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Oscillator Discussion Thread

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

Re: Oscillator Discussion Thread

Postby Majestas32 » December 14th, 2017, 6:45 pm

Saka wrote:Has this smiley interaction been discovered?


It was mentioned somewhere in the middle of Gustavo's Patterns.
Please, stop spam searching Snowflakes.
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Re: Oscillator Discussion Thread

Postby Sokwe » December 15th, 2017, 12:38 am

2718281828 wrote:A new minimal period 48 oscillator with 55 cells:
x = 19, y = 22, rule = B3/S23
5b2o$5bo$7bo2$5bobo$4b2o$b2ob2o2$bo4bo$o5bo$2o3bo$2o$10bo3bo$9bobobobo
$10b2ob2o2$7bo9bo$6bobo7bobo$6bo3b2ob2o3bo$7bo3bobo3bo$8b2obobob2o$10b
o3bo!

Unix can interact with Rich's p16 to form a nontrivial 52-cell p48 oscillator:
x = 21, y = 19, rule = B3/S23
4bo3bo$3bobobobo$4b2ob2o2$bo9bo$obo7bobo$o3b2ob2o3bo$bo3bobo3bo$2b2obo
bob2o$4bo3bo2$17b2o$13b2o2b2o$13b2o2bob2o$18b3o3$18b2o$18b2o!

I was not able to find a combination where the minimal phase of unix and the minimal phase of Rich's p16 occurred at the same time.

2718281828 wrote:I just noticed that http://www.conwaylife.com/wiki/Talk:Oscillator lists some of the recent 'founds' like the p135

Some of these are now out of date. I posted here about the smallest known oscillators of various periods (in response to a post by muzik). There are three updates and one correction to what I wrote there:
  • The smallest known p48 is unix on Rich's p16.
  • The smallest known p108 now uses Tanner's new T-nose:
    x = 33, y = 33, rule = B3/S23
    15b2o$15b2o5$13b2o$14b2o$10bo4bo$10bo3bo$10b2o7b3o$19bo2$2o21bo$2o5b2o
    11bob2o$6b2obo11b2o5b2o$6bo21b2o2$10bo$8b3o7b2o$15bo3bo8bo$14bo4bo8bo$
    14b2o11b3o$15b2o2$28b2o$25b2ob3o$24bobo$13b2o9bo4b4o$13b2o10bo$26bo$
    23b3o$23bo!
  • The smallest known p130 is now the p130 engine with stable supports:
    x = 46, y = 27, rule = B3/S23
    5b2o32b2o$5b2o32b2o3$24b2o$2o4b2o18bo11b2o4b2o$2o3bobo16b3o10bo2bo3b2o
    $5b3o13bo16bobo$18b3ob2o15bo$18bo3b2o$3bo20bo17bo$2bobo14bo3bo17bobo$
    2b2o16b4o18b2o2$2b2o16b4o18b2o$2bobo14bo3bo17bobo$3bo20bo17bo$18bo3b2o
    $18b3ob2o15bo$5b3o13bo16bobo$2o3bobo16b3o10bo2bo3b2o$2o4b2o18bo11b2o4b
    2o$24b2o3$5b2o32b2o$5b2o32b2o!
  • Correction: I couldn't find any way to combine a mazing or mold with a p46 shuttle to get a nontrivial p92. The best I could manage was this 50-cell oscillator:
    x = 41, y = 12, rule = B3/S23
    22b2o$12b2o7bobo15b2o$12b2o7bo17b2o$7bo13b3o$5b2obo$2o2b2o$o2bobobo$b
    2o18b3o$2bo2bo15bo17b2o$b2o18bobo15b2o$4bobo15b2o$5b2o!
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Re: Oscillator Discussion Thread

Postby gameoflifemaniac » December 15th, 2017, 9:18 am

Reduced p92:
x = 41, y = 12, rule = B3/S23
22b2o$12b2o7bobo$12b2o7bo$7bo13b3o$5b2obo$2o2b2o$o2bobobo$b2o18b3o$2bo
2bo15bo17b2o$b2o18bobo15b2o$4bobo15b2o$5b2o!
https://www.youtube.com/watch?v=q6EoRBvdVPQ
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Re: Oscillator Discussion Thread

Postby dvgrn » December 15th, 2017, 9:31 am

gameoflifemaniac wrote:Reduced p92:
Code: Select all
x = 41, y = 12, rule = B3/S23
22b2o$12b2o7bobo$12b2o7bo$7bo13b3o$5b2obo$2o2b2o$o2bobobo$b2o18b3o$2bo
2bo15bo17b2o$b2o18bobo15b2o$4bobo15b2o$5b2o!
#C [[ AUTOSTART STOP 92 THUMBNAIL ]]

Unfortunately that's not reduced, in the sense of the actual p92 oscillator having a smaller minimum population.

It's a smaller-population predecessor of a p92 oscillator, but if we started collecting those we'd have to start taking one cell out of every four in every block, and so on and so forth.
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Re: Oscillator Discussion Thread

Postby gameoflifemaniac » December 15th, 2017, 9:38 am

By the way, can someone post a list of the smallest oscillators with a specific period in an attachment?
https://www.youtube.com/watch?v=q6EoRBvdVPQ
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Re: Oscillator Discussion Thread

Postby mniemiec » December 20th, 2017, 8:28 pm

(Originally posted to Useless Discoveries)

It comes as no surprise that two 26-bit P40s can share the same block. As expected, if the phase separation between the two oscillators is 5-20, this works seamlessly, and with 3 or 4, it also works because the rear half of the block reforms as the front half eats. This also fails as expected with phase separations of 0 and 2. However, what is unexpected is a phase separation of 1 results in a hassler that mutates the block to non-trivially attack the original oscillator, and produces a different spark, but reforms the block and leaves the oscillator unharmed:
x = 32, y = 26, rule = B3/S23
oo8boo$oo7bo$12bo$8boobo$8boo5$7boo$5boboo$4bo$7bo7boo8bo$5boo8boo8boo
$23b3o$23b3o$23b3o5$21b3o$21b3o$21b3o$20boo8boo$21bo8boo!

(When the block is shared along a diagonal axis of symmetry, phase separations of 11 and 13-20 work.)

EDIT: For completeness, a mostly vanilla 21-glider synthesis (of the 50-bit minimum phase):
x = 160, y = 78, rule = B3/S23
93bo$91bobo$bobo88boo$bboo102bo$bbo103bobo$106boo$48boo38boo38boo$48b
oo38boo38boo7bo$bbo132bobbo$obo132bo3bo$boo23bo108bo3bo$26bobo19boo38b
oo49bo$26boo19bobbo12boo22bobbo12boo29bo$5boo41boo12bobbo22boo12bobbo
32bo$4bobo56boo38boo28bo$6bo23boo101bo3bo$30bobo100bo3bo$30bo103bobbo$
63boo38boo30bo7boo$63boo38boo38boo$85boo$30bo53bobo$29boo55bo$29bobo
67boo$99bobo$99bo21$8boo38boo38boo38boo$8boo7bo30boo7bo30boo7bo30boo7b
o$15bobbo36bobbo36bobbo36bobbo$15bo3bo35bo3bo35bo3bo35bo3bo$15bo3bo35b
o3bo35bo3bo35bo3bo$19bo39bo39bo39bo$14bo39bo39bo39bo$18bo39bo39bo39bo$
13bo39bo39bo39bo$13bo3bo12bobo20bo3bo10bo24bo3bo10bo13bo10bo3bo$13bo3b
o12boo21bo3bo10b3o22bo3bo10b3o9boo11bo3bo$14bobbo13bo22bobbo13bo22bobb
o13bo9boo11bobbo$15bo7boo30bo7boo5boo23bo7boo5boobbobo18bo7boo$23boo7b
3o28boo38boo9boo27boo$32bo82bo35bobo$33bo115b3oboo$41bo111b3o$41bobo
19boo38boo$22boo17boo19bobbo12boo22bobbo12boo$21bobo39boo12bobbo22boo
12bobbo$23bo54boo38boo$25boo18boo100b3o$25bobo17bobo100boob3o$25bo19bo
103bobo$78boo38boo38boo$78boo38boo38boo$100boo$45bo55boo$44boo54bo$44b
obo67boo$113boo$115bo!
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Re: Oscillator Discussion Thread

Postby Bullet51 » December 22nd, 2017, 9:56 pm

P8, P9 & P11:
x = 58, y = 22, rule = B3/S23
43b2o$43bobo4b2o$18b2o5b2o18bo3bobo$2o16bo5bobo18b2o2bo$obo16bo4bo14b
2o7b2o$2bo15b2o2b2ob4o10bobo3b3o$2b2o12bo2bobobobo2bo12bo2bo3b2o$5bo
10b2o3b2o2bo14b2obo2bobobob2o$2b4o14bo2bobobo2b2o11bob3o2bobobob2o$2bo
3bo13b4o4bo2bo11bo5b2obobobo$3b2obo17bobob3o10b2ob2o3bo2bobobo$4bob2o
12b3obobo13bobobo2bo3b2ob2o$4bo3bo10bo2bo4b4o9bobobob2o5bo$5b4o10b2o2b
obobo2bo8b2obobobo2b3obo$5bo19bo2b2o3b2o8b2obobobo2bob2o$7b2o13bo2bobo
bobo2bo12b2o3bo2bo$8bo13b4ob2o2b2o16b3o3bobo$8bobo15bo4bo15b2o7b2o$9b
2o13bobo5bo14bo2b2o$24b2o5b2o12bobo3bo$45b2o4bobo$52b2o!


Found by Sokwe's dr2.
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Re: Oscillator Discussion Thread

Postby A for awesome » December 23rd, 2017, 12:29 pm

New p35 TL hassler:
x = 40, y = 46, rule = B3/S23
16b2o6b2o$10bob2obobo6bobob2obo$10b2obobo10bobob2o$16bo8bo$14b3o8b3o2$
17b3o2b3o2$20b2o$13b2obo8bob2o$13b2obo8bob2o$17bo6bo$18b6o3$32bo2b2o$
31bobo2bo$31bobobo$6b2o22b2obob2o$5bo2bo10bobo8bo2bo3bo$o2bo2bobo10bo
2bo8bo2b3obo$5obob2o9bobo8bo2b2o3bo$6bo2bo21bo2b4o$2b4o2bo21bo2bo$bo3b
2o2bo8bobo9b2obob5o$bob3o2bo8bo2bo10bobo2bo2bo$2bo3bo2bo8bobo10bo2bo$
3b2obob2o22b2o$4bobobo$3bo2bobo$3b2o2bo3$16b6o$15bo6bo$11b2obo8bob2o$
11b2obo8bob2o$18b2o2$15b3o2b3o2$12b3o8b3o$14bo8bo$8b2obobo10bobob2o$8b
ob2obobo6bobob2obo$14b2o6b2o!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

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Re: Oscillator Discussion Thread

Postby Sokwe » December 23rd, 2017, 10:46 pm

A for awesome wrote:New p35 TL hassler:
x = 40, y = 46, rule = B3/S23
16b2o6b2o$10bob2obobo6bobob2obo$10b2obobo10bobob2o$16bo8bo$14b3o8b3o2$
17b3o2b3o2$20b2o$13b2obo8bob2o$13b2obo8bob2o$17bo6bo$18b6o3$32bo2b2o$
31bobo2bo$31bobobo$6b2o22b2obob2o$5bo2bo10bobo8bo2bo3bo$o2bo2bobo10bo
2bo8bo2b3obo$5obob2o9bobo8bo2b2o3bo$6bo2bo21bo2b4o$2b4o2bo21bo2bo$bo3b
2o2bo8bobo9b2obob5o$bob3o2bo8bo2bo10bobo2bo2bo$2bo3bo2bo8bobo10bo2bo$
3b2obob2o22b2o$4bobobo$3bo2bobo$3b2o2bo3$16b6o$15bo6bo$11b2obo8bob2o$
11b2obo8bob2o$18b2o2$15b3o2b3o2$12b3o8b3o$14bo8bo$8b2obobo10bobob2o$8b
ob2obobo6bobob2obo$14b2o6b2o!

Very nice! The large domino sparkers can be replaced with fumaroles:
x = 40, y = 30, rule = B3/S23
19b2o4b2o$19bobo2bobo$21bo2bo$20bo4bo$20b2o2b2o$22b2o2$32bo2b2o$31bobo
2bo$31bobobo$6b2o22b2obob2o$5bo2bo10bobo8bo2bo3bo$o2bo2bobo10bo2bo8bo
2b3obo$5obob2o9bobo8bo2b2o3bo$6bo2bo21bo2b4o$2b4o2bo21bo2bo$bo3b2o2bo
8bobo9b2obob5o$bob3o2bo8bo2bo10bobo2bo2bo$2bo3bo2bo8bobo10bo2bo$3b2obo
b2o22b2o$4bobobo$3bo2bobo$3b2o2bo2$16b2o$14b2o2b2o$14bo4bo$15bo2bo$13b
obo2bobo$13b2o4b2o!

How did you find it?

Edit: Reduction of new billiard tables by Bullet51:
x = 59, y = 18, rule = B3/S23
25b2o$2o22bobo$bo16b2o4bo25bo$o18bo2b2ob4o19b3o$2o17bobobobo2bo18bo3b
2o$3bo13b2o2bobo22bo2bo3bob2o$3obo13bobo25bob2o3bobo$o17bob3obo2b2o16b
2o6bobo$2b2o15bo4b2o2b3o13bo2b2o6bob2o$3b2o15b3o2b2o4bo12b2obo6b2o2bo$
6bo15b2o2bob3obo14bobo6b2o$2bob3o23bobo14bobo3b2obo$3bo23bobo2b2o12b2o
bo3bo2bo$5b2o15bo2bobobobo18b2o3bo$6bo15b4ob2o2bo20b3o$5bo20bo4b2o19bo
$5b2o17bobo$24b2o!
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Re: Oscillator Discussion Thread

Postby A for awesome » December 24th, 2017, 12:18 am

Sokwe wrote:
A for awesome wrote:New p35 TL hassler:
pattern
reduction

How did you find it?

Thanks for the reduction! I found it through manually messing around with TLs for lack of something better to do and luck.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

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Re: Oscillator Discussion Thread

Postby gameoflifemaniac » December 24th, 2017, 5:32 am

How about a list of the smallest oscillators witha specific period up to some period?
https://www.youtube.com/watch?v=q6EoRBvdVPQ
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Re: Oscillator Discussion Thread

Postby Sokwe » December 24th, 2017, 3:34 pm

gameoflifemaniac wrote:How about a list of the smallest oscillators witha specific period up to some period?

That can be found on the oscillator wiki page.
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Re: Oscillator Discussion Thread

Postby gameoflifemaniac » December 24th, 2017, 3:58 pm

Sokwe wrote:
gameoflifemaniac wrote:How about a list of the smallest oscillators witha specific period up to some period?

That can be found on the oscillator wiki page.

It's incomplete. I mean, there are known oscillator periods on the list that haven't got the corresponding oscillators.
https://www.youtube.com/watch?v=q6EoRBvdVPQ
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Re: Oscillator Discussion Thread

Postby Bullet51 » December 26th, 2017, 12:02 am

x = 11, y = 14, rule = LifeHistory
4.A$2A.A.A$2A.A.A$3.A.A.2A.A$2A.A.A.A.2A$AB.ABAB$2.AB.BA$.2A3B$.2A3BC
$2.BA2B$5.2BA$5.2A.A$8.A$8.2A!

It may have some use if it were an external sparker. But we already have p7 single-cell sparkers.
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Re: Oscillator Discussion Thread

Postby Sokwe » December 26th, 2017, 1:33 am

Bullet51 wrote:
x = 11, y = 14, rule = LifeHistory
4.A$2A.A.A$2A.A.A$3.A.A.2A.A$2A.A.A.A.2A$AB.ABAB$2.AB.BA$.2A3B$.2A3BC
$2.BA2B$5.2BA$5.2A.A$8.A$8.2A!

It may have some use if it were an external sparker. But we already have p7 single-cell sparkers.

I minimized the stator using JLS and found that the minimum form is only 28 bits. This makes it part of a four-way tie (not counting stator variants) for smallest known period-7 oscillator:
x = 10, y = 13, rule = B3/S23
obo$2obo$3bo2b2o$2obobobo$o2bo2bo$2bo$4bo$2b3o2$6b2o$6bobo$8bo$8b2o!

How did you find it?

Edit: do you want to name it? For now I am calling it 28P7.3.
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Re: Oscillator Discussion Thread

Postby Bullet51 » December 26th, 2017, 8:48 am

Sokwe wrote:I minimized the stator using JLS and found that the minimum form is only 28 bits. This makes it part of a four-way tie (not counting stator variants) for smallest known period-7 oscillator:
x = 10, y = 13, rule = B3/S23
obo$2obo$3bo2b2o$2obobobo$o2bo2bo$2bo$4bo$2b3o2$6b2o$6bobo$8bo$8b2o!

How did you find it?


Thanks for your optimization. I found it with dr2, by using the following input file:
H80
rot180symm
v127 1
c46
h10
w9
r39 39
444
444!


It is originally found in its dimerized form:
x = 11, y = 20, rule = b3s23
4bo$2obobo$2obobo$3bobob2obo$2obobobob2o$2obob2o$2bo2bo$2bobo$2bobo$3b
2o$6b2o$6bobo$6bobo$5bo2bo$4b2obob2o$2obobobob2o$ob2obobo$5bobob2o$5bo
bob2o$6bo!


Do you want to name it? For now I am calling it 28P7.3.

28P7.3 is fine with me.
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Re: Oscillator Discussion Thread

Postby gameoflifemaniac » December 29th, 2017, 11:56 am

Here are all rectangular billiard tables I know off:
x = 460, y = 38, rule = B3/S23
b2o2b2o10bo11b2obo9b2obo10b2o12b2o12b2o14bo15b2o13b2o13b2o13b2o17b2o
16b2o16b2o14b2o13b2o13b2o13b2o13b2o13bo2bo2bo13bo2bo2bo13bo2bo2bo13bo
2bo2bo13bo2bo2bo13bo2bo2bo13bo2bo2bo13bo2bo2bo$bo2bo2bob2o4b3o11bob2o
9bob2o10b2o12b2o12b2o13bobo14b2o13b2o13b2o13b2o15bo2bo14bo2bo14bo2bo
14b2o13b2o13b2o13b2o13b2o13b7o13b7o13b7o13b7o13b7o13b7o13b7o13b7o$2bob
o2bobo4bo85bo77b3o15b3o15b3o$b2obo2bo2bo3bo2b3o10b3o10b3o10b4o10b4o10b
4o26b6o9b6o9b6o9b6o65b6o9b6o9b6o9b6o9b6o9b11o9b11o9b11o9b11o9b11o9b11o
9b11o9b11o$5b2o2b2o2b2obo3bo8bo3bob2o5bobobob2o5bobo2bob2o5bo4bob2o5bo
4bob2o6b5o10bo6bo7bo6bo7bo6bo7bo6bo10b7o11b7o11b7o10bo6bo7bobo4bo7bo6b
o7bobo4bo7bo6bo7bo11bo7bo11bo7bobo9bo7bobo9bo7bobo7bobo7bobo7bobo7bobo
9bo7bobo9bo$16bo3bo8bo3bob2o5bo2b2ob2o5bo4bob2o5b2o3bob2o5bobo2bob2o5b
o3bobo9bob2o3bo7bob2o3bo7bob2o3bo7bo3b2obo9bobo5bo9bo3bo3bo9bo7bo9bo3b
2obo7b2o2b2obo7bo3b2obo7b2o2b2obo7bo2b3obo7bo3b2ob2o3bo7bo3b2ob2o3bo7b
2o2b2ob2o3bo7b2o2b2ob2o3bo7b2o2b2ob2o2b2o7b2o2b2ob2o2b2o7b2o2b2ob2o3bo
7b2o2b2ob2o3bo$5b2o9bo3bob2o2b2obobobo5b2obo3bo5b2obo3b2o5b2obo2bobo5b
2obobo2bo5bo2bo4b2o2bo3b2obob2o3bob2ob2obobo4bob2ob2obobo4bob2ob2obobo
bo2bob2o3bo2bo3b2o2bo2bo3bo2bobo3bobo2bo6bo2b3o2bo2b2o2b2obo4bobob2ob
2obo4bobob2ob2obo3b2obob2ob2obo4bobob2ob2obobo2bobob2ob2obo4bobo4bob2o
b2obo4bobo4bob2ob2obo4bobo4bob2ob2obo4bobo4bob2ob2obo4bobo4bob2ob2obo
4bobo4bob2ob2obo4bobo4bob2ob2obo4bobo4bob2o$4bo2bo9b3o2bo3b2obo3bo5b2o
bo3bo5b2obo4bo5b2obobo2bo5b2obo2bobo4bobobo5bobobo2b2obo3b2obob2ob2obo
bo2bobob2ob2obobo2bobob2ob2obobo3b2ob2o2bobobo2bo3b2obobobobobo2bobo2b
obobo2b2obobo3bobobobo3bobobo2bobobo3bobobo2bobobo3bobob2o3bobo3bobobo
4bobo3bobobo4bobo3bobobo2bobo2bobobo3bobobo2bobo2bobobo3bobobo2bobo2bo
bobo3bobobo2bobo2bobobo3bobobo2bobo2bobobo3bobobo2bobo2bobobo3bobobo2b
obo2bobobo3bobobo2bobo2bobobo$bo2bo2bo2bo11bo7b3o10b3o10b4o10b4o10b4o
6bo2b2o4bo2bo6bo3b2obo7bo2b3obo7bob4obo7bob2o3bo6bo2bo3b2o2bo2bo3bo2b
2obobob2o2bo4bobobo3bobobo5bobob4obobo3bobob4obobo3bobob2o3bobo3bobob
2o3bobo3bobob2o3bobo3bobob3o3b3obobo3bobob4ob4obobo3bobob3o3b3obobo3bo
bob4ob4obobo3bobob3o3b3obobo3bobob4ob4obobo3bobob3o3b3obobo3bobob4ob4o
bobo$obobo2bobobo7b3o75bobo3bo9bo6bo7bo6bo7bo6bo7bo4bobo9bobo5bo9bo7bo
5bobobobo3bobob2o3b2obo6bob2ob2obo6bob2ob2obo5b2ob2ob2obo5b2ob2ob2obo
5b2ob2ob2obo11bob2ob2obo11bob2ob2obo11bob2ob2obo11bob2ob2obo11bob2ob2o
bo11bob2ob2obo11bob2ob2obo11bob2o$bo2b4o2bo8bo10b2obo9b2obo11b2o12b2o
12b2o10b5o11b6o9b6o9b6o9b6o11b7o11b7o6b2o2bo2b3o2bo7bobob4obobo3bobob
4obobo3bobob2o3bobo3bobob2o3bobo3bobob2o3bobo3bobob3o3b3obobo3bobob4ob
4obobo3bobob3o3b3obobo3bobob4ob4obobo3bobob3o3b3obobo3bobob4ob4obobo3b
obob3o3b3obobo3bobob4ob4obobo$4bo2bo22bob2o9bob2o11b2o12b2o12b2o123bo
7bo7bobobo2bobobo3bobobo2bobobo3bobob2o3bobo3bobob2o3bobo3bobob2o3bobo
3bobobo2bobo2bobobo3bobobo2bobo2bobobo3bobobo2bobo2bobobo3bobobo2bobo
2bobobo3bobobo2bobo2bobobo3bobobo2bobo2bobobo3bobobo2bobo2bobobo3bobob
o2bobo2bobobo$5b2o93bo15b2o13b2o13b2o13b2o15b3o15b3o13b7o7b2obo4bobob
2ob2obo4bobob2ob2obo3b2obob2ob2obo3b2obob2ob2obo3b2obob2ob2obo4bobo4bo
b2ob2obo4bobo4bob2ob2obo4bobo4bob2ob2obo4bobo4bob2ob2obo4bobo4bob2ob2o
bo4bobo4bob2ob2obo4bobo4bob2ob2obo4bobo4bob2o$99bobo14b2o13b2o13b2o13b
2o15bo2bo14bo2bo29bo3b2obo7bo3b2obo7bo3b2obo7bo3b2obo7bo3b2obo7bo3b2ob
2o3bo7bo3b2ob2o3bo7bo3b2ob2o3bo7bo3b2ob2o3bo7bo3b2ob2o3bo7bo3b2ob2o3bo
7bo3b2ob2o2b2o7bo3b2ob2o2b2o$5b2o93bo79b2o16b2o14b3o12bo6bo7bo6bo7bo6b
o7bo6bo7bo6bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo9bobo7bo9bob
o$4bo2bo205bo2bo13b6o9b6o9b6o9b6o9b6o9b11o9b11o9b11o9b11o9b11o9b11o9b
11o9b11o$2o2bo2bo205b2o$obobo2bob2o221b2o13b2o13b2o13b2o13b2o13b7o13b
7o13b7o13b7o13b7o13b7o13b7o13b7o$2bob4obo222b2o13b2o13b2o13b2o13b2o13b
o2bo2bo13bo2bo2bo13bo2bo2bo13bo2bo2bo13bo2bo2bo13bo2bo2bo13bo2bo2bo13b
o2bo2bo$b2obo2bobobo$4bo2bo2b2o$4bo2bo$5b2o4$5b2o$5b2o4$5b2o$5b2o4$5b
2o$5b2o!

Are there any more?
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One big dirty Oro. Yeeeeeeeeee...
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Re: Oscillator Discussion Thread

Postby dvgrn » December 29th, 2017, 2:09 pm

gameoflifemaniac wrote:Here are all rectangular billiard tables I know off...
Are there any more?

Up to the size you have there, with stable cells allowed in part of the area? Sure!

There are truly hideously large numbers of them, in fact -- almost certainly more than would fit in any reasonable stamp collection. Billiard tables are like methuselahs, in that there are way too many of them, and it's way too easy for people to discover "new" examples... which may in fact be new in some cases, but may still not be interesting. I'd advise reading through some earlier threads covering some of this same ground before posting any more new finds.

If you're really interested in making a larger collection of these things, it's a good idea to use WLS or JLS instead of relying on random trials with Python scripts. For the smaller sizes and periods you'll be able to run through all the possibilities in seconds or less, without missing any cases.

Here's JavaLifeSearch, and its instruction manual.

Just to get you started, one of the intermediate smallish sizes that you don't have an example of is 7x6. Here's one way to set up period-2 and period-3 searches in JLS:

sample7x6p2search.txt
Sample search file for 7x6 rectangle, period 2
(3.58 KiB) Downloaded 22 times

sample7x6p3search.txt
Sample search file for 7x6 rectangle, period 3
(11.59 KiB) Downloaded 15 times

Just load these files from File > Open after running JLS, then choose Search > Start.

You may want to send output to a file. In that case go to Search > Options first, and check or uncheck "Pause search after each solution" and "Append solutions to file" as you wish.

Familiarize yourself with all the other options in Search > Options and in Edit > Properties, too, while you're at it. You'll need the Edit > Properties options to set up your own searches at different sizes and periods.

#C 1 result from p2 search inside 7x6
x = 15, y = 16, rule = B3/S23
8boo$6bobbo$6b3o$$4b7o$3bo7bo$3bobb3obbo$oobobo3boboboo$oobobo3boboboo$3bobb3obb
o$3bo7bo$4b7o$$6b3o$6bobbo$8boo!

#C 36 results from p3 search inside 7x6
#C (many of them are rotations or reflections of other cases)
x = 1276, y = 15, rule = B3/S23
7b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o$7b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o2$5b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b
6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b
6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o$4bo6bo28bo2bo3bo
28bo6bo28bo6bo28bo6bo28bo3bo2bo28bo3bo2bo28bo3bo2bo28bo6bo28bo3bo2bo
28bo3bo2bo28bo6bo28bo3bo2bo28bo3bo2bo28bo6bo28bo6bo28bo6bo28bo3bo2bo
28bo6bo28bo6bo28bo3bo2bo28bo6bo28bo2bo3bo28bo2bo3bo28bo6bo28bo2bo3bo
28bo2bo3bo28bo6bo28bo2bo3bo28bo2bo3bo28bo6bo28bo2bo3bo28bo6bo28bo6bo
28bo2bo3bo28bo6bo$2o2b2o3bobo2b2o20b2o2b2o2b2obo2b2o20b2o2b2obobobo2b
2o20b2o2bobobob2o2b2o20b2o2bobo3b2o2b2o20b2o2bob2o2b2o2b2o20b2o2b2o5bo
2b2o20b2o2bobo4bo2b2o20b2o2bobo2bobo2b2o20b2o2b2o5bo2b2o20b2o2bobo4bo
2b2o20b2o2bobo2bobo2b2o20b2o2b2o5bo2b2o20b2o2bobo4bo2b2o20b2o2bobo2bob
o2b2o20b2o2bobobob2o2b2o20b2o2bobo3b2o2b2o20b2o2bob2o2b2o2b2o20b2o2bob
obob2o2b2o20b2o2bobo3b2o2b2o20b2o2bob2o2b2o2b2o20b2o2bobo2bobo2b2o20b
2o2bo5b2o2b2o20b2o2bo4bobo2b2o20b2o2bobo2bobo2b2o20b2o2bo5b2o2b2o20b2o
2bo4bobo2b2o20b2o2bobo2bobo2b2o20b2o2bo5b2o2b2o20b2o2bo4bobo2b2o20b2o
2b2o3bobo2b2o20b2o2b2o2b2obo2b2o20b2o2b2obobobo2b2o20b2o2b2o3bobo2b2o
20b2o2b2o2b2obo2b2o20b2o2b2obobobo2b2o$obobo3b2obobobo20bobobo3b2obobo
bo20bobobo3b2obobobo20bobobob2o3bobobo20bobobob2o3bobobo20bobobob2o3bo
bobo20bobobo5b2obobo20bobobob2o2b2obobo20bobobob4obobobo20bobobo5b2obo
bo20bobobob2o2b2obobo20bobobob4obobobo20bobobo5b2obobo20bobobob2o2b2ob
obo20bobobob4obobobo20bobobob2o3bobobo20bobobob2o3bobobo20bobobob2o3bo
bobo20bobobob2o3bobobo20bobobob2o3bobobo20bobobob2o3bobobo20bobobob4ob
obobo20bobob2o5bobobo20bobob2o2b2obobobo20bobobob4obobobo20bobob2o5bob
obo20bobob2o2b2obobobo20bobobob4obobobo20bobob2o5bobobo20bobob2o2b2obo
bobo20bobobo3b2obobobo20bobobo3b2obobobo20bobobo3b2obobobo20bobobo3b2o
bobobo20bobobo3b2obobobo20bobobo3b2obobobo$2bobo6bobo24bobo6bobo24bobo
6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bob
o24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24b
obo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo
6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bob
o24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24bobo6bobo24b
obo6bobo24bobo6bobo$b2obob4obob2o22b2obob4obob2o22b2obob4obob2o22b2obo
b4obob2o22b2obob4obob2o22b2obob4obob2o22b2obob2o3bob2o22b2obob2o3bob2o
22b2obob2o3bob2o22b2obob2o3bob2o22b2obob2o3bob2o22b2obob2o3bob2o22b2ob
ob2o3bob2o22b2obob2o3bob2o22b2obob2o3bob2o22b2obob2o2b2ob2o22b2obob2o
2b2ob2o22b2obob2o2b2ob2o22b2obo5b2ob2o22b2obo5b2ob2o22b2obo5b2ob2o22b
2obo3b2obob2o22b2obo3b2obob2o22b2obo3b2obob2o22b2obo3b2obob2o22b2obo3b
2obob2o22b2obo3b2obob2o22b2obo3b2obob2o22b2obo3b2obob2o22b2obo3b2obob
2o22b2ob2o5bob2o22b2ob2o5bob2o22b2ob2o5bob2o22b2ob2o2b2obob2o22b2ob2o
2b2obob2o22b2ob2o2b2obob2o$4bobo2bobo28bobo2bobo28bobo2bobo28bobo2bobo
28bobo2bobo28bobo2bobo28bobobob2o28bobobob2o28bobobob2o28bobo3b2o28bob
o3b2o28bobo3b2o28bob2o2b2o28bob2o2b2o28bob2o2b2o28bobo4bo28bobo4bo28bo
bo4bo28b2o5bo28b2o5bo28b2o5bo28b2obobobo28b2obobobo28b2obobobo28b2o3bo
bo28b2o3bobo28b2o3bobo28b2o2b2obo28b2o2b2obo28b2o2b2obo28bo5b2o28bo5b
2o28bo5b2o28bo4bobo28bo4bobo28bo4bobo$4bo6bo28bo6bo28bo6bo28bo6bo28bo
6bo28bo6bo28bo6bo28bo6bo28bo6bo28bo6bo28bo6bo28bo6bo28bo3bo2bo28bo3bo
2bo28bo3bo2bo28bo3bo2bo28bo3bo2bo28bo3bo2bo28bo3bo2bo28bo3bo2bo28bo3bo
2bo28bo6bo28bo6bo28bo6bo28bo6bo28bo6bo28bo6bo28bo2bo3bo28bo2bo3bo28bo
2bo3bo28bo2bo3bo28bo2bo3bo28bo2bo3bo28bo2bo3bo28bo2bo3bo28bo2bo3bo$5b
6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b
6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o30b
6o30b6o30b6o30b6o30b6o30b6o30b6o30b6o2$7b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o$7b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o
34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o!

Then there aren't any p4, p5, or p6 solutions at that size. Those searches take about three seconds, fifteen seconds, and a minute, respectively.

Then you can find almost two hundred p7s in about five minutes of JLS searching. They're all incredibly boring variants of your rightmost 6x6 billiard table, except for a few slightly interesting ones that fit two copies of the rotor into the space:

x = 15, y = 16, rule = B3/S23
8b2o$6bo2bo$6b3o2$4b7o$3bo7bo$3bob4o2bo$2obobobo3bob2o$2obobo3bobob2o$
3bob5obo$3bo7bo$4b7o2$6b3o$6bo2bo$8b2o!

Again, most of them are rotated or reflected duplicates. If you get to the point where you're processing a lot of these things, it's probably worth borrowing some Python code from apgsearch -- find the apgcode of each oscillator so you can easily throw out the duplicates.

-------------------------------------------------

One last word and warning (as the cold Duke said):

You can keep on with this series of searches to look at higher periods, but the search time rises exponentially: maybe half an hour for p8, several hours for p9, a day for p10 (if you're lucky), a week for p11, a month for p12, etc. Maybe you can squeeze more speed out of JLS by choosing a different sort order in Edit > Properties, but then again you might only make things worse.

Moving up to 7x7 and larger rectangles will also make searches proportionally slower. You may or may not find anything that someone else hasn't found before -- or you may find something "new" that is one of a billion similar variants, which means any given example has only a 0.000000001 Interestingness Score.

WLS/JLS beginners find it very tempting to run ambitious searches -- maybe there's a p19 oscillator in an 11x11 box! It's true, it might actually be there, but the odds are very poor that a simple JLS search will find it for you in any reasonable amount of time.

Searches that can't be run to completion are most likely stuck in some useless corner of a huge search space -- and they will likely remain stuck there for more than a century, or until your power goes out, or until your computer needs rebooting... whichever comes first.
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Re: Oscillator Discussion Thread

Postby Bullet51 » January 4th, 2018, 10:11 pm

x = 17, y = 15, rule = B3/S23
6b2o$b2o2bobo2b2obo$bo3bobobo2b2o$2b3obobobo$4bobo3bob4o$6b2o2b2obo2bo
$5b2o8b2o2$2o8b2o$o2bob2o2b2o$b4obo3bobo$6bobobob3o$3b2o2bobobo3bo$3bo
b2o2bobo2b2o$9b2o!
Still drifting.
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Re: Oscillator Discussion Thread

Postby A for awesome » January 7th, 2018, 10:48 pm

A p42 TL hassler supported by p21 glider streams:
x = 57, y = 57, rule = B3/S23
27b2o25bo$21bob2obobo25bobo$21b2obobo27b2o$25b2o$26bo$27b2o2bo2b2o14bo
$30bobo2bo12b2o$25bo4bobobo14b2o$33bo$21b2o3b7o$21bobo20bo$23bo7b2o2bo
7bo$23b2o5bob4o7b3o$26b2o2bo$21b5o3b5o$20bo4bo3bo3bo$21b3o6b3o5bobo$
23bob4obo7b2o$24b6o9bo$25b4o$15bo$b2o6b2o3bobo27b2o4b2o$2bo6bo4bobo19b
2o6bo4bobo$bo8b3obob2o17bo5b2obo3bo$b2o9bobo2bo22bobob2obob2o$3bo10bob
o10bo12bobo2bobo3bo$b4o9bobo11bo10b2ob3o2bob2o$o5b3o5bobo8bo2bo9bo2b2o
4bo$2o4b3ob5obo9b2ob2o6b3o7bo3bo3b2o$7bo3bo5bo8bobo2bo5b3o3bo3bo3bo4bo
$5bo3bobob2ob2o9b2o8b3o3bo3bo4b4o$5bo3bobo2bobo12bo7b3ob2o6bo3bo$6b2ob
ob2obobo21bo3bobo9b2o$8bo3bob2o5b3o15b2obob3o8bo$5bobo4bo10bo16bobo4bo
6bo$5b2o4b2o9bo17bobo3b2o6b2o$41bo2$16b2o$17b2o7b2o4b2o$16bo7b3ob4ob3o
$23bo12bo$23b4ob8o$11b2o13bobo$10bobo8b4o3bo3b2o$12bo8bo2b5o4bo$28bo4b
obo$24b3o7b2o$6bo16bo4b2o$6b2o14bobo2b3o$5bobo13bo2bo3b2o$21b2o2b2o$
30bo$30b2o$3o27bobob2o$2bo25bobob2obo$bo26b2o!

The streams are just there to delete beehives, but I can't find a way to delete them without guns.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

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Re: Oscillator Discussion Thread

Postby Bullet51 » January 7th, 2018, 11:33 pm

P16:
x = 20, y = 18, rule = b3s23
9b2o$8bo2bo$9b2o3b2o$6b3o5bo$2o3bo3b2o4bo$obobob3o2bo2b2o$2bobobobobob
o$b2obobo3bobob2o$4bobo3bobo2bo$4bobo3bobo2bob2o$2bobobobobob2obobo$2b
2obob2obo2bobobobo$5bo5bobobo2b2o$5b7obobo$14bo$7b3o$6bo2bo$6b2o!
Still drifting.
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Re: Oscillator Discussion Thread

Postby BlinkerSpawn » January 8th, 2018, 12:09 am

Bullet51 wrote:P16:
x = 20, y = 18, rule = b3s23
9b2o$8bo2bo$9b2o3b2o$6b3o5bo$2o3bo3b2o4bo$obobob3o2bo2b2o$2bobobobobob
o$b2obobo3bobob2o$4bobo3bobo2bo$4bobo3bobo2bob2o$2bobobobobob2obobo$2b
2obob2obo2bobobobo$5bo5bobobo2b2o$5b7obobo$14bo$7b3o$6bo2bo$6b2o!

You know the drill:
x = 18, y = 14, rule = B3/S23
7bo5b2o$5b3o5bo$4bo3b2o4bo$3bob3o2bo2b2o$3bobobobobo$2obobo3bobob2o$bo
bobo3bobo2bo$bobobo3bobo2bob2o$2b2obobobob2obob2o$4bob2obo2bobo$4bo5bo
bobo$5b5obobo$7bo3bo$11b2o!
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Re: Oscillator Discussion Thread

Postby Sokwe » January 8th, 2018, 7:00 am

Bullet51 wrote:P16:
x = 20, y = 18, rule = b3s23
9b2o$8bo2bo$9b2o3b2o$6b3o5bo$2o3bo3b2o4bo$obobob3o2bo2b2o$2bobobobobob
o$b2obobo3bobob2o$4bobo3bobo2bo$4bobo3bobo2bob2o$2bobobobobob2obobo$2b
2obob2obo2bobobobo$5bo5bobobo2b2o$5b7obobo$14bo$7b3o$6bo2bo$6b2o!

This one is already known.
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Re: Oscillator Discussion Thread

Postby A for awesome » January 9th, 2018, 11:08 pm

A fairly small p5 sparker with two different types of sparks, both new for that period (I think):
x = 27, y = 22, rule = B3/S23
12bob2o$13bobo3$5b2o7b4o3bob2o$5bobob2obo3bobo2b2obo$7bobo2bo5b3o$o6bo
6bobo5b2o$b2obo2b2o2b3o4b2obo2bobo$o3bobob2o8b2o3bob2o$8b2o11bobo$o3bo
bob2o8b2o3bob2o$b2obo2b2o2b3o4b2obo2bobo$o6bo6bobo5b2o$7bobo2bo5b3o$5b
obob2obo3bobo2b2obo$5b2o7b4o3bob2o3$18b2o$17b2o$19bo!
(Reduced and another interaction added via edit)

A few small p2/3 rotors/bushings that I couldn't find in jslife for some reason:
x = 88, y = 14, rule = B3/S23
5bo31b2o13b2o2b2o6bo2bo$4bobo12b2o3b2o11bo13bo2bo2bo6b4o$3bo2bo12bobob
o2bo11bo2b2o8b2o2b2o25b2ob2o$3b2obob2o11bobo2bo10b2o3bo10b2o7b8o6bob2o
bobobobo$6bobo8b4obob2ob2o2bob2obo2b3o9b2ob3o5bo7bo5b2obobo5bo$8bo8bo
2bobob2obo3b2obobob2obobob2o3bo6bo6b3obobo10bobo2bo$2obob3o14bo4bo8bo
4bob2obo2bobo2b3o10bob2ob2o6bob2obo$ob2o17bo3b2o8bo3b2o8bobo2bo12bo3bo
bo5bobo2bo$5b3o13b2o2bo9b2o2bo10bo13b3ob3o8bob3o$b4o2bo18bo13bo21bo5bo
11bo$bo2bo20b2o12b2o21b6o13bo$80b2o$64b2o$64b2o!


And a weird 30-cell p4 thumb:
x = 8, y = 15, rule = B3/S23
7bo$6b2o$6b2o$b3o2bo2$4b2o$o3b2o$bo2bo$2b3o$2bo2bo$2bo$b2o3bo$6b2o$6b
2o$7bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

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Aidan F. Pierce
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Re: Oscillator Discussion Thread

Postby BlinkerSpawn » January 10th, 2018, 9:37 am

A for awesome wrote:
x = 88, y = 14, rule = B3/S23
5bo31b2o13b2o2b2o6bo2bo$4bobo12b2o3b2o11bo13bo2bo2bo6b4o$3bo2bo12bobob
o2bo11bo2b2o8b2o2b2o25b2ob2o$3b2obob2o11bobo2bo10b2o3bo10b2o7b8o6bob2o
bobobobo$6bobo8b4obob2ob2o2bob2obo2b3o9b2ob3o5bo7bo5b2obobo5bo$8bo8bo
2bobob2obo3b2obobob2obobob2o3bo6bo6b3obobo10bobo2bo$2obob3o14bo4bo8bo
4bob2obo2bobo2b3o10bob2ob2o6bob2obo$ob2o17bo3b2o8bo3b2o8bobo2bo12bo3bo
bo5bobo2bo$5b3o13b2o2bo9b2o2bo10bo13b3ob3o8bob3o$b4o2bo18bo13bo21bo5bo
11bo$bo2bo20b2o12b2o21b6o13bo$80b2o$64b2o$64b2o!

#5, but smaller:
x = 10, y = 14, rule = B3/S23
2b2o$2bo$4bo2bo$8o$o$2b3obobo$5bob2o$5bo$2b3ob2obo$o5bob2o$6o2$2b2o$2b
2o!
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