$29boo$23b3obbobo9boo$25bo13boo$24bo8bo7bo$33boo14b3o$32bobo14bo$50bo9$11bo$10bo$7bobb3o$8bo$6b3o$$10bo9bobo4bobo3bo13bobobbo14bobobbo24bobobbo14bobobbo14bobobbo14bobobbo14bobobbo14bobobbo24bobobbo14bobobbo14bobobbobb3ob4o12b3ob4o12b3ob4o22b3ob4o12b3ob4o12b3ob4o12b3ob4o12b3ob4o12b3ob4o22b3ob4o12b3ob4o12b3ob4obo19bo19bo29bo19bo19bo19bo19bo19bo29bo19bo19bobobb3oboo11bobb3oboo11bobb3oboo21bobb3oboo11bobb3oboo11bobb3oboo11bobb3oboo11bobb3oboo11bobb3oboo21bobb3oboo11bobb3oboo11bobb3oboooobobbobobo9boobobbobobo9boobobbobobo19boobobbobobo9boobobbobobo9boobobbobobo9boobobbobobo9boobobbobobo9boobobbobobo19boobobbobobo9boobobbobobo9boobobbobobo3bo5bo13bo5bo13bo5bo9bo13bo6bo12bo6bo12bo6bo12bo6bo12bo6bo12bo6bo22bo6bo12bo6bo12bo6bo3boo18boo18boo13bo14boo4bo13boo4bo13boo4bo13boo4bo13boo4bo13boo4bo20booboo4bo10booboo4bo10booboo4bo51boo5b3o18boo18boo18boo18boo18boo18boo18bobobo5boo8bobobo5boo9boobo5boo52boo59boo18boo18boo18boo25bo3bo15bo3bo19bo51bo3b3o36b3o16boo18boo18boo18boo30bobo8b3o6bobo17bobo55bo38bo111boo10bo7boo18boo56bo38bo61boo5boo11boo38bobboo91b3o63bobo5boo10bobo40bobo93bo64bo5bo13bo13b4o24bo92bo98b6o184boo4boob4o148bo35bobo4boo147bo28boo6bo147b3o17boo6boo143b3o22boo7bo136b3o4bo23bo3b3o138bo5bo26bo137bo34bo8135bo134bo50bo134b3o47bo8bo184b3o4boo133bo58boo13bo120bo13bobo38bo6bo30bo10bo28b3o13boo40bo4bo32bo8bo75bo9bo43b3o4b3o12boobboo10b3oboobboob3o25bo23boo23bo4boo7bobo66bobbo16bobbo15boobboo9boo3boobboo13bobobboo16b3o4bobobboo26bobbo5boo4bobobbo16bobbo16bobbo15bo4bo14bo4bo14bo4bo8bobo3bo4bo14bo4bo24bo4bo27bo3bo8b3ob4o16b4o16b4o16b4o16b4o16b4o16b4o16b4o13bobo10b4o26b3ob3o7bo162boo24boo18boo5boo4bobb3oboo14b3oboo14b3oboo14b3oboo14b3oboo14b3oboo14b3oboo14b3oboo14bo9b3oboo6boobboo3booboo10boo3booboo15booboo6boobboobobbobobo12bobbobobo12bobbobobo12bobbobobo12bobbobobo12bobbobobo12bobbobobo12bobbobobo22bobbobobo4boo9bobobo15bobobo15bobobo5bo7bo6bo12bo6bo12bo6bo12bo6bo12bo6bo12bo6bo12bo6bo12bo6bo22bo6bo6bo5bo6bo12bo6bo12bo6bo10booboo4bo10booboo4bo10booboo4bo10booboo4bo10booboo4bo10booboo4bo10booboo4bo10booboo4bo20booboo4bo13boo4bo13boo4bo13boo4bo10boobo5boo9boobo5boo9boobo5boo9boobo5boo9boobo5boo9boobo5boo9boobo5boo9boobo5boo19boobo5boo18boo18boo18boo14bo19bo19bo19bo19bo19bo19bo19bo29bo18boo18boo18boo3o12bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo19bo7bobo15bobobo15bobobo15bobobobbo13boo18boo18boo18boo18boo18boo18boo18boo20boo6boo18boo18boo18boobo175boo3179bo179boo178bobo6boo187bobo172b3o12bo174bo173bo! mniemiec Posts: 878 Joined: June 1st, 2013, 12:00 am ### Re: Synthesising Oscillators 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/S239bo7bobo8bobo8b2o8b2o12bo6bo43bo12bobo49bo12b2o25bo22b3o6bo31bo38bobo29bobo29bobo33b2o2bo2bo24b2o2bo2bo28bo2bo3o2b2o7bo18b2o3b2ob2o22b2o3b2ob2o27b2ob2o2bob2o7b2o26bo31bo31bobo4bo6bobo22b2obo28b2obo28b2obo38b2ob2o27b2ob2o27b2ob2o! 17.3192 (xs17_4aab94ozx321) in 14 gliders: x = 117, y = 24, rule = B3/S2310bo9bo9b3o4101bo102b2o101b2o3bobo4bo68bo32b2o5bo65b2o34bo3b3o66b2o20bo15bo15bo15bo15bo15bo13bo5b3o10b3o13b3o13b3o13b3o4bo8b3o13b3o7bo5bobo5bo11bo15bo15bo15bo6b2o7bo15bo8b2o6b2o6bo11b3o13b3o13b3o13b3o3bobo7b5o11b5o4b2o2b2ob2o18bo15bo15bo15bo16bo15bo8boboobo17b2o14b2o3bo10bobo13bobo13bo15bo10bo2bo37bo11b2o14b2o6b3o5b2o14b2o40b3o33bo77bo38b3o40bo39bo! 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/S2337bo3b2o10bo15bo3b2o7b2o28b3o2bo26b3o2bo6bobo31b2o11bo18b2o2b2o4bo28b3o29b3o3b2o8b2o21bo2bo13bo14bo2bo2bo10bobo15b3o2bobo29b2o13bo19bo3bo15bo32bo31b2o37b2o14bo9bobo5b2o30bobo25bo4bobo2b2o26bo15bo13b3o6bo2bobo55bo9bo43bo14bobob2o50boobo53bo! Last edited by gmc_nxtman on August 4th, 2017, 4:41 pm, edited 3 times in total. gmc_nxtman Posts: 1094 Joined: May 26th, 2015, 7:20 pm ### Re: Synthesising Oscillators 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/S23oobo16boobo16boobo16boobo16boobo16boobooboo16boboo16boboo16boboo16boboo16boboo$$b3o17b3o17b3o17b3o17b3o17b3o$bobbo16bobbo16bobbo16bobbo16bobbo16bobbo$bbobobb3o13boo17bobo18boo11bo5bobo18boo$3bo3bo35bo33bo5bo$8bo66b3o$bboo75boo$bobo34boobboo34boo$3bo35boobobo35bo$38bo3bo9$oobo16boobo16boobo16boobo16boobo16boobo16boobo16boobo16boobo16boobo$oboo16boboo16boboo16boboo16boboo16boboo16boboo16boboo16boboo16boboo$$b3o17b3o17b3o17b3o17b3o17b3o17b3o17b3o17b3o17b3obobbo16bobbo16bobbo16bobbo16bobbo16bobbo16bobbo16bobbo16bobbo16bobbo3boo17boo19boo17boo19boo17boo19boo17boo19boo17boo$$7boo39bobo$7bobo34boobboo$7bo36boo3bo115boo$3b3o45boo37bo30boo43boo$5bo45bobo29boo4boo31boo41bo3boo$4bo46bo22boo6boo5bobo29bo3boo41boo$75boo7bo39boo35boo7bo$74bo3b3o45bo35boo$78bo82bo$79bo$125boo$125bobo$125bo!
mniemiec

Posts: 878
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

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

x = 118, y = 31, rule = B3/S2326b2o$25b2o$17bo3b3o3bo$17b2o4bo$16bobo3bo$47b2o3bo26b2o3bo26b2o3bo$46bo2bobobo24bo2bobobo24bo2bobobo$46b2obob2o25b2obob2o25b2obob2o$48bobo29bobo29bobo$48bobo29bobo29bobo$49bo31bo31bo$32bo21bo31bo$31b2o20bobo29bobo$31bobo18bo2bo28bo2bo$53b2o30b2o2b2o$89bobo$89bo$3o18b2o$2bo18bobo$bo19bo6$4b2o$3bobo$5bo$28b2o$28bobo$28bo! EDIT: 17.3522 (xs17_j96o8a6z121) in ten gliders, very messy: x = 156, y = 75, rule = B3/S2315bo$16bo$14b3o29$86b2o30b2o30b2o$86bobo29bobo29bobo$55bo32bo31bo31bo$53b2o33b2o30b2o30b2o$54b2o30b2o2bo27b2o2bo27b2o2bo$85bo2bo2bo25bo2bo2bo25bo2bo2bo$85b2o2b2o26b2o2b2o26b2o2b2o$15bobo76b2o30b2o$16b2o76b2o30b2o$16bo$128b3o$128bo$129bo5$47bo$45b2o$46b2o$51b3o$37bo13bo$37bobob3o8bo$37b2o2bo$42bo5$19bo$19b2o$18bobo10$3o$2bo$bo!

EDIT2: 17.3639 (xs17_c8ad1e8z33) in eight gliders:

x = 48, y = 23, rule = B3/S2325bo$10bo12b2o$11bo12b2o$9b3o2$17bo$16bo$16b3o2$7bo$b2o5bo$2b2o2b3o35bo$bo40b3o$8bo32bo$7b2o32bob2o$7bobo32bobo$3o41bob2o$2bo40b2ob2o$bo2$25b2o$25bobo$25bo! EDIT3: 17.1247 (xs17_4aajkcz253) in eight gliders: x = 117, y = 31, rule = B3/S2317bo$17bobo$17b2o2$77bo$76bo$16bo59b3o$14b2o$15b2o25b2o30b2o$42b2o30b2o2$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/S2334bo$32b2o$5bo27b2o$3bobo15b2o14b2o$4b2o15b2o7bo6b2o$b2o28b2o19bo$obo10bo10bo5b2o8bo10bobo$2bo5b2o2b2o10bo15bo10bobo$9b2obobo9bo9bobo3bo7b2obob2o$8bo26b2o11bo2bobo$35bo14bo2bo$51b2o$34b2o$33bobo$35bo!

EDIT5: 17.1068 (xs17_ci6o8brzw1) in nine gliders:

x = 122, y = 29, rule = B3/S239bo$10bo10bo$8b3o8bobo$20b2o$92bo$93bo$8bo82b3o$9b2o52b2o30b2o$8b2o52bo2bo28bo2bo$63bobo29bobo$19bo44bo31bo$17bobo$18b2o6b3o24bo31bo31bo$26bo25bobo2bo26bobo2bo26bobo2bo$27bo23bo2b4o25bo2b4o25bo2b4o$51bobo29bobo29bobo$52b2o2b2o26b2o2b2o26b2o2b2o$56b2o30b2o30b2o4$5b2o$6b2o$bo3bo$b2o$obo$21b2o$20bobo$22bo! gmc_nxtman Posts: 1094 Joined: May 26th, 2015, 7:20 pm ### Re: Synthesising Oscillators I tried to get synthesis of pseudo-mold, but I couldn't complete this. x = 34, y = 23, rule = B3/S232bo24b2o$2bo24bobo$2bo$3o$3bo20b3o$o2bo20bo2b2o$b3o20bo$24bo4bo$25bo3bo2b2o$26b3o2bo$30bo$30bo$30bo$26b3o2bo$25bo3bo2b2o$24bo4bo$b3o20bo$o2bo20bo2b2o$3bo20b3o$3o$2bo$2bo24bobo$2bo24b2o! yootaa Posts: 35 Joined: May 26th, 2016, 1:08 am Location: Japan ### Re: Synthesising Oscillators yootaa wrote:I tried to get synthesis of pseudo-mold, but I couldn't complete this. x = 34, y = 23, rule = B3/S232bo24b2o$2bo24bobo$2bo$3o$3bo20b3o$o2bo20bo2b2o$b3o20bo$24bo4bo$25bo3bo2b2o$26b3o2bo$30bo$30bo$30bo$26b3o2bo$25bo3bo2b2o$24bo4bo$b3o20bo$o2bo20bo2b2o$3bo20b3o$3o$2bo$2bo24bobo$2bo24b2o! The middle part is easy; how do you make the sides? x = 28, y = 23, rule = B3/S2316bo$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.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1592
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: Synthesising Oscillators

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

x = 48, y = 23, rule = B3/S2325bo$10bo12b2o$11bo12b2o$9b3o2$17bo$16bo$16b3o2$7bo$b2o5bo$2b2o2b3o35bo$bo40b3o$8bo32bo$7b2o32bob2o$7bobo32bobo$3o41bob2o$2bo40b2ob2o$bo2$25b2o$25bobo$25bo! Reduced to 6: x = 18, y = 26, rule = B3/S239bo$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).
AbhpzTa

Posts: 373
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: Synthesising Oscillators

AbhpzTa wrote:Reduced to 6...

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

x = 105, y = 34, rule = B3/S235bo$5bobo$5b2o2$65bo$64bo$4bo59b3o$2b2o$3b2o25b2o30b2o$30b2o30b2o2$36bo31bo31bo$7b2o26bobo29bobo29bobo$6b2o28b2o30b2o30b2o$8bo29b2o30b2o30b2o$36b2o2bo27b2o2bo27b2o2bo$35bo3b2o26bo3b2o26bo3b2o$5bo30b3o29b3o29b3o$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/S2312bo$13bo$11b3o2$8bo$9bo$7b3o2$10bo$10bobo5bobo$10b2o6b2o$19bo3$15bo$14b2o$14bobo7$b2o$obo$2bo!

gmc_nxtman

Posts: 1094
Joined: May 26th, 2015, 7:20 pm

### Re: Synthesising Oscillators

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/S233boo13boo13boo13boo13boo13boo$bbobbo11bobbo11bobbo11bobbo11bobbo11bobbo$3bobobbo9bobobbo9bobobbo9bobobbo9bobobbo9bobobbo$bboob4o8boob4o8boob4o8boob4o8boob4o8boob4o$bobbo11bobbo11bobbo14bo4boo5bobbo11bobbo$obo3bo9boobboo9boobboo12bobobbo7bobobo10bobboboo$bo3boo14bo14bo13bobobo8bobobo10boo3bo$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/S2317bobo581bobo$17b2o482bo100b2o19bo$18bo482bobo98bo18b2o$501b2o44bo74b2o$12bo473bo18bo42b2o44bobo$11bo475b2o16bobo39b2o46b2o$11b3o472b2o17b2o88bo$7bobo305bo237bo$8b2o303bobo220bo14b2o$8bo305b2o126bo94bo10bo3b2o40bo$438bo2b2o92b3o11b2o41bobo$bo317bo116bobo2bobo96bo7b2o43b2o3bo$2bo315bo118b2o102b2o53b2o$3o315b3o146b2o28b2o41b2o55b2o40bo$368bo31bo29bo29bo5bobo21bo5bobo79b2o28b2o26b4o$39bo29bo29bo29bo29bo29bo29bo29bo5bo3bo19bo29bo29bo5b2o19bo3bo28bobo3b2o22bobo3b2o2b3o17bobo3bo23bobo3bo23bo16bo12bo27bo2bo26bo2bo26bo2bo$35b2obobo24b2obobo24b2obobo24b2obobo24b2obobo24b2obobo24b2obobo24b2obobo5b2obobo13b2obobob2o21b2obobob2o3b3o2bobo10b2obobobobobo48b2obobobobobo18b2obobobobobo2bo15b2obobobobo20b2obobobobo20b2obobo2bo13b2o6b2obobo2bo24bobo2bo24bobo2bo24bobo2bo$35bob2obo24bob2obo24bob2obo24bob2obo24bob2obo24bob2obo24bob2obo24bob2obo4b2o2b2o14bob2obob2o21bob2obob2o3bo4b2o11bob2obob2o21bo5bo23bob2obob2o21bob2obob2o6bo14bob2obob2o21bob2obob2o21bob2ob4o12b2o7bob2ob4o23b2ob4o23b2ob4o23b2ob4o$39bo29bo29bo29bo29bo29bo29bo29bo29bo29bo8bo4bo15bo59bo29bo29bo29bo29bo29bo26bo2bo26bo2bo26bo2bo$36b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o32bo25b2o28b2o28b2o28b2o28b2o2b2o24b2o2b2o24b2o2b2o24b2o2b2o24b2o2b2o$36bo29bo29bo29bo29bo29bo10bo18bo29bo29bo29bo29bo59bo29bo29bo29bo29bo4bo18b2o4bo4bo29bo29bo29bo$38bo29bo28bo29bo29bo29bo9bobo17bo2b3o24bo2b3o24bo2b3o24bo2b3o10bo13bo2b3o25bo28bo2b3o24bo2b3o24bo2b3o24bo2b3o7bo16bo2bo20b2o4bo2bo29bo29bo29bo$37b2o28b2o27b2o28b2o27bobo27bobo9b2o16bobo27bobo27bobo27bobo14b2o11bobo57bobo27bobo27bobo27bobo12bobo12bobo2b2o18bo4bobo2b2o28b2o28b2o28b2o$15bo106bo9bo22b2o28b2o28b2o28b2o28b2o28b2o15bobo10b2o31bo26b2o28b2o28b2o28b2o13b2o13b2o28b2o$14bo108b2o5b2o62b3o$14b3o105b2o7b2o61bo302b3o$11bo183bo172bo128bo44bo$b2o6bobo50bo67bo367bo43b2o$2b2o6b2o3b3o44b2o11bo53b2o410bobo$bo13bo45bobo10b2o45b3o5bobo$16bo48b3o6bobo44bo$65bo56bo152b3o204bo$66bo208bo206b2o16b2o$3o273bo204bobo15b2o$2bo498bo$bo66bo416bo$67b2o416b2o$67bobo414bobo$15b2o$14b2o$16bo3$20b2o$19b2o$21bo! Goldtiger997 Posts: 351 Joined: June 21st, 2016, 8:00 am Location: 11.329903°N 142.199305°E ### Re: Synthesising Oscillators 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/S2327bo$6b3o18bo$7bo17bobo4b2o$7bo22b2o$4bob3o17bob2o$27b2o$4bo5b2o16bo4b2o$2obobobobobo11b2obobobobobo$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 Aidan F. Pierce A for awesome Posts: 1555 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Synthesising Oscillators Alternate 6-glider unix synthesis that doesn't seem useful either: x = 41, y = 41, rule = B3/S2328bo$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/S23o$b2o$2o13$5b2o$5bobo$b2o2bo$2b2o$bo$11bo$10b2o$10bobo$4b2o$5b2o12b2o$4bo14bobo$19bo!

gmc_nxtman

Posts: 1094
Joined: May 26th, 2015, 7:20 pm

### Re: Synthesising Oscillators

I actually did that problem step very differently:
x = 186, y = 39, rule = B3/S2325bo$23bobo$24b2o2$26bo$26bobo$26b2o78bo$37bo66bobo$22bo13bo68b2o11bobo$23bo12b3o79b2o$21b3o95bo$143bo$144bo2bo$34bo107b3obo$34bobo109b3o$34b2o$142b2o19bo$18b2obob2o32b2obob2obo37b2obob2obo24b2obobo2bo14b2obobo2bo$18bob3o2bo31bob2obob2o37bob2obob2o24bob2ob4o14bob2ob4o$obobo19bobo34bo45bo32bo22bo17bobobo$19b2o4bo32b2o44b2o31b2o2b2o17b2o2b2o$19bo38bo45bo32bo4bo17bo4bo$20bo7bo30bo45bo2b3o7bo19bo2bo19bo2bo$18bobo6bobo27bobo43bobo12bobo15bobo2b2o16bobo2b2o$18b2o7bobo27b2o14b2o28b2o13b2o16b2o21b2o$28bo43bobo2b2o$74bob2o37b3o$78bo36bo$34b3o79bo$34bo46b2o$35bo45bobo$81bo$100bo$100b2o16b2o$99bobo15b2o$119bo$103bo$103b2o$102bobo! I Like My Heisenburps! (and others) Extrementhusiast Posts: 1669 Joined: June 16th, 2009, 11:24 pm Location: USA ### Re: Synthesising Oscillators 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/S23141bo$139bobo228bo$140b2o227bo$369b3o$134bo$132bobo$133b2o3$131bo$132b2o$131b2o212bo$344bo$344b3o3$159bo$160bo$158b3o2$347bo$346bo$146bobo11bo185b3o$147b2o12bo$147bo4bo6b3o$153bo10bo$151b3o11b2o183bo$164b2o182b2o$148bo200b2o$149bo20bo$147b3o21bo$169b3o173bo$343b2o$344b2o12$344bo$343bo$343b3o2$200bo$201bo$199b3o2$311bo$310bo$310b3o2$321bo$198bo122bobo$196bobo122b2o$197b2o2$319bo$318bo$318b3o4$318bo$317bo$209bobo105b3o$210b2o95bo$210bo94b2o$306b2o32$222bo55bo$223b2o18bo32b2o$222b2o20b2o31b2o$243b2o3$255bo$229bo23b2o$227bobo24b2o$228b2o2$247bo$248bo20bo$237bo8b3o13bo4b2o$238b2o2bo7bo9b2o6b2o$237b2o4b2o5b2o9b2o$242b2o5bobo4$257b3o4bo$259bo3b2o$258bo4bobo$245b3o$247bo$246bo$254b3o$254bo$255bo4$243bo$243b2o$242bobo9$233b3o$235bo$234bo5$276bo$275b2o$267b3o5bobo$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$341bobo$341bo5$151b3o10b2o178bo$153bo11b2o176b2o$152bo11bo178bobo2$167b2o$168b2o$153b2o12bo$152bobo$154bo10$213bo$211bobo238bobo$bo152bo57b2o239b2o19bo$2b2o151b2o296bo18b2o$b2o151b2o21bobo34bo193bo64b2o$177b2o35bobo192b2o34bobo$178bo35b2o93bo98b2o36b2o$13bo211bo81bobo136bo$11b2o197bo13bo83b2o11bobo90bo$12b2o197bo12b3o94b2o74bo14b2o$209b3o110bo75bo10bo3b2o30bo$363bo32b3o11b2o31bobo$5bo358bo2bo33bo7b2o33b2o3bo$6bo215bo139b3obo35b2o43b2o$4b3o13bo201bobo141b3o32b2o45b2o60bo$o7bo9b2o202b2o235b2o46b4o$b2o5b2o9b2o341b2o33bo12bo47bo2bo46bo2bo$2o5bobo46b2obob2o43b2obob2o43b2obob2o43b2obob2o43b2obob2obo41b2obob2obo41b2obobo2bo33b2o6b2obobo2bo44bobo2bo44bobo2bo$47bo8bob3obo43bob3obo43bob3obo43bob3o2bo42bob2obob2o41bob2obob2o41bob2ob4o32b2o7bob2ob4o43b2ob4o43b2ob4o$48bo163bobo6bo38bo49bo49bo49bo46bo2bo46bo2bo$46b3o8b2o48b2o48b2o48b2o4bo7bobo33b2o48b2o48b2o2b2o44b2o2b2o44b2o2b2o44b2o2b2o$15b3o4bo34b2o48bo49bo12b2o35bo13b2o34bo49bo49bo4bo38b2o4bo4bo49bo49bo$17bo3b2o85bo49bo12b2o35bo49bo49bo2b3o7bo36bo2bo40b2o4bo2bo49bo49bo$16bo4bobo37b2o44b2o47bobo11bo3b2o30bobo47bobo47bobo12bobo32bobo2b2o38bo4bobo2b2o48b2o48b2o$3b3o56b2obobo35bo9bo42b2o15b2o31b2o48b2o14b2o32b2o13b2o33b2o48b2o$5bo49bobo3bo3b2o37b2o5b2o62bo42b2o51bobo2b2o$4bo51b2o8bo36b2o7b2o104bobo52bob2o41b3o$12b3o41bo161bo58bo40bo84bo$12bo98bo110b3o94bo83b2o$13bo96b2o46b2o62bo57b2o120bobo$102b3o5bobo44bobo63bo56bobo$102bo56bo120bo$103bo199bo$52b2o249b2o16b2o$51bobo248bobo15b2o$53bo268bo$155bo150bo$155b2o149b2o$154bobo148bobo! Are there any converters that will convert the above Elkies' P5 variant into either of these?: x = 28, y = 10, rule = B3/S233bo19bo$4o16b4o$bo2bo16bo2bo$2bobo2bo14bobo2bo$b2ob4o13b2ob4o$o2bo16bo2bo$2o2b2o14b2o3bo$5bo18b2o$5bobo$6b2o!

Goldtiger997

Posts: 351
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: Synthesising Oscillators

57 gliders:

x = 746, y = 57, rule = B3/S2339bobo$40b2o$40bo45bo$85bo$85b3o7$392bo$390bobo308bobo$391b2o309b2o19bo$702bo18b2o$393bo249bo78b2o$393bobo248b2o48bobo$393b2o121bo126b2o50b2o$404bo109bobo178bo$389bo13bo111b2o11bobo118bo$390bo12b3o122b2o102bo14b2o$388b3o138bo103bo10bo3b2o44bo$8bo575bo46b3o11b2o45bobo$7bo577bo2bo47bo7b2o47b2o3bo$7b3o391bo181b3obo49b2o57b2o$401bobo183b3o46b2o59b2o42bo$bo4bo58bo335b2o273b2o30b2o28b4o$b2o4bo55bobo485b2o30b2o28bo18bo12bo29bo2bo28bo2bo28bo2bo$obo2b3o28bob2o24b2o2bob2o25b2obob2o25b2obob2o25b2obob2o25b2obob2o25b2obob2o14bobo8b2obob2o25b2obob2o25b2obob2o25b2obob2o25b2obob2o25b2obob2obo23b2obob2obo23b2obob2obo23b2obob2obo23b2obobo2bo23b2obobo2bo23b2obobo2bo15b2o6b2obobo2bo26bobo2bo26bobo2bo26bobo2bo$36b2o2bo20b2o5b2o2bo24bob3o2bo24bob3o2bo24bob3o2bo24bob3o2bo24bob3o2bo14b2o8bob3o2bo24bob3o2bo24bob3o2bo24bob3o2bo24bob3o2bo24bob2obob2o23bob2obob2o23bob2obob2o23bob2obob2o23bob2ob4o23bob2ob4o23bob2ob4o14b2o7bob2ob4o25b2ob4o25b2ob4o25b2ob4o$4bo34bobo18bobo8bobo29bobo29bobo29bobo29bobo29bobo13bo15bobo29bobo29bobo29bobo29bobo27bo31bo31bo31bo31bo31bo31bo31bo28bo2bo28bo2bo28bo2bo$3b2o35bo21bo9bo25b2o4bo25b2o4bo25b2o4bo25b2o4bo25b2o4bo25b2o4bo25b2o4bo25b2o4bo6bo18b2o4bo25b2o4bo25b2o30b2o30b2o30b2o30b2o2b2o26b2o2b2o26b2o2b2o26b2o2b2o26b2o2b2o26b2o2b2o26b2o2b2o$3bobo92b2o30b2o30bo31bo31bo31bo31bo31bo11bo19bo31bo31bo31bo31bo31bo31bo4bo26bo4bo26bo4bo20b2o4bo4bo31bo31bo31bo$164bo31bo30bo31bo31bo31bo10b3o18bo7bo23bo7bo23bo31bo31bo2b3o26bo2b3o7bo18bo2bo28bo2bo28bo2bo22b2o4bo2bo31bo31bo31bo$65bobo95b2o30b2o29b2o30b2o29bobo29bobo29bobo6bobo20bobo6bobo20bobo29bobo29bobo29bobo12bobo14bobo2b2o25bobo2b2o25bobo2b2o20bo4bobo2b2o30b2o30b2o30b2o$66b2o221b2o30b2o8b3o19b2o7bobo20b2o7bobo20b2o30b2o14b2o14b2o30b2o13b2o15b2o30b2o30b2o30b2o$66bo204bo59bo31bo31bo68bobo2b2o$271bobo58bo133bob2o55b3o$65b3o73bo125bo3b2o197bo54bo112bo$67bo71b2o49bo75bo134b3o122bo111b2o$66bo66bobo4b2o48b2o11bo62b3o132bo71b2o162bobo$133b2o54bobo10b2o198bo70bobo$134bo58b3o6bobo62bo205bo$193bo72b2o242bo$132b2o60bo71bobo241b2o16b2o$131b2o376bobo15b2o$133bo395bo$196bo316bo$195b2o64b2o250b2o$195bobo63bobo248bobo$261bo$145b2o$144b2o$146bo$81b2o$81bobo$81bo!

gmc_nxtman

Posts: 1094
Joined: May 26th, 2015, 7:20 pm

### Re: Synthesising Oscillators

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

x = 43, y = 54, rule = B3/S235$16bo$17bo$15b3o2$12bo$13b2o$12b2o7$15bo9b2o$16bo8bo2b2o$14b3o9b2o2bo$22bo5bobo2bo$12b2o8bo5bob4o$11bobo8bo6bo$13bo16b2o$26b2o3bo$26bobo2bobo$27bo4b2o6$14b3o$16bo$15bo2$25bo7b2o$24b2o7bobo$24bobo6bo3$15b3o$17bo$16bo2$26bo$25b2o$25bobo!

Goldtiger997

Posts: 351
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: Synthesising Oscillators

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/S2344bo$45boo$44boo6$3booboboo13booboboo33booboboo13booboboo$3bob3obbo12bob3obbo32bob3obbo12bob3obbo$9bobo17bobo37bobo17bobo$4boo4bo13boo4bo33boo4bo13boo4bo$4boo18boo38boo18bo$85bo$51bo32boo$49bobo$50boo$$22boo38boo$boo18bobbo36bobbo$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. mniemiec Posts: 878 Joined: June 1st, 2013, 12:00 am ### Re: Synthesising Oscillators 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/S2344bo$45bo$43b3o2$86bo11bo$39bo31bo12bobo10bo$40bo31bo12b2o10b3o$38b3o29b3o4$52b2o30b2o$48b3o2bo26b3o2bo$48b3o29b3o$14b3o16b3o13bo31bo$16bo16bo$15bo18bo$48b2o30b2o$15b2o15b2o14b2o30b2o$15bobo13bobo18b2o30b2o$3b3o9bo17bo18b2o30b2o$3bo$4bo$b2o$obo$2bo12bo17bo18b2o30b2o$15bobo13bobo18b2o30b2o$15b2o15b2o14b2o30b2o$2b2o44b2o30b2o$b2o12bo18bo$3bo12bo16bo$14b3o16b3o13bo31bo$48b3o29b3o$48b3o2bo26b3o2bo$52b2o30b2o4$38b3o29b3o$40bo31bo12b2o10b3o$39bo31bo12bobo10bo$86bo11bo! gmc_nxtman Posts: 1094 Joined: May 26th, 2015, 7:20 pm ### Re: Synthesising Oscillators 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/S2380bo38bo$81bo36bo$79b3o36b3o4$88bo$89boo28bo$88boo27boo$83bo15bo18boo$bbo81bo12boo$obo79b3o13boo$boo133boo4boo22boo4boo22boo4boo$91bo19bo24bo6bo22bo6bo22bo6bo$4bo19boo18boo18boo23boo13boo4bo18boobboobobobboboboobboo8boobboobobobboboboobboo12boobobobboboboo$3bo20boo18boo18boo19b3obboo12boo4b3obboo12boobbobbobobbobobbobboo8boobbobbobobbobobbobboo12bobbobobbobobbo$3b3o79bo28boo19bobbobbobbo10b3o7bobbobbobbo7b3o10bobbobbobbo$36bo49bo29bo19boo4boo13bo8boo4boo8bo13boo4boo$bbo19boo10bobo5boo12boo4boo32boo4boo52bo26bo$boo19boo11boo5boo12boo4boo32boo4boo3b3o$bobo28boo45boo28bo$31bobo46boo26bo$33bo45bo4boo28boo$85boo26boo$84bo30bo$93boo10boo$92boo12boo$94bo10bo$85boo26boo$86boo24boo$85bo28bo6$75b3o44b3o$77bo44bo$76bo46bo! EDIT: gmc_nxtman wrote:EDIT: Unix + Glider in 6 gliders: ... This is edgy, unlike any of the other unix syntheses I know. 2 gliders to edgy block plus 5 glider block to unix = 7 glider edgy unix, so this costs the same. Of course, this is edgy along both block surfaces, so it would be useful when creating something where a unix is sandwiched between two other difficult-to-add objects. mniemiec Posts: 878 Joined: June 1st, 2013, 12:00 am ### Re: Synthesising Oscillators mniemiec wrote: gmc_nxtman wrote:EDIT: Unix + Glider in 6 gliders: ... This is edgy, unlike any of the other unix syntheses I know. 2 gliders to edgy block plus 5 glider block to unix = 7 glider edgy unix, so this costs the same. Of course, this is edgy along both block surfaces, so it would be useful when creating something where a unix is sandwiched between two other difficult-to-add objects. It turns out that it's possible to synthesise it cleanly with just 6 gliders: x = 45, y = 26, rule = LifeHistory.BA$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$7.5B2.4B2A6B$6.4B5.12B$5.4B6.13B12.B2AB$4.2A2B8.13B10.B4A$3.ABAB8.2A5B.6B10.A2BABA$4.BA8.ABA6B.5B8.BA.A.B2A$15.BA7B2.2B8.BABA3.B$17.7B12.2AB$19.6B11.3AB$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/S2337bo$36bo$36b3o2$15bo$16bo$14b3o12$10b2o$2o7bobo$2o7bo$9b3o4$9b3o$9bo$9bobo$10b2o12$14b3o$16bo$15bo2$36b3o$36bo\$37bo!

gmc_nxtman

Posts: 1094
Joined: May 26th, 2015, 7:20 pm

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