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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 Goldtiger997 » September 1st, 2017, 9:02 am

mniemiec wrote:Other than trivially growing the hook, I have no clue how to make either one.


Could this approach work?...:

x = 16, y = 14, rule = B3/S23
4b2o$4bo2bobo$6b3obo$10bo$8b2o5bo$7bo5b2o$7bo6b2o$4b2ob2o$3bobo7bo$3bo
bo6b2o$4bo7bobo$bo7bo$b2o5b2o$obo5bobo!
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Re: Synthesising Oscillators

Postby Extrementhusiast » September 1st, 2017, 9:54 am

Goldtiger997 wrote:
mniemiec wrote:Other than trivially growing the hook, I have no clue how to make either one.


Could this approach work?...:

RLE


It can be altered and simplified to completely solve it:
x = 28, y = 21, rule = B3/S23
2o$o2bobo$2b3obo9b2o$6bo8b2o$4b2o11bo$4bo8b2o$5bo6bobo$4b2o8bo$25b3o$
25bo$26bo8$16b2o$15b2o$17bo!


Besides, isn't there another variant of the oscillator itself?
x = 6, y = 11, rule = B3/S23
2b2o$bo2bo$o2bobo$3o2bo2$2b3o$bo$bobo2$2bobo$3b2o!


EDIT: Got that one done, too:
x = 184, y = 36, rule = B3/S23
158bo$157bo$26bo130b3o$25bo129bo$20bobo2b3o125bobo7bo$21b2o131b2o7bobo
$21bo53bo87b2o$o72b2o$b2o7bo20bo32b2o8b2o5bo13b2o23b2o30b2o26b2o$2o6b
2o15b2o4bobo20bobo6bo2bo12b2o13bo2bo21bo2bo28bo2bo24bo2bo$4b3o2b2o12bo
2bo4b2o5bo16b2o5bo2bobo12b2o11bo2bobo19bo2bobo26bo2bobo22bo2bobo$6bo
16b3o12bobo14bo6b3o2bo25b3o2bo19b3o2bo26b3o2bo22b3o2bo$5bo32b2o27b2o
29b2o23b2o30b2o$25b3o7b2o27b3o5bobo20b3o2bo19b3o2bo26b3o2bo22b3o$24bo
2bo6b2o27bo2bo5b2o20bo4b2o18bo4b2o25bo4b2o21bo$24b2o10bo17b3o5bo2bo7bo
20b2o23b2o30b2o26bobo$56bo6b2o10b3o42bo31bo$31b2o22bo19bo44bobo6bo22bo
bo25bobo$30b2o44bo13b3o28b2o6bobo21bobo25b2o$4b3o13b3o9bo59bo4b3o25b2o
2b2o23b2o8b2o$4bo17bo35b3o6b3o21bo5bo27bobo36bobo$5bo15bo38bo6bo30bo
26bo38bo$59bo8bo24b3o25b2o$95bo26b2o$94bo26bo40b2o$46b3o47b3o62b2o$48b
o47bo50b3o13bo$47bo49bo51bo$148bo$54b3o$56bo$55bo2$142b3o$144bo$143bo!
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Re: Synthesising Oscillators

Postby codeholic » September 2nd, 2017, 3:03 pm

I wonder if this simple oscillator had been known:

x = 15, y = 15, rule = B3/S23
7bo$7bo$7bo2$5b5o$5b3o2bo$5bo4bo$3o3bo2b2ob3o$5bobob2o$4bobob3o$5bo2$
7bo$7bo$7bo!

It results from depolymerization of this oscillator.
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Re: Synthesising Oscillators

Postby mniemiec » September 2nd, 2017, 4:28 pm

Extrementhusiast wrote:Besides, isn't there another variant of the oscillator itself? ... EDIT: Got that one done, too: ...

Splendid! This converter can also make the cis-carrier version, although the trans-carrier and snake stick out a bit too much and might need some work to use directly (although both can be made from the cis-carrier one). If the corresponding still-life could be made for under 38 gliders, this converter would improve it. If it could be made for under 27, it would also improve the trans-carrier and snake versions.
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Re: Synthesising Oscillators

Postby BlinkerSpawn » September 2nd, 2017, 6:31 pm

codeholic wrote:I wonder if this simple oscillator had been known:

x = 15, y = 15, rule = B3/S23
7bo$7bo$7bo2$5b5o$5b3o2bo$5bo4bo$3o3bo2b2ob3o$5bobob2o$4bobob3o$5bo2$
7bo$7bo$7bo!

It results from depolymerization of this oscillator.

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Re: Synthesising Oscillators

Postby mniemiec » September 20th, 2017, 1:09 am

I decided to try tackling the remaining unsynthesized P5s up to 26 bits, all of which are Elkies's P5s with a claw w/tub, or similar appendage. Two existing converters for adding an inconvenient tub use a mechanism below the claw that has the same effect as one of the block-to-boat converters, which is much cheaper. This allows simplification of those two converters, plus creation of a third that solves the base form that is used for most of the above-mentioned Elkies's P5s. The only 2 remaining unsolved P5s up to 26 bits are now ones with the tub plus a snake or carrier.
x = 170, y = 40, rule = B3/S23
15bo29bo29bo29bo$14bobo27bobo27bobo27bobo27boo28boo$8boo5bo29bo22boo5b
o29bo22boo3bobbo26bobbo$7bobbo56bobbo56bobbo3bobobbo24bobobbo$bobo4boo
3b5o25b5o20boo3b5o25b5o13bobo4boo3boob4o23boob4o$bboo8bobbobbo23bobbo
bbo13bobo7bobbobbo23bobbobbo13boo8bobbo26bobbo$bbo9boo3boo22bobo3boo
14boo7boo3bobo21bobo3bobo12bo9boo3bo6bo16bobo3bo$42bo20bo3boo9bo23bo5b
o27boo4boo18bo3boo$6boo58bobo57boo15boo$5bobo60bo56bobo$7bo65boobboo
48bo4boo3boo$73boobbobo51bobbobboo21boo$78boo51bobbo11boo12boo$9boo5b
3o113boo6bobobboo$10boo4bo61bo4bo42bo13boo5bo$boo6bo7bo59boo3bo43boo
13bo$obo74bobobb3o40bobo8b3o$bbo12boo119bo$16boo119bo$15bo11$12bo29bo$
11bobb3o24bobb3o$13bo29bo$14bobobbo24bobobbo$13boob4o23boob4o$12bobbo
26bobbo$11bobobboo23bobobboo$12bo4bo24bo4bo$16bo28bo$16boo27boo!
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Re: Synthesising Oscillators

Postby Extrementhusiast » Yesterday, 11:58 pm

mniemiec wrote:The only 2 remaining unsolved P5s up to 26 bits are now ones with the tub plus a snake or carrier.


I did not expect this to go as directly as it did:
x = 54, y = 32, rule = B3/S23
14bobo$15b2o$15bo2$12b2o34b2o$11bo2bo32bo2bo$12bobo6bobo24bobo2bo$11b
2ob2o5b2o24b2ob4o$10bo2bo2bo5bo4bo18bo2bo$9bobo2b2o11bobo15bobo2b2o$
10bo9b3o4b2o17bo4bo$3bobo14bo28bo$4b2o8bo6bo27b2o$4bo8bobo$13bobo7b2o$
14bo8bobo3b2o$23bo4b2o$8bo8bo12bo$b2o5b2o7b2o$obo4bobo6bobo$2bo9$32b2o
$31b2o$33bo!

There might be a less sparky place for the last cleanup glider, though.

Plus, a special freaky bonus component!
x = 58, y = 28, rule = B3/S23
bo$2bo$3o18b2o29b2o$20bo2bo27bo2bo$21bobo2bo6bo18bobo2bo$20b2ob4o6bobo
15b2ob4o$19bo2bo10b2o15bo2bo$18bobo3bo24bobo2b2o$3bobo13bo3b2o25bo4bo$
3b2o46b4o$4bo$49b4o$5b2o42bo2bo$6b2o29b3o$5bo31bo$38bo3$13b2o26b2o$12b
obo25b2o$14bo27bo3$28b3o$28bo$11b3o15bo$13bo$12bo!
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Re: Synthesising Oscillators

Postby Goldtiger997 » Today, 1:32 am

Extrementhusiast wrote:
mniemiec wrote:The only 2 remaining unsolved P5s up to 26 bits are now ones with the tub plus a snake or carrier.

I did not expect this to go as directly as it did:...


Great work Extrementhusiast!

Here is the full synthesis in 24 and 28 gliders:

x = 178, y = 92, rule = B3/S23
155bobo$156b2o19bo$156bo18b2o$176b2o$148bobo$149b2o$14bo134bo$15b2o$
14b2o$2bo17bobo125bo$3b2o15b2o42bobo79bobo$2b2o17bo43b2o80b2o3bo$65bo
84b2o$bo149b2o$2o8b2o12bo37b2o48b2o48b2o$obo7bobo11bobo34bo2bo46bo2bo
46bo2bo$10bo13b2o36bobo6bobo38bobo2bo44bobo2bo$61b2ob2o5b2o38b2ob4o43b
2ob4o$60bo2bo2bo5bo4bo32bo2bo46bo2bo$59bobo2b2o11bobo29bobo2b2o43bobo
2b2o$60bo9b3o4b2o31bo4bo44bo4bo$53bobo14bo42bo50bo$12b3o39b2o8bo6bo41b
2o49b2o$14bo39bo8bobo$13bo49bobo7b2o$64bo8bobo3b2o$73bo4b2o$58bo8bo12b
o38bo$51b2o5b2o7b2o37bo11b2o$34b2o14bobo4bobo6bobo37b2o10bobo$34bobo
15bo52bobo6b3o$34bo81bo$115bo3$113bo$113b2o$112bobo2$82b2o$81b2o$83bo
9$105bobo$106b2o19bo$106bo18b2o$126b2o$98bobo$99b2o$14bo84bo$15b2o$14b
2o$2bo17bobo75bo$3b2o15b2o42bobo29bobo$2b2o17bo43b2o30b2o3bo$65bo34b2o
$bo99b2o$2o8b2o12bo37b2o48b2o$obo7bobo11bobo34bo2bo46bo2bo$10bo13b2o
36bobo6bobo38bobo2bo$61b2ob2o5b2o38b2ob4o$60bo2bo2bo5bo4bo32bo2bo$59bo
bo2b2o11bobo29bobo2b2o$60bo9b3o4b2o31bo4bo$53bobo14bo42bo$12b3o39b2o8b
o6bo41b2o$14bo39bo8bobo$13bo49bobo7b2o$64bo8bobo3b2o$73bo4b2o$58bo8bo
12bo$51b2o5b2o7b2o$34b2o14bobo4bobo6bobo$34bobo15bo$34bo8$82b2o$81b2o$
83bo!


Your method will reduce many syntheses of Elkies P5 variants. It obsoletes the recently solved variant without a tub. Unfortunately your snake-to-eater converter doesn't work here because the tub gets in the way, which I haven't been able to work out how to fix.

Anyway, while I'm here, I added a lot more clearance to the ship-to-tripole converter:

x = 103, y = 61, rule = LifeHistory
10.4D.D4.3D$10.D2.D.D4.D2.D45.2D2.D.3D2.D3.D$10.D2.D.D4.D2.D45.D.D.D.
D4.D.D.D16.B$10.D2.D.D4.D2.D45.D.D.D.3D2.D.D.D15.3B$10.4D.4D.3D46.D.D
.D.D4.D.D.D14.4B$69.D2.2D.3D3.D.D14.4B$97.4B$96.4B$95.4B$94.A3B$93.A
3B$93.3A3$29.3B$28.4B$27.4B$26.4B$25.4B$24.4B$23.4B$22.A3B$22.ABA$22.
2A3$26.2B$25.3B45.2B$24.4B45.3B15.3B$23.4B46.4B13.4B$22.4B48.4B11.4B$
21.4B50.4B9.4B$20.4B52.4B7.4B$19.A3B54.4B5.4B$18.A3B56.2BAB3.4B$18.3A
58.2B2A.ABAB$80.2A2.2AB$85.A$25.2B51.B$24.4B30.2B17.3B$16.A6.4B30.4B
15.4B$15.B2A4.4B32.4B13.4B$14.BABA3.4B34.4B11.4B$13.4B3.4B36.4B9.4B$
12.4B3.4B38.4B7.4B$11.4B3.BA2B40.4B5.A3B$10.4B3.2A2B42.3BA3.A3B17.2A$
9.4B5.2A44.ABA3.3A17.A.A$8.4B53.2A22.A$8.3B57.A19.A$8.2A7.3A47.B2A17.
A$7.ABA7.A3B45.BABA16.A$6.3BA8.A3B43.4B16.A$5.4B10.4B41.4B16.A$4.4B7.
2A3.4B39.4B8.2A6.A$3.4B7.A.A4.4B37.4B3.A4.A.A5.A$2.4B3.2A3.2A6.4B35.
4B3.A.A3.2A5.A$.4B4.A2.2A9.4B33.4B5.A2.2A6.A$4B6.2A.A5.2A3.3B33.3B7.
2A.A5.A$3B10.A.2A.A.A4.2B46.A.2A.A$13.2A.2A55.2A.2A!


I also found a reduction to up beacon on up long bookend with tub which also acts as a converter:

x = 24, y = 28, rule = B3/S23
21bobo$2bo18b2o$obo19bo$b2o2$18bo$16b2o$17b2o4$7bo$5bobo$6b2o$14bobo$
10bo3b2o$11b2o2bo$10b2o3$7b2o$6bo2bo$7b2o2$7b4o$7bo3bo$10bobo$11bo!
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Re: Synthesising Oscillators

Postby mniemiec » 43 minutes ago

Extrementhusiast wrote:I did not expect this to go as directly as it did: ...

Goldtiger997 wrote:Here is the full synthesis in 24 and 28 gliders: ...

(Actually, it's 26 and 30; you forgot to add the beehive). Thanks guys! Now all known P5s up to 26 bits have syntheses.
Goldtiger997 wrote:Your method will reduce many syntheses of Elkies P5 variants.

This reduces the 25-bit tubless snake+carrier ones (and the derived 26-bit eater and feather ones)
but I'm not sure which other would benefit from this.
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