Oscillator Discussion Thread

[Bullet51]

Notice the similarities: (Left: P11 Right: P10)

Maybe a P19 could be found in this way by tweaking a P18 or P17.

Variations on a Theme, Opus 2:

Code: Select all

x = 40, y = 19, rule = b3s23
13b2o$6b2o3bo2bo13b2o3bo2bo$6bobo2b3o14bobo2b4o$8bo21bo$7bob7o13bob6o$
7bo7bo13bo7bo$8b6o16b7obo$36bobo$4b2o2b3o15b2o2b3o4bo$bo2bo2bo3bo3b2o
6bo2bo2bo3bo$obobob2obo6bo5bobobob2obo$bo2bo2bob4obobob2o3bo2bo2bob4ob
o$4b2o2bo3bobobob2o6b2o2bo3bobo$9b2obob2o15b2obob3o$11bo21bo5bo$9b2o
20b2o5b2o$9bo21bo$7bobo19bobo$7b2o20b2o!

(Left: P11 Right: P12)

[Scorbie]

Found the third movement for the Opus 1, using A for awesome's block trick.

Code: Select all

x = 78, y = 37, rule = B3/S23
3b2o5b2obo21b2o4b2o22b2o3b2obo$4bo5bob2o22bo5bo23bo3bob2o$3bo4b2o4b2o
19bo5bo23bo8b2o$3b2o3bo5bo20b2o4b2o22b2o7bo$9bo5bo59bo$3b2o3b2o4b2o19b
2o4b2o22b2o7b2o$4bo3bo5bo21bo5bo23bo3b2obo$3bo5bo5bo19bo5bo23bo4bob2o$
3b2o3b2o4b2o19b2o4b2o22b2o7b2o$8bo5bo59bo$3b2o4bo5bo19b2o4b2o22b2o8bo$
4bo3b2o4b2o20bo5bo23bo7b2o$3bo6b2obo21bo5bo23bo4b2obo$3b2o5bob2o21b2o
4b2o22b2o3bob2o7$7bob2o19bo5b2o2b2o5bo19bob2o$2o4bob2obo4b2o10b5o4bo2b
o4b5o10b2o4bob2obo4b2o$o5bo4bo5bo9bo5bo2bo4bo2bo5bo9bo5bo4bo5bo$2bob2o
b4ob2obo12b3obo2bob4obo2bob3o12bob2ob4ob2obo$b3obobo2bobob3o13bob2obob
o2bobob2obo13b3obobo2bobob3o$5bo6bo22bo6bo22bo6bo$b3ob2o4b2ob3o14b3ob
2o4b2ob3o14b3ob2o4b2ob3o$o2bob2o4b2obo2bo12bo2bob2o4b2obo2bo12bo2bob2o
4b2obo2bo$2o14b2o12b2o14b2o12b2o14b2o3$3b2o8b2o49b2o6b2o$b2o2b2o4b2o2b
2o47b2o6b2o$bo4bo4bo4bo$2bo2bo6bo2bo$obo2bobo2bobo2bobo$2o4b2o2b2o4b2o
!

[Sokwe]

Stator reduction for the "new" p20 pre-pulsar hassler:

Code: Select all

x = 61, y = 23, rule = B3/S23
4bo4bo4b2o6b2o13b2o6b2o4bo4bo$3bobo2bobobo2bo2b2o2bo15bo2b2o2bo2bobobo
2bobo$3bobo2bobob2obobo2bobo15bobo2bobob2obobo2bobo$2b2ob2obobo4bobob
2ob2o13b2ob2obobo4bobob2ob2o$bo8bob2obo8bo11bo8bob2obo8bo$3ob2ob2ob2o
2b2ob2ob2ob3o9b3ob2ob2ob2o2b2ob2ob2ob3o$3o2bob2o2bo2bo2b2obo2b3o9b3o2b
ob2o2bo2bo2b2obo2b3o$2o8b2o2b2o8b2o3b3o3b2o8b2o2b2o8b2o$b2o3b2ob2o4b2o
b2o3b2o4bobo4b2o3b2ob2o4b2ob2o3b2o$b3obo14bob3o4b3o4b3obo14bob3o$6b2o
10b2o21b2o10b2o2$6b2o10b2o21b2o10b2o$b3obo14bob3o4b3o4b3obo14bob3o$b2o
3b2ob2o4b2ob2o3b2o4bobo4b2o3b2ob2o4b2ob2o3b2o$2o8b2o2b2o8b2o3b3o3b2o8b
2o2b2o8b2o$3o2bob2o2bo2bo2b2obo2b3o9b3o2bob2o2bo2bo2b2obo2b3o$3ob2ob2o
b2o2b2ob2ob2ob3o9b3ob2ob2ob2o2b2ob2ob2ob3o$bo8bob2obo8bo11bo8bob2obo8b
o$2b2ob2obobo4bobob2ob2o13b2ob2obobo4bobob2ob2o$3bobo2bobob2obobo2bobo
15bobo2bobob2obobo2bobo$3bobo2bobobo2bo2b2o2bo15bo2b2o2bo2bobobo2bobo$
4bo4bo4b2o6b2o13b2o6b2o4bo4bo!

The original p5 supports were found by Bullet51 based on a suggestion by Aidan F. Pierce. p20 supports for this reaction had previously been found by hought99. Thanks to Scorbie for pointing out the previous stabilization, since I had completely forgotten it.

[Scorbie]

Anytime. And congrats for the rediscovery/reduction!

[PHPBB12345]

viewtopic.php?f=2&t=335&p=30515#p30515
How to reducing stator for p6 osc?

[Sokwe]

How to reducing stator for p6 osc?

The best program for stator reductions is probably JavaLifeSearch. I described my personal step-by-step process here.

[2718281828]

The new 28p7.3 allows for a smaller p21 and p42:
40p21 (caterer on 28p7.3)

Code: Select all

x = 17, y = 13, rule = B3/S23
obo$2obo$3bo2b2o$2obobobo2b2o$o2bo2bo5bo$2bo6bo$4bo4bo3bo$2b3o4bo3b4o$
11bo$6b2o$6bobo$8bo$8b2o!

and 55p42:

Code: Select all

x = 18, y = 13, rule = B3/S23
obo$2obo$3bo2b2o3b2ob2o$2obobobo4bobo$o2bo2bo4bo2bo$2bo11bob2o$4bo5bob
obobo$2b3o4bobob2obo$10b2o3bo$6b2o4b3o$6bobo3bo$8bo$8b2o!

(maybe there is a smaller version for the rotor)

[2718281828]

Does someone know a 4G synthesis of one of the four still life constellations shown left:

Code: Select all

x = 69, y = 48, rule = B3/S23
2$50bo$48bobo$14b2o33b2o6b2o$2b2o9bobo6b2o21b2o9bobo6b2o$2b2o9b2o7b2o
21b2o9b2o7b2o8$50bo$48bobo$14b2o33b2o6b2o$13bobo6b2o32bobo6b2o$2b2o9b
2o7b2o21b2o9b2o7b2o$2b2o41b2o7$50bo$48bobo$14b2o33b2o6b2o$2b2o9bobo29b
2o9bobo$2b2o9b2o7b2o21b2o9b2o7b2o$22b2o41b2o7$50bo$48bobo$14b2o33b2o6b
2o$13bobo40bobo$2b2o9b2o7b2o21b2o9b2o7b2o$2b2o18b2o21b2o18b2o!

The reason is shown right, a potential reduction of a queen-bee shuttle.

[Extrementhusiast]

Does someone know a 4G synthesis of one of the four still life constellations shown left:

Code: Select all

RLE

The reason is shown right, a potential reduction of a queen-bee shuttle.

The most likely candidate would probably be one of the two-glider B-heptomino collisions plus two other gliders.

[Mandelbrot]

This is probably known, but it's my first ever find so it's kinda special to me, so I thought I'd post it.

Code: Select all

#CXRLE Pos=-16,-4
x = 25, y = 15, rule = B3/S23
8b2o5bo5b2o$b2o4bo2bo3bobobo2bo2bo$b2o5bobo3bobob3o2b2o$3b2ob2ob2ob3o
2bo3b2o$b2obo2bobo3bo4bob2ob2o$5b2ob2o2bo2b4o5bo$o2b2o2bobo3b2o2bo2bob
2o$b2o3bo2bob2ob2obob2obo$b2o3bobo2bo5b2obobobo$2b4o2b2obob2o3bobo2b2o
$8bo2bo2bo2bo2bo$2b2o6b2o2bobo3b2o$4bo10bo$bo$2b2o!

[BlinkerSpawn]

This is probably known, but it's my first ever find so it's kinda special to me, so I thought I'd post it.

Code: Select all

#CXRLE Pos=-16,-4
x = 25, y = 15, rule = B3/S23
8b2o5bo5b2o$b2o4bo2bo3bobobo2bo2bo$b2o5bobo3bobob3o2b2o$3b2ob2ob2ob3o
2bo3b2o$b2obo2bobo3bo4bob2ob2o$5b2ob2o2bo2b4o5bo$o2b2o2bobo3b2o2bo2bob
2o$b2o3bo2bob2ob2obob2obo$b2o3bobo2bo5b2obobobo$2b4o2b2obob2o3bobo2b2o
$8bo2bo2bo2bo2bo$2b2o6b2o2bobo3b2o$4bo10bo$bo$2b2o!

Well, this exact oscillator isn't known, but it's a composition of known p2 rotors.
I'm assuming this came out of WinLifeSearch or similar?

[velcrorex]

This p7 is sparky. I didn't see it in jslife. Could it be new?

Code: Select all

x = 28, y = 13, rule = B3/S23
2bo22bo$bob3o4bob4obo4b3obo$6bo2bo8bo2bo$b2o3bo2bo8bo2bo3b2o$o4bo4bob
4obo4bo4bo$b4o18b4o2$b4o18b4o$o4bo4bob4obo4bo4bo$b2o3bo2bo8bo2bo3b2o$
6bo2bo8bo2bo$bob3o4bob4obo4b3obo$2bo22bo!

EDIT: Variation with one cap out of phase from the other:

Code: Select all

x = 28, y = 15, rule = B3/S23
24bo$2bo19bo2bo$bob3o4bob4obo8bo$6bo2bo8bo2bo4bo$b2o3bo2bo8bo2bo2b4o$o
4bo4bob4obo3bo5bo$b4o17b5o2$b4o17b5o$o4bo4bob4obo3bo5bo$b2o3bo2bo8bo2b
o2b4o$6bo2bo8bo2bo4bo$bob3o4bob4obo8bo$2bo19bo2bo$24bo!

[Sokwe]

This p7 is sparky. I didn't see it in jslife. Could it be new?

It looks new to me. A single copy of the central component can be supported by a known oscillator, but the clearance for the spark is much worse:

Code: Select all

x = 26, y = 15, rule = B3/S23
3b2o16b2o$4bo16bo$3bo18bo$3b2o16b2o2$b5o3bob4obo3b5o$o4bo2bo8bo2bo4bo$
obob2o2bo8bo2b2obobo$b3o5bob4obo5b3o2$b3o18b3o$o2bo3b2o8b2o3bo2bo$2o5b
obo6bobo5b2o$9bo6bo$9b2o4b2o!

[Scorbie]

A single copy of the central component can be supported by a known oscillator, but the clearance for the spark is much worse:

There's another monomer stablization I know, with the same clearance (wink!)

Code: Select all

x = 28, y = 15, rule = B3/S23
3bo20bo$2bo2bo16bo2bo$bo24bo$bo4bo2b2o6b2o2bo4bo$4o2bo2b2o6b2o2bo2b4o$
o5bo14bo5bo$b5o16b5o2$b5o7b2o7b5o$o5bo5bo2bo5bo5bo$4o2bo2b2obo2bob2o2b
o2b4o$bo4bo2b2obo2bob2o2bo4bo$bo10bo2bo10bo$2bo2bo7b2o7bo2bo$3bo20bo!

Anyway, the sparks are super nice (as nice as Ellison's p4 to me). Hope we use it somewhere.

[velcrorex]

Much better clearance, horrible size.

Code: Select all

x = 75, y = 30, rule = B3/S23
12bo18b2o6b2obo$11bobo3b2o3bo2bo5bo7bob2o2bo3b2o10bo$11bobo3bobo2b4o3b
obo4b2obo3b5o2bo10b3o$10b2ob3obobo8bobo5bobob2o6b2o14bob2obo$16bobob6o
2bo9bobob2o2b2o8b2ob4obobob2o$8b7o3bo4bo2bob2o8bobobo2bobo4b2o3bobo2bo
bobo$3b2o2bo5bob2obob2o4bo3bo2bobobo2bob2o6bo4bobo6bo2b3o$3b2obo2b3o4b
obo3bobob4o3bobobobo2bo2bo6bo2bobo5bo2b2o2bo$7bobob2o9bobo4b2ob2obo2bo
2b2ob2o4b2ob2o2bo2bo2bo5bo$9b2obo6bobobobo8bo2bobob2o2b2obo7b2obob3o6b
3o$2b2o15bobobobo9b2o2bobo4bobo2bo7bo6bo6bo$2b2o14bo3bo2b3o4bo6bob6obo
bobo3b2obob6o5bobo$19b2obobo3bo3b7obo6bob2ob3o2bob2o12bo$b4o8b2ob3o2bo
2bob2o10bobo2b2o2bo7b2o5b2ob2o$o4bo8bobo2bobobobo8b2o4bobo2bobob2ob2ob
o7bobo$o4bo8bobo2bobobobo8b2o4bobo2bobob2ob2obo7bobo$b4o8b2ob3o2bo2bob
2o10bobo2b2o2bo7b2o5b2ob2o$19b2obobo3bo3b7obo6bob2ob3o2bob2o12bo$2b2o
14bo3bo2b3o4bo6bob6obobobo3b2obob6o5bobo$2b2o15bobobobo9b2o2bobo4bobo
2bo7bo6bo6bo$9b2obo6bobobobo8bo2bobob2o2b2obo7b2obob3o6b3o$7bobob2o9bo
bo4b2ob2obo2bo2b2ob2o4b2ob2o2bo2bo2bo5bo$3b2obo2b3o4bobo3bobob4o3bobob
obo2bo2bo6bo2bobo5bo2b2o2bo$3b2o2bo5bob2obob2o4bo3bo2bobobo2bob2o6bo4b
obo6bo2b3o$8b7o3bo4bo2bob2o8bobobo2bobo4b2o3bobo2bobobo$16bobob6o2bo9b
obob2o2b2o8b2ob4obobob2o$10b2ob3obobo8bobo5bobob2o6b2o14bob2obo$11bobo
3bobo2b4o3bobo4b2obo3b5o2bo10b3o$11bobo3b2o3bo2bo5bo7bob2o2bo3b2o10bo$
12bo18b2o6b2obo!

EDIT:
Smaller

Code: Select all

x = 22, y = 28, rule = B3/S23
6bo4bo3bo$4b3o3bobo2b3ob2o$3bo6bob3o3b2o$b3ob2o2b2o4b2o4bo$o4bobo4b2ob
ob2ob2o$b3o3b5obobo2bobo$3b2obo4bobobobo2bo$8bo4bobobobo$8b3o6bob2o$2b
2o6b6obo2bo$bo2bo4bo6bobo$10b5o2bo$bo2bo10b2o$bo2bo7b2obo$bo2bo7b2obo$
bo2bo10b2o$10b5o2bo$bo2bo4bo6bobo$2b2o6b6obo2bo$8b3o6bob2o$8bo4bobobob
o$3b2obo4bobobobo2bo$b3o3b5obobo2bobo$o4bobo4b2obob2ob2o$b3ob2o2b2o4b
2o4bo$3bo6bob3o3b2o$4b3o3bobo2b3ob2o$6bo4bo3bo!

EDIT2:
Smaller and better clearance. I'm happy with this version.

Code: Select all

x = 17, y = 28, rule = B3/S23
9bo$5bob5o$5b2o5bo$8b2obo$5b3obob2o$4bo4bo3bo$4b2o3bob3o$4b2obo$11b3o$
2b2o5bo4bo$bo2bo7b2o2bo$bo2bo8bob2o$o4bo7bo$o4bo4b2obob2o$o4bo4b2obob
2o$o4bo7bo$bo2bo8bob2o$bo2bo7b2o2bo$2b2o5bo4bo$11b3o$4b2obo$4b2o3bob3o
$4bo4bo3bo$5b3obob2o$8b2obo$5b2o5bo$5bob5o$9bo!

[Scorbie]

I'm happy with this version.

Oh, the supporting end works like an eater! I suspect there might be a happier support! Just give me a few hours (or search jslife for anyonr interested )

[Sokwe]

A single copy of the central component can be supported by a known oscillator, but the clearance for the spark is much worse:

There's another monomer stablization I know, with the same clearance (wink!)

Code: Select all

x = 28, y = 15, rule = B3/S23
3bo20bo$2bo2bo16bo2bo$bo24bo$bo4bo2b2o6b2o2bo4bo$4o2bo2b2o6b2o2bo2b4o$
o5bo14bo5bo$b5o16b5o2$b5o7b2o7b5o$o5bo5bo2bo5bo5bo$4o2bo2b2obo2bob2o2b
o2b4o$bo4bo2b2obo2bob2o2bo4bo$bo10bo2bo10bo$2bo2bo7b2o7bo2bo$3bo20bo!

Why didn't I think of this? I wanted to claim that mine was smaller by minimum population, but even that isn't true (they're tied).

EDIT2: Smaller and better clearance.

Nice! Here it is with minimized bounding box and minimized population (for this bounding box):

Code: Select all

x = 17, y = 27, rule = B3/S23
5bob2o$5b2obo$8bob2ob2o$5b3obob2obo$4bo4bo$4b2o3bob3o$4b2obo5bo$11b2o$
2b2o5bo$bo2bo7b3o$bo2bo8bobo$o4bo5bo3bo$o4bo4bob3o$o4bo5bo$o4bo6bo$bo
2bo8bo$bo2bo7b2o$2b2o5bo4b2o$11b3o2bo$4b2obo6b2o$4b2o3bob3o$4bo4bo3bo$
5b3obob2o$8b2obo$5b2o5bo$5bob5o$9bo!

The bounding box manages to minimize both width and height for this rotor variant.

The supporting component makes for a relatively small p7 by itself:

Code: Select all

x = 17, y = 13, rule = B3/S23
5bob2o$5b2obo$8bob2ob2o$5b3obob2obo$4bo4bo$4b2o3bob3o$4b2obo5bo$11b2o$
2b2o5bo$3bo8b3obo$3o10bob2o$o10bo$11b2o!

Oh, the supporting end works like an eater! I suspect there might be a happier support!

Here is a smaller variant with worse clearance based on a known p7 oscillator (top stabilization is minimum width, bottom is minimum height):

Code: Select all

x = 12, y = 27, rule = B3/S23
b2ob2ob2o$ob2obobobo$o6bo2bo$b3obob2obo$3bob2o2bo$4b2o2bo$9b3o$2b2o7bo
$bo2bo$bo2bo$o4bo$o4bo$o4bo$o4bo$bo2bo$bo2bo$2b2o2$4b2o2b2o$3bob2o2bo$
b3obob2o$o6bo$b3obobobo$3b2obob2o$6bo$6bob2o$7bobo!

It can probably replace the high-clearance variant in most cases.

Finally, here is the smallest variant by minimum population:

Code: Select all

x = 12, y = 28, rule = B3/S23
10b2o$10bo$2bob2ob2obo$2b2obobobo$5bo$5ob3o$o2bob2o2bo$8b2o2$2b2o$bo2b
o2$bo2bo$bo2bo$bo2bo$bo2bo2$bo2bo$2b2o2$8b2o$o2bob2o2bo$5ob3o$5bo$2b2o
bobobo$2bob2ob2obo$10bo$10b2o!

Edit: Here's a collection of all the known p7 sparkers in the style of jslife:

Code: Select all

#C Period 7 oscillators with sparks
#C
#C A1 [Karel Suhajda, 3 Jul 2013]
#C A2 [??]
#C A3 [Nicolay Beluchenko, 17 Feb 2009]
#C A4 [Matthias Merzenich, Aug 2014]
#C A5 [Josh Ball, 17 Dec 2016]
#C A6 [Noam Elkies, 11 Nov 1997]
#C A7 [??]
#C A8 [??]
#C
#C B1 "p7 pipsquirter" [Noam Elkies, Aug 1999]
#C                     [Improved by Karel Suhajda, 24 Jan 2003]
#C B2 [Noam Elkies, 1 Apr 1998 (top component) / Aug 1999 (bottom component)]
#C    [Improved by Karel Suhajda, 24 Jan 2003]
#C B3 [Dongook Lee, 18 Mar 2017]
#C B4 [Dongook Lee, 18 Mar 2017]
#C
#C C1 [Dongook Lee, 17 Dec 2016]
#C C2 "Hebdarole" [Noam Elkies, Nov 1997]
#C C3 [Josh Ball, 28 Mar 2018]
#C C4 [Josh Ball, 28 Mar 2018]
#C
#C D1 [David Buckingham, 19 Jun 1977]
#C D2 [Nicolay Beluchenko, 23 Feb 2009]
#C
#C E1 [Dean Hickerson, 5 Oct 1998]
#C E2 [??]
#C
#C F1 [Nicolay Beluchenko, 17 Feb 2009]
#C F2 [??]
#C F3 [Josh Ball, 17 Dec 2016]
x = 306, y = 245, rule = B3/S23
2bob2o26bo32bobobo30bobobo30bo3bo30bobobo30bobobo30bobobo30bobobo$2b2o
bo$6b2o24bo36bo34bo30bo3bo30bo34bo38bo30bo3bo$7bo$6bo25bo32bobobo30bob
obo30bobobo30bobobo30bobobo34bo30bobobo$6b2o$4b2o26bo32bo38bo34bo34bo
30bo3bo34bo30bo3bo$5bo$4bo27bo32bobobo30bobobo34bo30bobobo30bobobo34bo
30bobobo$4b2o$2b2o$3bo$2bo$2b2o13$176b2ob2o$172b2obo2b2o2bo2bo2bo$172b
o3bo4b2o2b4o$169b2obob2ob4o2b2o6bo$2bo29bo30bo7bo32bo29bo6bo16bo10bobo
bobobo2bobo2b7o17bo28b2o2bo2b2o26bob2o5bo14b2o5bo$29bo5bo25bo3bo3bo3bo
28bo2bo27bo3b2o3bo13bo3bo10bo6bobobobo20b2o3bo27bo7bo26b2ob4o3bo12bob
4o3bo$bobo25bo5bo24bo4bo3bo4bo31bo25bo3b4o3bo16bo7bo2bo5b3o6b6o13bo4bo
28bo5bo37bo11bo9bo$29bo2bo2bo30bobo28b2o2bo4bo25bobob4obobo11bo5b2obo
4bob2o2bo5b4o2b2obobo13b4o26b3o7b3o24b3o5bo13b3o5bo$o3bo57b3obobob3o
24b2o2bo2b4o21b2obobo6bobob2o8b2o2b2obobob2obobo3b5o8bo3bo10b3o30bo2b
2o3b2o2bo24bo5bo21bo$25b2o4bobo4b2o17bo4bo3bobo3bo4bo23bo5bo21bobo2b2o
4b2ob2obo13bobo2bobobob4o4bobob4obobob2o9bo2b2ob3o25bo4bo4bo26b2obobob
o12bob2obobobo$obobo18bo2bo3b2ob2o3bo2bo14bo9bobo9bo23b5o25b2o3b2o21bo
bob2obob2o4b2o4b2o4bob2o2bo11bo4bobo23b2ob3ob3ob2o26bobob2obo11b2obobo
b2obo$23b2o15b2o17b2o5bobo5b2o58b2obo23b2obo2bo4b2o2bo3bo3b2obo3bo14b
3obobo22bo2bo3bo3bo2bo25bob2o3bo15bobo3bo$o3bo23bob5obo18bo3bo6bobo6bo
3bo22b5o27bo2bo27bobob3ob2o5b2ob2ob2o3b2o10b3o2b2o2b2o21b2o2b3ob3o2b2o
26bo3b2o18bo3b2o$28bob5obo22bo5bo3bo5bo25bo5bo27b2o29b2obo33bo2bo2bo2b
o28bobo33b3o20b2o$56b2o6bo5bo6b2o18b2o2bo2b4o97bo2bobobo66bo$25b2o11b
2o18b6o7b6o20b2o2bo4bo99b5ob2o$25bo5bobo5bo66bo104bo$26b2o2bo3bo2b2o
19b6o7b6o25bo2bo100b4obo$31bobo22b2o6bo5bo6b2o25bo101bo2b2o$24b7o3b7o
18bo5bo3bo5bo$24bo6bobo6bo14bo3bo6bobo6bo3bo$26bob9obo20b2o5bobo5b2o$
25b2obo3bo3bob2o16bo9bobo9bo$29b2obob2o21bo4bo3bobo3bo4bo$30b2ob2o27b
3obobob3o$28bo7bo29bobo$26b3ob2ob2ob3o21bo4bo3bo4bo$25bo13bo21bo3bo3bo
3bo$26bob2obobob2obo24bo7bo$25b2obo2bobo2bob2o$28bob2ob2obo$28bo2bobo
2bo$29b2o3b2o12$obo24bo36bo37bo34bo$27bo36bo31b2o4bo4b2o28bo$o3bo27b2o
7b2o52bo2bo7bo2bo$25bo3bo2bo2bob2obo2bo18bo3bo28bobo2bo3bo2bobo25bo3bo
$obo20b3obob3o2b2obo3bobo16b3o3b3o27bob3o3b3obo24b3o3b3o$22bo4bo4b2o5b
2obo16bo3b3o3bo24bobo4b3o4bobo21bo3b3o3bo$o3bo17b2ob2ob3o4b4obo18bob2o
3b2obo24b2obobo5bobob2o21bob2o3b2obo$26bobo3b2o4bobo19bobobobobo28bo3b
obo3bo22b2obobobobobob2o$obo23bobobo4b4ob2o16bobobobobobobo26bo3bobo3b
o22bo2bobobobobo2bo$25b2obob4obo2bobo16bobobo5bobobo23bobobo5bobobo21b
2obo5bob2o$29bo4bo2bo2bo16bobo3bobo3bobo22bobo3b5o3bobo21bo3bobo3bo$
30b3o5b2o16b2obo9bob2o21bo2b2o3bo3b2o2bo21bo9bo$32b2o25b2o2b3o2b2o25b
2o2b3ob3o2b2o20bob2o2b3o2b2obo$59bo2bobobo2bo27bobobobobobo21bobo3bobo
bo3bobo$60b3o3b3o28bo2bo3bo2bo21bo3b3o3b3o3bo$57b3o9b3o26b2o5b2o23b3o
9b3o$57bo2bo7bo3bobob2o55bo7bo$58b2o4bo4bobob2obo2bo52bo4bo4bo$63b3o2b
2obo5b3o52b2o2b3o2b2o$62bobobo2bo2bob3o58bobobo$60b3o3b3o2b2obo3b2o52b
4o3b4o$59bo4b2o3b2o3bob2obo51bo4bobo4bo$59b2ob2ob2obo2bob3obo51bo2b3o
5b3o2bo$63bobo2bob2o5bo51b2obo2b2ob2o2bob2o$63bobobo4b3o2b2o53bo9bo$
62b2obob4obo2bobo54bob2o3b2obo$66bo4bo2bo2bo52b2o2b2o3b2o2b2o$67b3o5b
2o52bo2b2o3bo3b2o2bo$69b2o59b2o2b7o2b2o$132bobo2bo2bobo$132bo2bo3bo2bo
$133b2o5b2o9$2bo29b2o30b2o36b2o33b2o$28b2o6b2o19b2o3bo4bo3b2o27b6o22bo
6b6o6b2o$o3bo22bo10bo18bo2bobo4bobo2bo26b8o20bobo4b8o4bo2bo$27bobo6bob
o15b2obob2obo4bob2obob2o22bo8bo19bobo3bo8bo3bob2o$o24b3obobo2bobob3o
13bo2bo2bobob2obobo2bo2bo19bob2o8b2obo15b2ob2ob2o8b2ob2obo$24bo4b2ob2o
b2o4bo14bobo4bo2bo4bobo20bob2ob8ob2obo14bo4b2ob8ob2o4bo$o3bo20b3obo6bo
b3o16bo6b2o6bo17b2obo2bo3b6o3bo2bob2o11bobobo3b6o3bobob2o$27bo4b2o4bo
21bo2bo2bo2bo21bobob2o5b2o5b2obobo9b3o4bo5b2o5bo$2bo25bo3b2o3bo21bob2o
4b2obo19bo2bo18bo2bo7bo3b3o16b4o$29bo6bo21bobo8bobo18bobo2bo14bo2b3o8b
obo2bobo12bobo2bo$30b6o22bo12bo17b2ob3o16b2o10b2ob2o2b2o11bobo2bo$27bo
2b6o2bo17bobo12bobo16bo4b2o6bo5b2o2bo29bo2b2o$25b3o2b2o2b2o2b3o15b2ob
4o4b4ob2o16bob2o4bo3bobo2bo4b2o28b2o$24bo5b2o2b2o5bo17bobobo2bobobo20b
obobobobobobo2bobobobo$25b3o2b2o2b2o2b3o18bo3b4o3bo23b2obob2o2bob2o2b
2o2bo$27bo2b6o2bo21b2o6b2o26bobo4bo2bo5b2o$30b6o26b2o2b2o28bobo5b2o$
29bo6bo25bo2bobo29bo$28bo3b2o3bo25b2o$27bo4b2o4bo$25b3obo6bob3o$24bo4b
2ob2ob2o4bo$25b3obobo2bobob3o$27bobo6bobo$27bo10bo$28b2o6b2o$32b2o14$o
bo61b2o$64b2o$o3bo55b2o6b2o$35bo27b4o$o3bo29bobo22bo10bo$34bobo22bobob
4obobo$o3bo28b2ob2o19b2ob2obo2bob2ob2o$31bo5bo17bo3bo2bo4bo2bo3bo$obo
28bob4o18bo2b2o10b2o2bo$35bo24bo8bo$28b2o2b2o3bo18bob2o10b2obo$31bo2b
4o15b2obobo12bobob2o$27bobobobo19b2obobo12bobob2o$25b3obo2bo2bo20bob2o
10b2obo$24bo4b2obob2o24bo8bo$25b3obo2bo22bo2b2o10b2o2bo$27b2o2b2o22bo
3bo2bo4bo2bo3bo$57b2ob2obo2bob2ob2o$59bobob4obobo$59bo10bo$63b4o$60b2o
6b2o$64b2o$64b2o17$obobo30b2o$34bobo$o33bo$33b2o26bo7bo$obobo24bo29bo
3bo3bo3bo$28bo3b3o23bo4bo3bo4bo$o34bo28bobo$27bobo2b2o2bo23b3obobob3o$
obobo20b3obobo2b2o19bo4bo3bobo3bo4bo$24bo4b2ob2o20bo9bobo9bo$25b4o4bo
23b2o5bobo5b2o$29b4o20bo3bo6bobo6bo3bo$27bo2bo26bo5bo3bo5bo$27b2o25b2o
6bo5bo6b2o$56b6o7b6o2$56b6o7b6o$54b2o6bo5bo6b2o$57bo5bo3bo5bo$53bo3bo
6bobo6bo3bo$57b2o5bobo5b2o$54bo9bobo9bo$55bo4bo3bobo3bo4bo$60b3obobob
3o$64bobo$58bo4bo3bo4bo$59bo3bo3bo3bo$61bo7bo9$111b2ob2o$107b2obo2b2o
2bo2bo2bo$107bo3bo4b2o2b4o$104b2obob2ob4o2b2o6bo$obobo28bo59bo10bobobo
bobo2bobo2b7o$31bo2bo20bo6b2o3b2o6bo15bo3bo10bo6bobobobo$o34bo20b2o4bo
bobobo4b2o20bo7bo2bo5b3o6b6o$26b2o2bo4bo17bo23bo12bo5b2obo4bob2o2bo5b
4o2b2obobo$obo23b2o2bo2b4o15bo4bo3bo7bo3bo4bo11b2o2b2obobob2obobo3b5o
8bo3bo$30bo5bo14bob2o2b2obobo5bobob2o2b2obo15bobo2bobobob4o4bobob4obob
ob2o$o30b5o14bo4bo2bobobobobobobobo2bo4bo14bobob2obob2o4b2o4b2o4bob2o
2bo$51b3obobo2bobobobobobo2bobob3o16b2obo2bo4b2o2bo3bo3b2obo3bo$o30b5o
17bo2bob2o3b2ob2o3b2obo2bo22bobob3ob2o5b2ob2ob2o3b2o$30bo5bo17bobo17bo
bo24b2obo$26b2o2bo2b4o18b2o17b2o$26b2o2bo4bo$35bo$31bo2bo$33bo!

It's sorted roughly by spark type. Oscillators with multiple sparks are included more than once. Unfortunately, I wasn't able to easily find all of the credits, so a few are missing.

[Bullet51]

It could better be a thumb:

Code: Select all

x = 14, y = 13, rule = B3/S23
4b2o$2obobo$2obo4bo$3bobo3bo$2obobo4bo$bobo4bobo$bob2obobobob2o$2bo3bo
b2o2bo$3b2ob2o4bo$4bo4b3o$4bob3obo$3b2obo5bo$11b2o!

[BlinkerSpawn]

It could better be a thumb:

Code: Select all

p9 sparker

Code: Select all

x = 14, y = 11, rule = B3/S23
4b2o$2obobo$2obo4bo$3bobo3bo$3bobo4bo$2obo4bobo$o2b2obobobobo$2bo3bob
2obobo$3b3obo3bobo$5bobo3b2o$6bo!

[Sokwe]

Code: Select all

x = 14, y = 11, rule = B3/S23
4b2o$2obobo$2obo4bo$3bobo3bo$3bobo4bo$2obo4bobo$o2b2obobobobo$2bo3bob
2obobo$3b3obo3bobo$5bobo3b2o$6bo!

That has a bit more clearance than the traditional p9 thumb on one side, but much less clearance on the other. The minimal population is one less, but with worse clearance:

Code: Select all

x = 14, y = 11, rule = B3/S23
4b2o$3bobo$3bo4bo$2obobo3bo$bobobo4bob2o$bobo4bobobo$2ob2obobobo2bo$2b
o3bob2o2b2o$2bob2obo$3bobobo$6bo!

[wwei23]

OH MY GOODNESS IS THIS A NEW PHOENIX(technically it's not an expansion of phoenix 1): ... EDIT: what about this?: ... or this: ...

It is ridiculously easy to create period 2 oscillators by combining small pieces together as one would toy train tracks. It's even easy to create glider syntheses of rectangular phoenixes like your last two examples. I have syntheses for those two that were last updated in 2002, and I think Dave Buckingham first synthesized them in the 1990s or earlier. You should familiarize yourself with some of the existing pattern collections, like jslife. You will find many expandable oscillators like this one there.

This is possible with P4 oscillators also, as mentioned in the soup search results thread:

Code: Select all

x = 11, y = 18, rule = B3/S23
o$o2bo$o2bo$bobo$bobo$3b2o$3b2o$4bobo$4bobo$4bobo$4bobo$6b2o$6b2o$7bobo$7bobo
$7bo2bo$7bo2bo$10bo!

Code: Select all

x = 44, y = 36, rule = B3/S23
$6bo8bo$6b3o4b3o$6b3o4b3o2$7b3o2b3o$7b2o4b2o5$6bo$6b3o$6b3o2$7b3o3b2o$
7b2o3b3o19b2o$32b4o$13b3o16bo$13b3o18bo$15bo16b3o$25bo6bo$25b3o4bo$25b
3o4b2o4b2o$33b2o2b3o$5bo20b3o2b2o$5b3o10bo7b2o4b2o4b3o$5b3o8b3o14bo4b
3o$33bo6bo$6b3o3b2o3b3o11b3o$6b2o3b3o3b3o11bo$19bo13bo$12b3o15b4o$12bo
17b2o!

And possible extensions to e.g.

Code: Select all

x = 17, y = 27, rule = B3/S23
$b2o$b4o$4bo$2bo$2b3o$4bo$5bo$5b3o$7bo$5bo$5b3o$7bo$8bo$8b3o$10bo$8bo$
8b3o$10bo$11bo$11b3o$13bo$11bo$11b4o$13b2o!

are trivial.[/quote]

[Sokwe]

A recent discovery by Jormungant gives some nice 2G-to-H converters:

Code: Select all

x = 26, y = 110, rule = B3/S23
8b2o$8bo$2o3b2obo$o4bobo$b3obo$3bob2o2$23bo$8b2o13bo$9b2ob2o9b3o$obo5b
o3b2o11bo$b2o$bo6$7b2obo$7b2ob3o$13bo$7b2ob3o$8bobo$8bobo$9bo6$8b2o$8b
o$2o3b2obo$o4bobo$b3obo$3bob2o2$23bo$8b2o13bo$9b2ob2o9b3o$8bo3b2o11bo
8$8b3o$8bo$9bo10$8b2o$8bo$2o3b2obo$o4bobo$b3obo$3bob2o2$23bo$8b2o13bo$
9b2ob2o9b3o$8bo3b2o11bo7$3o$2bo$bo11$8b2o$8bo$2o3b2obo$o4bobo$b3obo$3b
ob2o2$23bo$8b2o13bo$9b2ob2o9b3o$8bo3b2o11bo7$b2o$obo$2bo!

The first of these works at p52, although an extra glider stream is needed to suppress the first natural glider of the output herschel. If anyone can find a way to get 4 output glider from 3 input gliders, we might be able to build a p52 gun:

Code: Select all

x = 403, y = 269, rule = B3/S23
359b2o$360b2o$359bo2$298b2obo$298bob2o2$296b6o$296bo5bo4bo$298bobobo2b
3o$297b2obobobo$287b2o7bo5bobob2o$286bo2bo5bo2b3obo2bobo$84b2obob2o43b
2obob2o43b2obob2o43b2obob2o45bobobo3bob2o3bob2o41b2o$84bob2obobo42bob
2obobo42bob2obobo42bob2obobo45bobobo2bo2bo3bo3b2o40b2o$89bo2bo46bo2bo
46bo2bo46bo2bo46bo2bob2obob2ob2o3bo38bo$85b2ob2ob2o42b2ob2ob2o42b2ob2o
b2o42b2ob2ob2o45b2ob2o4b2o3bob2obo$86bobobo2b2o41bobobo2b2o41bobobo2b
2o41bobobo2b2o43bobo2b2obo3bo3bobo$86bobob2o3bo40bobob2o3bo40bobob2o3b
o40bobob2o3bo39b2obob2o3b2ob2o4bo$84b2obo4b3o39b2obo4b3o39b2obo4b3o39b
2obo4b3o38b3obo4b2o4bo2b3obo$83bo3bobo2bo40bo3bobo2bo40bo3bobo2bo40bo
3bobo2bo39bo4bobo2bob3obob2obobo$84b3ob4o42b3ob2o44b3ob4o42b3ob2o43b4o
b4o4bobob3o2bob2obo$86bo3bo45bobob2o44bo3bo45bobob2o39bobo2bo3bo7bo6bo
bob2o$78b2o8bob2o36b2o8bo39b2o8bob2o36b2o8bo41bobo5bob2o5bobo5bo$78bo
8b2o39bo8b2obo37bo8b2o39bo8b2obo38bobo5b2o8bo3bobobo2b3o$79bo10b2o37bo
9b2o38bo10b2o37bo9b2o38bo10b2o2b2obob2ob2obobo2bo$78b2o7b2o39b2o7b2obo
37b2o7b2o39b2o7b2obo37b2o7b2o6bobo4bob2o2bo24b2o$71b2ob2o2bo7bobobo30b
2ob2o2bo7bobob2o29b2ob2o2bo7bobobo30b2ob2o2bo7bobob2o29b2ob2o2bo7bobob
o3bo3b3o5bob2o24b2o$72bobobobo7bobo33bobo2b3o6bo35bobobobo7bobo33bobo
2b3o6bo35bobobobo7bobo6b3o2bob5o3bo22bo$72bobo2bo5b2obo2b2o31bobo3b2o
3b2obo3b2o30bobo2bo5b2obo2b2o31bobo3b2o3b2obo3b2o30bobo2bo5b2obo2b2o7b
o9b2o$70b2o2b4ob2obo2bob4o4b2o23b2o2b2o6bo2bob2ob2o3b2o23b2o2b4ob2obo
2bob4o4b2o23b2o2b2o6bo2bob2ob2o3b2o23b2o2b4ob2obo2bob4o4b2ob2obo3b3o$
71bobo3b2o4bobobo6bobo24bobo2b3o4bobobob2o3bobo24bobo3b2o4bobobo6bobo
24bobo2b3o4bobobob2o3bobo24bobo3b2o4bobobo8bobo8bo$obo67bo2b2o6b3obobo
3bo2bo25bo2b4obob4obobo2b2o2bo25bo2b2o6b3obobo3bo2bo25bo2b4obob4obobo
2b2o2bo25bo2b2o6b3obobo3bo3bo2bobob2o$b2o68b2o3b5o4bob2o3bob2o25b2o3bo
3bo4bob2o3bob2o25b2o3b5o4bob2o3bob2o25b2o3bo3bo4bob2o3bob2o25b2o3b5o4b
ob2o3bobob2o5bob2o$bo70bob2ob4ob2obo3bob2o2bo26bob2o6b2obo3b4o2bo26bob
2ob4ob2obo3bob2o2bo26bob2o6b2obo3b4o2bo26bob2ob4ob2obo3bob2obo3b5o6b2o
$72bo2bo6bobob2o5bo28bo2bobo2bobobob2o2bo2bo28bo2bo6bobob2o5bo28bo2bob
o2bobobob2o2bo2bo28bo2bo6bobob2o5bobobo2b3o4bo2bo$71b2obo2bo2bo3bo2b2o
b3o28b2obo2b4o3bo2bobob2o28b2obo2bo2bo3bo2b2ob3o28b2obo2b4o3bo2bobob2o
28b2obo2bo2bo3bo2b2ob3o2bob2o6b3obo$72bob5obobo2bo36bob2o2bobobo2bo36b
ob5obobo2bo36bob2o2bobobo2bo36bob5obobo2bo9bo7b2o4b2o$71bo5b4ob2ob4o6b
2o24bo10b2ob5o5b2o24bo5b4ob2ob4o6b2o24bo10b2ob5o5b2o24bo5b4ob2ob4o7b4o
bobob3o$70bob3obo3bo3bo5b4o2bo23bob4o4bo3bo3bob2obo2bo23bob3obo3bo3bo
5b4o2bo23bob4o4bo3bo3bob2obo2bo23bob3obo3bo3bo5b4o5bo3b2o2bob2o9b2o$
70bo3bobob2ob2obo2bo3bob3o24bo3bob2obob2obo2b2o4b3o24bo3bobob2ob2obo2b
o3bob3o24bo3bob2obob2obo2b2o4b3o24bo3bobob2ob2obo2bo3bob6obo3bo2bobo
11b2o$68b3o10bob2obobo2bo26b3o5bo2bobob2obo3b2o26b3o10bob2obobo2bo26b
3o5bo2bobob2obo3b2o26b3o10bob2obobo2bo5bo2b2o4b2o2bo9bo$67bo7b2obo7b2o
3b3o23bo7b2o9bo5b2o23bo7b2obo7b2o3b3o23bo7b2o9bo5b2o23bo7b2obo7b2o3b3o
b4ob2o2bo3b2o$67b2o9bo7bo7bo22b2o4b2obo2bo6bo3bo3bo22b2o9bo7bo7bo22b2o
4b2obo2bo6bo3bo3bo22b2o9bo7bo7b2ob2o2bo3b3o$69bo2bob2o2bo8b2ob3o2bo23b
o3b2obo10b2o2b2o2bo23bo2bob2o2bo8b2ob3o2bo23bo3b2obo10b2o2b2o2bo23bo2b
ob2o2bo8b2ob3o4bo5bo3bo$13bobo51b2o2bo2bob3o4b2o8b2o22b2o2bobobob2o4b
2o4bo2b3o22b2o2bo2bob3o4b2o8b2o22b2o2bobobob2o4b2o4bo2b3o22b2o2bo2bob
3o4b2o8b5ob2o2b3o$14b2o52bob2obobobo5b2o2b2o2bo26bob2obobo7b2o6bo26bob
2obobobo5b2o2b2o2bo26bob2obobo7b2o6bo26bob2obobobo5b2o2b2o2bo6b5o$14bo
53bobo2b2obo2b2o6b3obob2o23bobo2b7o8b3o2b2o23bobo2b2obo2b2o6b3obob2o
23bobo2b7o8b3o2b2o23bobo2b2obo2b2o6b3obob3o5bobo2bo$67b2obobo15bo4bo
23b2obobo5b2o9bobobo23b2obobo15bo4bo23b2obobo5b2o9bobobo23b2obobo15bo
4bo2bo2bo5bo$67bo3bob2ob3o4b2o3b3o2bo23bo3bob4o6b2o5b2obo23bo3bob2ob3o
4b2o3b3o2bo23bo3bob4o6b2o5b2obo23bo3bob2ob3o4b2o3b3o2bo2bo4b3o$68b2obo
2bo3bo4b2o3b3ob2ob2o21b2obo2bobo6b2o5b2obob2o21b2obo2bo3bo4b2o3b3ob2ob
2o21b2obo2bobo6b2o5b2obob2o21b2obo2bo3bo4b2o3b3ob2ob2o3bobo$69bobob2o
3bo10bo3bobo23bob2o3bo13bo2bobo23bobob2o3bo10bo3bobo23bob2o3bo13bo2bob
o23bobob2o3bo10bo3bobob2o3b2o$69bobob3o2bo11b2obo2bo7b2o13bobo4bo2bo
10b2obo2bo7b2o13bobob3o2bo11b2obo2bo7b2o13bobo4bo2bo10b2obo2bo7b2o13bo
bob3o2bo11b2obob2ob3ob2o3b2o$68b2obo2b2obo13bobob2o7bo13b2obob2o3bo12b
obob2o7bo13b2obo2b2obo13bobob2o7bo13b2obob2o3bo12bobob2o7bo13b2obo2b2o
bo13bobobobo10b2o$71bo3b2o14bobo8bobo16bob4o14bobo8bobo16bo3b2o14bobo
8bobo16bob4o14bobo8bobo16bo3b2o14bobo2bo10bo$71bo20b2o8b2o17bo2b2o16b
2o8b2o17bo20b2o8b2o17bo2b2o16b2o8b2o17bo20b2o$72b2o48b2o48b2o48b2o48b
2o13b2o$73bo49bo49bo14b2o33bo13b3o33bo13bobo$26bobo32bo8b3o15bo22bo8b
3o15b3o20bo8b3o15bobo20bo8b3o14bo23bo8b3o14bo23bo$27b2o32b3o6bo18b2o
20b3o6bo17bo22b3o6bo17bo22b3o6bo17bo22b3o6bo40b3o$27bo36bo24bo24bo10b
3o12bo23bo49bo14bo34bo14b2o33bo13b4o$47b2o14b2o10b3o8bo26b2o10b4o7bo
26b2o13b2o33b2o14b2o32b2o14bobo31b2o13bo2b2o$47bo26b2ob2o7bobo35b2o2b
2o6bo42b2o49b2o47bob2o46bo2b2o$39b2o3b2obo26b2o2bo7bobo3b2o31b2obo49b
2o50bo14b3o32b2o15bo31bo2bo$39bo4bobo29b2o14b4o29b3o13bo3bo30b3o16b3o
31bo50bo17b2o30b2o$40b3obo46bo4bo29bo16bo2b2o28bo15bobobobo26bobo13b2o
bobob2o43b2o2b3o$42bob2o44b4o2bo46bo3bo25b4o14b2obo3bo24bobo18bobo2bo
23b2o18b2o5bo$90b2obob2o25b3o18bo3bo25b2o17bobo2b2o13bobo30bob3o25bo
16b3o4bo14b2o25bo$59bobo10b3o15b2o21bo8b3o15b2o3b2o14b4o8b3o14bo5bo14b
o3bo9bo15b2o17bobo2b2o24b2o2bo3bo11bob4o23bobo$47b2o10bobobo9bo18b3o
16b2obo5b2o2bo16b4o20bo8bobo13b2obo2bo14bo4bo8bo15bo4bo13bo2b2o2bo23bo
5bo12b2obo3b2o22bo$48b2ob2o11b2o4b2ob2o26b2o9bob2o4b2o21bo7b2o8bo4bo2b
o2bo3bo12b2ob2obo5b2o8bo4bo4bobo18bo8b2o10b2o2bo33b2o8bo2b2ob2o$39bobo
5bo3b2o10bo7b3o2bobo9b2o11b2o11bo5b2o3b3o10b2o11b2o9b2obo4b6o12b2o11b
2o9bo3bo2b2o5bo11b2o3bo7b2o8b2o2bobo20b2o11b2o9b6o$40b2o30bo4bo11bo33b
ob3o11bo24bo6b2o2b2o12bo22bo2bo8bobo12bo34b3o12bo23bo13bo$40bo31b2o2bo
9b3o6bo28bobo9b3o6bo40b3o6bo40b3o6bo40b3o6bo29bobo$73b2o11bo8b3o24bo2b
o10bo8b3o28bo9bo8b3o26bo11bo8b3o26bo11bo8b3o10bo17b2o$74bo23bo24b3o22b
o24b3o22bo24bo2bo21bo8b3o13b2o23bo8b3o$97b2o48b2o24b3o21b2o8b3o13bo23b
2o8b3o13b2o22b2o7bo3bo$77b2o17bo4bo15b2o8b2o17bo10b3o7b2o8b2o17bo4bo4b
o3bo6b2o5bo3bo17bo9bo3bo6b2o8b2o17bo4bo6b2o7b2o3bo$77bobo16bo4bo5b3o6b
obo8bobo16b2ob3o4bo2bo6bobo8bobo16bo4bo4b2ob2o5bobo7b2obo16b2ob3o8bo5b
obo8bobo16bo4bo4b3o7bobo2bo$46b2obo29bo13b2obobo2b2o3bo2bo6bobob2o7bo
13b2obobo3bo2bo3bo6bobob2o7bo13b2obobo2b2o2bobo8bobob2o7bo13b2obobo3bo
3b2o8bobob2o7bo13b2obobo2b2o13bobobo3b2obo$46b2ob3o27b2o13bobobobobo2b
o9b2obo2bo7b2o13bobo4b3o11b2obo2bo7b2o13bobobobobo12b2obo2bo7b2o13bobo
4b3o11b2obo2bo7b2o13bobobobobo12b2obo2b2o5bo$52bo41bob2o3b2o2bo5bo2bo
3bobo23bobo5b2ob2o6bo4bobo23bob2o3b2o11bo3bobo23bobo5b3o8bo4bobo23bob
2o3b2o11bo3b2o4bo3bo$34b2o10b2ob3o15b2o24b2obo2bob2o3bo4bo2bo3bob2o21b
2obo6bo5bo2bo3b3ob2o21b2obo2bob2o5b2o4bo3bob2o21b2obo6b2o3b2o6b3ob2o
21b2obo2bob2o5b2o4bo3bobobo4bo$35b2o10bobo17bobo22bo3bob2ob2o5b3o3bo3b
o23bo3bob3ob2o4b2o5b2obo23bo3bob2ob2o5bo5bo3bo23bo3bob3ob2o4b2o2bo2b2o
bo23bo3bob2ob2o5b2o4bo3bobo4b3obo$34bo12bobo17bo24b2obobo6bo8bo2bobo
23b2obobo3bob2o4b2o7bo23b2obobo6bo8bo2bobo23b2obobo3bob2o13bo23b2obobo
6bo8bo2bobo11bo$48bo44bobo2bob3obo8b2obob2o23bobo2b4o6b2o4b2o2b2o23bob
o2bob3obo8b2obob2o23bobo2b4o12b2o2b2o23bobo2bob3obo8b2obob4obob3ob2o9b
o$93bob2obo5bo3b2o3bo2bo26bob2obo5bo3b2o2bob2o27bob2obo5bo3b2o3bo2bo
26bob2obo5bo3b2o2bob2o27bob2obo5bo3b2o3bo2bo12b2o7bobo$92b2o2bobobobo
5b2o3bobo2b2o22b2o2bo6bo4b2o4b2o2b2o22b2o2bobobobo5b2o3bobo2b2o22b2o2b
o6bo4b2o4b2o2b2o22b2o2bobobobo5b2o3bobo2b5obo3b2o9b2o$94bo6bobo8b6o2bo
23bo3b4ob2o7bo3b2o2bo23bo6bobo8b6o2bo23bo3b4ob2o7bo3b2o2bo23bo6bobo8b
6o4bob2o6bo$92b2o4bo2b2o8bo7bo22b2o5bobob2o6bobobo3bo22b2o4bo2b2o8bo7b
o22b2o5bobob2o6bobobo3bo22b2o4bo2b2o8bo7b2o2b3o3b4o$92bo6bob2o2bo5b2o
2bob2o23bo9bo8bo4b3o23bo6bob2o2bo5b2o2bob2o23bo9bo8bo4b3o23bo6bob2o2bo
5b2o2bob2ob2o3bo7b2o$93b3o7bo2bob2obo4bo26b3o5bob4ob2obobob2o26b3o7bo
2bob2obo4bo26b3o5bob4ob2obobob2o26b3o7bo2bob2obo4bo5bo2bo4bobo2bo$95bo
3bob4ob2obo2b2o4b3o24bo3bo2bobob2obo2bo5b3o24bo3bob4ob2obo2b2o4b3o24bo
3bo2bobob2obo2bo5b3o24bo3bob4ob2obo2b2o4b5o3bo5bobo$95bob5o3bo3bo5bob
2o2bo23bob3obo7bo3bob2obo2bo23bob5o3bo3bo5bob2o2bo23bob3obo7bo3bob2obo
2bo23bob5o3bo3bo5bob2o5bo3bobobob2o$96bo7bo2b2ob6o4b2o24bo8bob2ob3o3b
2o2b2o24bo7bo2b2ob6o4b2o24bo8bob2ob3o3b2o2b2o24bo7bo2b2ob6o5b8o2b2o$
21b2o57b2o15bob2ob2obobo2bo3b2o31bob2o4bobo2bo3bobo30bob2ob2obobo2bo3b
2o31bob2o4bobo2bo3bobo30bob2ob2obobo2bo3b2o4bo5bo2bo4b2o$22b2o56bobo
13b2obo2bo2bo3bo2b2ob3o28b2obo2b3o4bo2b2o2b2o28b2obo2bo2bo3bo2b2ob3o
28b2obo2b3o4bo2b2o2b2o28b2obo2bo2bo3bo2b2ob3o2bob2obo4b3obo$21bo58bo
16bo2bobo2bobobob2o5bo28bo2bobo2bobobob2obo3bo28bo2bobo2bobobob2o5bo
28bo2bobo2bobobob2obo3bo28bo2bobo2bobobob2o5bobobob3o5bo2bo$97bob2o6b
2obo3b2obo2bo26bob2o4bob2obo5b2o2bo26bob2o6b2obo3b2obo2bo26bob2o4bob2o
bo5b2o2bo26bob2o6b2obo3b2obobo3bo3b2o5b2o17bo$96b2o3b2ob2o4bob2o3bob2o
25b2o3bo8bob2obobob2o25b2o3b2ob2o4bob2o3bob2o25b2o3bo8bob2obobob2o25b
2o3b2ob2o4bob2o3bobob2o7bo20bobo$95bo2b2o3bob4obobo2b2o2bo25bo2b2obo3b
4obobo6bo25bo2b2o3bob4obobo2b2o2bo25bo2b2obo3b4obobo6bo25bo2b2o3bob4ob
obo2b2o3bo2b3o3b3o20b2o$96bobo4b2o3bobobo6bobo24bobo3b4o2bobobob2o3bob
o24bobo4b2o3bobobo6bobo24bobo3b4o2bobobob2o3bobo24bobo4b2o3bobobo8bobo
b4obobo$95b2o2b3o2bo2bo2bob2o6b2o23b2o2b2o3bo2bo2bobo2bo4b2o23b2o2b3o
2bo2bo2bob2o6b2o23b2o2b2o3bo2bo2bobo2bo4b2o23b2o2b3o2bo2bo2bob2o6b2o2b
obob2ob2o$97bobo2bobo3b2obo2b3o30bobo4bo3b2obo3bo31bobo2bobo3b2obo2b3o
30bobo4bo3b2obo3bo31bobo2bobo3b2obo2b3o6bo4bo4b2o$97bobo2bo8bo2bo32bob
obobo7bobobo31bobo2bo8bo2bo32bobobobo7bobobo31bobo2bo8bo2bo5b3o5b4o3bo
$96b2ob2o10bobob2o29b2ob2o2bo7bobo32b2ob2o10bobob2o29b2ob2o2bo7bobo32b
2ob2o10bobob2o2bo3b4o4bob2o$103b2o7b2o39b2o7b2ob2o36b2o7b2o39b2o7b2ob
2o36b2o7b2o6bobo7bo2bo$104bo10b2o37bo9bo39bo10b2o37bo9bo39bo10b2o2b2ob
4ob2obobo2bo$8b2o83b2o8bo8b2obo37bo8b2o39bo8b2obo37bo8b2o40bobo5b2obo
6bobo3bobo2b3o$9b2o82bobo7b2o8bob2o36b2o8bob2o36b2o8bob2o36b2o8bob2o
38bobo5bob2o5bobo2bo2bo$8bo84bo17bobobo45bobo47bobobo45bobo42bobo2bobo
bo7bo6bobob2o$109b3o4bo42b3obo2bo42b3o4bo42b3obo2bo41b4o4bo4bobobo2bob
ob2obo30bo$108bo3bobo2bo40bo3bobo2bo40bo3bobo2bo40bo3bobo2bo39bo4bobo
2bob3obob2obobo33bobo$109b2obob2ob3o39b2obob2ob3o39b2obob2ob3o39b2obob
2ob3o38b3obob2ob2o4bo4bobo34b2o$111bobob2o3bo40bobob2o3bo40bobob2o3bo
40bobob2o3bo39b2obob2o3b2ob3o3bo$111bobo4b2o41bobo4b2o41bobo4b2o41bobo
4b2o43bo4b2obo5bobobo$110b2obo2b2o42b2obo2b2o42b2obo2b2o42b2obo2b2o45b
o2b2o4b2obobob2obo$114bo2bo46bo2bo46bo2bo46bo2bo46bo2bob2obo4b2o3bo$
109bob2obobo42bob2obobo42bob2obobo42bob2obobo45bobobo2bo2bobobo3b2o$
109b2obob2o43b2obob2o43b2obob2o43b2obob2o45bobobo3bob2obobob2o$311bo2b
o5bo2b3obo2bobo$106b2o204b2o7bo5bobob2o$106bobo213b4obobo$106bo216bobo
bo2b3o$321bo5bo4bo$321b6o2$323bob2o$323b2obo25$84b2obob2o43b2obob2o43b
2obob2o43b2obob2o43b2obob2o43b2obob2o$84bob2obobo42bob2obobo42bob2obob
o42bob2obobo42bob2obobo42bob2obobo$89bo2bo46bo2bo46bo2bo46bo2bo46bo2bo
46bo2bo$85b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob
2ob2o$86bobobo2b2o41bobobo2b2o41bobobo2b2o41bobobo2b2o41bobobo2b2o41bo
bobo2b2o$86bobob2o3bo40bobob2o3bo40bobob2o3bo40bobob2o3bo40bobob2o3bo
40bobob2o3bo$84b2obo4b3o39b2obo4b3o39b2obo4b3o39b2obo4b3o39b2obo4b3o
39b2obo4b3o$83bo3bobo2bo40bo3bobo2bo40bo3bobo2bo40bo3bobo2bo40bo3bobo
2bo40bo3bobo2bo57b3o$84b3ob4o42b3ob2o44b3ob4o42b3ob2o44b3ob4o42b3ob2o
62bo$86bo3bo45bobob2o44bo3bo45bobob2o44bo3bo45bobob2o59bo$78b2o8bob2o
36b2o8bo39b2o8bob2o36b2o8bo39b2o8bob2o36b2o8bo$78bo8b2o39bo8b2obo37bo
8b2o39bo8b2obo37bo8b2o39bo8b2obo$79bo10b2o37bo9b2o38bo10b2o37bo9b2o38b
o10b2o37bo9b2o$78b2o7b2o39b2o7b2obo37b2o7b2o39b2o7b2obo37b2o7b2o39b2o
7b2obo$71b2ob2o2bo7bobobo30b2ob2o2bo7bobob2o29b2ob2o2bo7bobobo30b2ob2o
2bo7bobob2o29b2ob2o2bo7bobobo30b2ob2o2bo7bobob2o$72bobobobo7bobo33bobo
2b3o6bo35bobobobo7bobo33bobo2b3o6bo35bobobobo7bobo33bobo2b3o6bo62b2o$
72bobo2bo5b2obo2b2o31bobo3b2o3b2obo3b2o30bobo2bo5b2obo2b2o31bobo3b2o3b
2obo3b2o30bobo2bo5b2obo2b2o31bobo3b2o3b2obo3b2o56bobo$70b2o2b4ob2obo2b
ob4o4b2o23b2o2b2o6bo2bob2ob2o3b2o23b2o2b4ob2obo2bob4o4b2o23b2o2b2o6bo
2bob2ob2o3b2o23b2o2b4ob2obo2bob4o4b2o23b2o2b2o6bo2bob2ob2o3b2o53bo$71b
obo3b2o4bobobo6bobo24bobo2b3o4bobobob2o3bobo24bobo3b2o4bobobo6bobo24bo
bo2b3o4bobobob2o3bobo24bobo3b2o4bobobo6bobo24bobo2b3o4bobobob2o3bobo$o
bo67bo2b2o6b3obobo3bo2bo25bo2b4obob4obobo2b2o2bo25bo2b2o6b3obobo3bo2bo
25bo2b4obob4obobo2b2o2bo25bo2b2o6b3obobo3bo2bo25bo2b4obob4obobo2b2o2bo
$b2o68b2o3b5o4bob2o3bob2o25b2o3bo3bo4bob2o3bob2o25b2o3b5o4bob2o3bob2o
25b2o3bo3bo4bob2o3bob2o25b2o3b5o4bob2o3bob2o25b2o3bo3bo4bob2o3bob2o41b
3o$bo70bob2ob4ob2obo3bob2o2bo26bob2o6b2obo3b4o2bo26bob2ob4ob2obo3bob2o
2bo26bob2o6b2obo3b4o2bo26bob2ob4ob2obo3bob2o2bo26bob2o6b2obo3b4o2bo43b
o$72bo2bo6bobob2o5bo28bo2bobo2bobobob2o2bo2bo28bo2bo6bobob2o5bo28bo2bo
bo2bobobob2o2bo2bo28bo2bo6bobob2o5bo28bo2bobo2bobobob2o2bo2bo44bo$71b
2obo2bo2bo3bo2b2ob3o28b2obo2b4o3bo2bobob2o28b2obo2bo2bo3bo2b2ob3o28b2o
bo2b4o3bo2bobob2o28b2obo2bo2bo3bo2b2ob3o28b2obo2b4o3bo2bobob2o$72bob5o
bobo2bo36bob2o2bobobo2bo36bob5obobo2bo36bob2o2bobobo2bo36bob5obobo2bo
36bob2o2bobobo2bo$71bo5b4ob2ob4o6b2o24bo10b2ob5o5b2o24bo5b4ob2ob4o6b2o
24bo10b2ob5o5b2o24bo5b4ob2ob4o6b2o24bo10b2ob5o5b2o$70bob3obo3bo3bo5b4o
2bo23bob4o4bo3bo3bob2obo2bo23bob3obo3bo3bo5b4o2bo23bob4o4bo3bo3bob2obo
2bo23bob3obo3bo3bo5b4o2bo23bob4o4bo3bo3bob2obo2bo$70bo3bobob2ob2obo2bo
3bob3o24bo3bob2obob2obo2b2o4b3o24bo3bobob2ob2obo2bo3bob3o24bo3bob2obob
2obo2b2o4b3o24bo3bobob2ob2obo2bo3bob3o24bo3bob2obob2obo2b2o4b3o$68b3o
10bob2obobo2bo26b3o5bo2bobob2obo3b2o26b3o10bob2obobo2bo26b3o5bo2bobob
2obo3b2o26b3o10bob2obobo2bo26b3o5bo2bobob2obo3b2o44b2o$67bo7b2obo7b2o
3b3o23bo7b2o9bo5b2o23bo7b2obo7b2o3b3o23bo7b2o9bo5b2o23bo7b2obo7b2o3b3o
23bo7b2o9bo5b2o41bobo$67b2o9bo7bo7bo22b2o4b2obo2bo6bo3bo3bo22b2o9bo7bo
7bo22b2o4b2obo2bo6bo3bo3bo22b2o9bo7bo7bo22b2o4b2obo2bo6bo3bo3bo42bo$
69bo2bob2o2bo8b2ob3o2bo23bo3b2obo10b2o2b2o2bo23bo2bob2o2bo8b2ob3o2bo
23bo3b2obo10b2o2b2o2bo23bo2bob2o2bo8b2ob3o2bo23bo3b2obo10b2o2b2o2bo$
13bobo51b2o2bo2bob3o4b2o8b2o22b2o2bobobob2o4b2o4bo2b3o22b2o2bo2bob3o4b
2o8b2o22b2o2bobobob2o4b2o4bo2b3o22b2o2bo2bob3o4b2o8b2o22b2o2bobobob2o
4b2o4bo2b3o$14b2o52bob2obobobo5b2o2b2o2bo26bob2obobo7b2o6bo26bob2obobo
bo5b2o2b2o2bo26bob2obobo7b2o6bo26bob2obobobo5b2o2b2o2bo26bob2obobo7b2o
6bo32b3o$14bo53bobo2b2obo2b2o6b3obob2o23bobo2b7o8b3o2b2o23bobo2b2obo2b
2o6b3obob2o23bobo2b7o8b3o2b2o23bobo2b2obo2b2o6b3obob2o23bobo2b7o8b3o2b
2o31bo$67b2obobo15bo4bo23b2obobo5b2o9bobobo23b2obobo15bo4bo23b2obobo5b
2o9bobobo23b2obobo15bo4bo23b2obobo5b2o9bobobo31bo$67bo3bob2ob3o4b2o3b
3o2bo23bo3bob4o6b2o5b2obo23bo3bob2ob3o4b2o3b3o2bo23bo3bob4o6b2o5b2obo
23bo3bob2ob3o4b2o3b3o2bo23bo3bob4o6b2o5b2obo$68b2obo2bo3bo4b2o3b3ob2ob
2o21b2obo2bobo6b2o5b2obob2o21b2obo2bo3bo4b2o3b3ob2ob2o21b2obo2bobo6b2o
5b2obob2o21b2obo2bo3bo4b2o3b3ob2ob2o21b2obo2bobo6b2o5b2obob2o$69bobob
2o3bo10bo3bobo23bob2o3bo13bo2bobo23bobob2o3bo10bo3bobo23bob2o3bo13bo2b
obo23bobob2o3bo10bo3bobo23bob2o3bo13bo2bobo$69bobob3o2bo11b2obo2bo7b2o
13bobo4bo2bo10b2obo2bo7b2o13bobob3o2bo11b2obo2bo7b2o13bobo4bo2bo10b2ob
o2bo7b2o13bobob3o2bo11b2obo2bo7b2o13bobo4bo2bo10b2obo2bo$68b2obo2b2obo
13bobob2o7bo13b2obob2o3bo12bobob2o7bo13b2obo2b2obo13bobob2o7bo13b2obob
2o3bo12bobob2o7bo13b2obo2b2obo13bobob2o7bo13b2obob2o3bo12bobob2o$71bo
3b2o14bobo8bobo16bob4o14bobo8bobo16bo3b2o14bobo8bobo16bob4o14bobo8bobo
16bo3b2o14bobo8bobo16bob4o14bobo29b2o$71bo20b2o8b2o17bo2b2o16b2o8b2o
17bo20b2o8b2o17bo2b2o16b2o8b2o17bo20b2o8b2o17bo2b2o16b2o28bobo$72b2o
48b2o48b2o48b2o48b2o13b2o33b2o12b3o35bo$73bo49bo49bo14b2o33bo13b3o33bo
13bobo33bo12bo$26bobo32bo8b3o15bo22bo8b3o15b3o20bo8b3o15bobo20bo8b3o
14bo23bo8b3o14bo23bo8b3o14bo16bo$27b2o32b3o6bo18b2o20b3o6bo17bo22b3o6b
o17bo22b3o6bo17bo22b3o6bo40b3o6bo31b3o6b3o$27bo36bo24bo24bo10b3o12bo
23bo49bo14bo34bo14b2o33bo13b4o19bo11bo$47b2o14b2o10b3o8bo26b2o10b4o7bo
26b2o13b2o33b2o14b2o32b2o14bobo31b2o13bo2b2o18b2o9bo$47bo26b2ob2o7bobo
35b2o2b2o6bo42b2o49b2o47bob2o46bo2b2o$39b2o3b2obo26b2o2bo7bobo3b2o31b
2obo49b2o50bo14b3o32b2o15bo31bo2bo$39bo4bobo29b2o14b4o29b3o13bo3bo30b
3o16b3o31bo50bo17b2o30b2o16b2o$40b3obo46bo4bo29bo16bo2b2o28bo15bobobob
o26bobo13b2obobob2o43b2o2b3o44bo4b2o$42bob2o44b4o2bo46bo3bo25b4o14b2ob
o3bo24bobo18bobo2bo23b2o18b2o5bo44b2o3b2o$90b2obob2o25b3o18bo3bo25b2o
17bobo2b2o13bobo30bob3o25bo16b3o4bo14b2o28b2o3b2o9b2o$59bobo10b3o15b2o
21bo8b3o15b2o3b2o14b4o8b3o14bo5bo14bo3bo9bo15b2o17bobo2b2o24b2o2bo3bo
11bob4o23b2o7bo9bobo$47b2o10bobobo9bo18b3o16b2obo5b2o2bo16b4o20bo8bobo
13b2obo2bo14bo4bo8bo15bo4bo13bo2b2o2bo23bo5bo12b2obo3b2o22b2o18bo$48b
2ob2o11b2o4b2ob2o26b2o9bob2o4b2o21bo7b2o8bo4bo2bo2bo3bo12b2ob2obo5b2o
8bo4bo4bobo18bo8b2o10b2o2bo33b2o8bo2b2ob2o$39bobo5bo3b2o10bo7b3o2bobo
9b2o11b2o11bo5b2o3b3o10b2o11b2o9b2obo4b6o12b2o11b2o9bo3bo2b2o5bo11b2o
3bo7b2o8b2o2bobo20b2o11b2o9b6o20b2o$40b2o30bo4bo11bo33bob3o11bo24bo6b
2o2b2o12bo22bo2bo8bobo12bo34b3o12bo23bo13bo11bo$40bo31b2o2bo9b3o6bo28b
obo9b3o6bo40b3o6bo40b3o6bo40b3o6bo29bobo8b3o8b2o9b2o$73b2o11bo8b3o24bo
2bo10bo8b3o28bo9bo8b3o26bo11bo8b3o26bo11bo8b3o10bo17b2o8bo11bo8bo2bo$
74bo23bo24b3o22bo24b3o22bo24bo2bo21bo8b3o13b2o23bo8b3o35b3o10b2o$97b2o
48b2o24b3o21b2o8b3o13bo23b2o8b3o13b2o22b2o7bo3bo34bo$77b2o17bo4bo15b2o
8b2o17bo10b3o7b2o8b2o17bo4bo4bo3bo6b2o5bo3bo17bo9bo3bo6b2o8b2o17bo4bo
6b2o7b2o3bo$77bobo16bo4bo5b3o6bobo8bobo16b2ob3o4bo2bo6bobo8bobo16bo4bo
4b2ob2o5bobo7b2obo16b2ob3o8bo5bobo8bobo16bo4bo4b3o7bobo2bo34b2o$46b2ob
o29bo13b2obobo2b2o3bo2bo6bobob2o7bo13b2obobo3bo2bo3bo6bobob2o7bo13b2ob
obo2b2o2bobo8bobob2o7bo13b2obobo3bo3b2o8bobob2o7bo13b2obobo2b2o13bobob
o3b2obo28b2o$46b2ob3o27b2o13bobobobobo2bo9b2obo2bo7b2o13bobo4b3o11b2ob
o2bo7b2o13bobobobobo12b2obo2bo7b2o13bobo4b3o11b2obo2bo7b2o13bobobobobo
12b2obo2b2o5bo$52bo41bob2o3b2o2bo5bo2bo3bobo23bobo5b2ob2o6bo4bobo23bob
2o3b2o11bo3bobo23bobo5b3o8bo4bobo23bob2o3b2o11bo3b2o4bo3bo$34b2o10b2ob
3o15b2o24b2obo2bob2o3bo4bo2bo3bob2o21b2obo6bo5bo2bo3b3ob2o21b2obo2bob
2o5b2o4bo3bob2o21b2obo6b2o3b2o6b3ob2o21b2obo2bob2o5b2o4bo3bobobo4bo$
35b2o10bobo17bobo22bo3bob2ob2o5b3o3bo3bo23bo3bob3ob2o4b2o5b2obo23bo3bo
b2ob2o5bo5bo3bo23bo3bob3ob2o4b2o2bo2b2obo23bo3bob2ob2o5b2o4bo3bobo4b3o
bo$34bo12bobo17bo24b2obobo6bo8bo2bobo23b2obobo3bob2o4b2o7bo23b2obobo6b
o8bo2bobo23b2obobo3bob2o13bo23b2obobo6bo8bo2bobo11bo$48bo44bobo2bob3ob
o8b2obob2o23bobo2b4o6b2o4b2o2b2o23bobo2bob3obo8b2obob2o23bobo2b4o12b2o
2b2o23bobo2bob3obo8b2obob4obob3ob2o9bo$93bob2obo5bo3b2o3bo2bo26bob2obo
5bo3b2o2bob2o27bob2obo5bo3b2o3bo2bo26bob2obo5bo3b2o2bob2o27bob2obo5bo
3b2o3bo2bo12b2o7bobo$92b2o2bobobobo5b2o3bobo2b2o22b2o2bo6bo4b2o4b2o2b
2o22b2o2bobobobo5b2o3bobo2b2o22b2o2bo6bo4b2o4b2o2b2o22b2o2bobobobo5b2o
3bobo2b5obo3b2o9b2o$94bo6bobo8b6o2bo23bo3b4ob2o7bo3b2o2bo23bo6bobo8b6o
2bo23bo3b4ob2o7bo3b2o2bo23bo6bobo8b6o4bob2o6bo$92b2o4bo2b2o8bo7bo22b2o
5bobob2o6bobobo3bo22b2o4bo2b2o8bo7bo22b2o5bobob2o6bobobo3bo22b2o4bo2b
2o8bo7b2o2b3o3b4o$92bo6bob2o2bo5b2o2bob2o23bo9bo8bo4b3o23bo6bob2o2bo5b
2o2bob2o23bo9bo8bo4b3o23bo6bob2o2bo5b2o2bob2ob2o3bo7b2o$93b3o7bo2bob2o
bo4bo26b3o5bob4ob2obobob2o26b3o7bo2bob2obo4bo26b3o5bob4ob2obobob2o26b
3o7bo2bob2obo4bo5bo2bo4bobo2bo$95bo3bob4ob2obo2b2o4b3o24bo3bo2bobob2ob
o2bo5b3o24bo3bob4ob2obo2b2o4b3o24bo3bo2bobob2obo2bo5b3o24bo3bob4ob2obo
2b2o4b5o3bo5bobo$95bob5o3bo3bo5bob2o2bo23bob3obo7bo3bob2obo2bo23bob5o
3bo3bo5bob2o2bo23bob3obo7bo3bob2obo2bo23bob5o3bo3bo5bob2o5bo3bobobob2o
$96bo7bo2b2ob6o4b2o24bo8bob2ob3o3b2o2b2o24bo7bo2b2ob6o4b2o24bo8bob2ob
3o3b2o2b2o24bo7bo2b2ob6o5b8o2b2o$21b2o57b2o15bob2ob2obobo2bo3b2o31bob
2o4bobo2bo3bobo30bob2ob2obobo2bo3b2o31bob2o4bobo2bo3bobo30bob2ob2obobo
2bo3b2o4bo5bo2bo4b2o$22b2o56bobo13b2obo2bo2bo3bo2b2ob3o28b2obo2b3o4bo
2b2o2b2o28b2obo2bo2bo3bo2b2ob3o28b2obo2b3o4bo2b2o2b2o28b2obo2bo2bo3bo
2b2ob3o2bob2obo4b3obo$21bo58bo16bo2bobo2bobobob2o5bo28bo2bobo2bobobob
2obo3bo28bo2bobo2bobobob2o5bo28bo2bobo2bobobob2obo3bo28bo2bobo2bobobob
2o5bobobob3o5bo2bo$97bob2o6b2obo3b2obo2bo26bob2o4bob2obo5b2o2bo26bob2o
6b2obo3b2obo2bo26bob2o4bob2obo5b2o2bo26bob2o6b2obo3b2obobo3bo3b2o5b2o
17bo$96b2o3b2ob2o4bob2o3bob2o25b2o3bo8bob2obobob2o25b2o3b2ob2o4bob2o3b
ob2o25b2o3bo8bob2obobob2o25b2o3b2ob2o4bob2o3bobob2o7bo20bobo$95bo2b2o
3bob4obobo2b2o2bo25bo2b2obo3b4obobo6bo25bo2b2o3bob4obobo2b2o2bo25bo2b
2obo3b4obobo6bo25bo2b2o3bob4obobo2b2o3bo2b3o3b3o20b2o$96bobo4b2o3bobob
o6bobo24bobo3b4o2bobobob2o3bobo24bobo4b2o3bobobo6bobo24bobo3b4o2bobobo
b2o3bobo24bobo4b2o3bobobo8bobob4obobo$95b2o2b3o2bo2bo2bob2o6b2o23b2o2b
2o3bo2bo2bobo2bo4b2o23b2o2b3o2bo2bo2bob2o6b2o23b2o2b2o3bo2bo2bobo2bo4b
2o23b2o2b3o2bo2bo2bob2o6b2o2bobob2ob2o$97bobo2bobo3b2obo2b3o30bobo4bo
3b2obo3bo31bobo2bobo3b2obo2b3o30bobo4bo3b2obo3bo31bobo2bobo3b2obo2b3o
6bo4bo4b2o$97bobo2bo8bo2bo32bobobobo7bobobo31bobo2bo8bo2bo32bobobobo7b
obobo31bobo2bo8bo2bo5b3o5b4o3bo$96b2ob2o10bobob2o29b2ob2o2bo7bobo32b2o
b2o10bobob2o29b2ob2o2bo7bobo32b2ob2o10bobob2o2bo3b4o4bob2o$103b2o7b2o
39b2o7b2ob2o36b2o7b2o39b2o7b2ob2o36b2o7b2o6bobo7bo2bo$104bo10b2o37bo9b
o39bo10b2o37bo9bo39bo10b2o2b2ob4ob2obobo2bo$8b2o83b2o8bo8b2obo37bo8b2o
39bo8b2obo37bo8b2o40bobo5b2obo6bobo3bobo2b3o$9b2o82bobo7b2o8bob2o36b2o
8bob2o36b2o8bob2o36b2o8bob2o38bobo5bob2o5bobo2bo2bo$8bo84bo17bobobo45b
obo47bobobo45bobo42bobo2bobobo7bo6bobob2o$109b3o4bo42b3obo2bo42b3o4bo
42b3obo2bo41b4o4bo4bobobo2bobob2obo30bo$108bo3bobo2bo40bo3bobo2bo40bo
3bobo2bo40bo3bobo2bo39bo4bobo2bob3obob2obobo33bobo$109b2obob2ob3o39b2o
bob2ob3o39b2obob2ob3o39b2obob2ob3o38b3obob2ob2o4bo4bobo34b2o$111bobob
2o3bo40bobob2o3bo40bobob2o3bo40bobob2o3bo39b2obob2o3b2ob3o3bo$111bobo
4b2o41bobo4b2o41bobo4b2o41bobo4b2o43bo4b2obo5bobobo$110b2obo2b2o42b2ob
o2b2o42b2obo2b2o42b2obo2b2o45bo2b2o4b2obobob2obo$114bo2bo46bo2bo46bo2b
o46bo2bo46bo2bob2obo4b2o3bo$109bob2obobo42bob2obobo42bob2obobo42bob2ob
obo45bobobo2bo2bobobo3b2o$109b2obob2o43b2obob2o43b2obob2o43b2obob2o45b
obobo3bob2obobob2o$311bo2bo5bo2b3obo2bobo$106b2o204b2o7bo5bobob2o$106b
obo213b4obobo$106bo216bobobo2b3o$321bo5bo4bo46bo$321b6o50bobo$378b2o$
323bob2o$323b2obo!

p4 oscillators might be helpful here. There was some previous discussion of a potential p52 gun starting here.

More immediately, these new converters should allow us to simplify the true-period p54 and p55 guns. Here is the p55 gun:

Code: Select all

x = 189, y = 167, rule = B3/S23
65b2o$64bo2bo$59b2o2bob2obo$59bo3bo4bo$60b3obobob2o$62bobobo2bo$63bo3b
2o$63b2obo$53b2o7b2ob4o2b2o$53bobo6bo6bo2bo$54b4o5b3o2b2obo$56bo13bob
3o$60b2o8bo4bo$55bobo2b2o7b2ob2ob3o$55b2o11bo2b2obo3bo$63bo3b3o6bo2bo$
62bobo2b3o5b3obo63b2o$58b2o2b2o3b2o2bo2bo4bobo60bo2bo$58b2o8bob2o2b5ob
2o59bob2obo2b2o$68bo3bobobobo62bobo2bo3bo$70b2o2bobobo61b2o3bob3o$65bo
5bobobobo62bo2bobobo$66bo4bobo2bo64b3o3bo$64b3o5b2o7bo$79b3o55b2o2b4o
2bo7b2o$78bo58bo2bo6bo8bo$78b2o58bob2o3b2o5bo2bo$135b3obo5bo6b2o$134bo
4bo8b2o3bo$132b3ob2ob2o7b2o4bo$51b2o78bo3bob2o3bo10b2o$50bobo12b2o63bo
2bo5bo6bo$52bo12bo64bob3o4bo3bobobo$66b3o59bobo4bo2bo7b2o2b2o$68bo59b
2obobobob3obo8b2o$78bo52bo3bobo$79b2o50bobobo2b2o$78b2o52bobobobo$133b
o2bobo$128bo7b2o$128b3o$131bo20b2o$130b2o19b2o$138bobo12bo$37b2o99b2o$
38b2o99bo$37bo$143b2o$144bo$93bo47b3o$91bobo47bo$92b2o4$165b3o$125bo
39bo$124bo41bo$23b3o98b3o$25bo$24bo$184b2o$184bo$105bobo78bo$106b2o58b
2o14b5o$106bo60bo13bo$3b2o96b2o64bobo12b3o$4bo96bobo64b2o4bo10bo$2bo
100bo70b2obo4b4o$2b5o14b2o80b2o68bo4bo3bo3b2o$7bo13bo90bo65bo4b3o2bo$
4b3o12bobo79b4o5b2o65bo7bob2o$3bo9b3o3b2o80bo2bo6b2o72bo$3b4o6b2obo85b
o14b2obo63b2o$b2o3bo5bo3bo82b3o15b2ob3o$o2b3o7b3o83bo23bo$2obo9b3o101b
2ob3o53b2o$3bo114bobo55bo$3b2o104bo8bobo56b3o$108bobo8bo59bo$107bo$11b
2o94bo2bo49b2o$12bo93b2obo7b2o40bobo$9b3o93b3o8bo2bo41bo$9bo15b2o79b2o
b2o5bobo2bo2bo$25bobo78bo2b2o4b2obob5o$25bo81b3o3bo3b2o$108bo7b2o2b3o$
96b2o14bo3bobo2bobo$97bo18b2o2b2obo$97bobo13bo3b2o3bo$98b2o15b2obob2o$
116bobobo$116bobobobo$117bobobobo$119bobobo22b2o$118b2obob2o22b2o$116b
o3b2o3bo20bo$39b2o78b2o2b2obo$38b2o66b2o7bo3bobo2bobo$40bo67b2o9b2o2b
3o$102b2o5bo6bo3b2o$101bo7bo8b2obob5o$101bo6bo10bobo2bo2bo$101bo3b2o
12bo2bo$120b2o2$90b2o35bo$89bo2bo32b3o$84bo2bo2bobo31bo7b3o$84b5obob2o
30b2o8bo$90bo3bo38bo$52b3o31b2obo4bo24bobo$52bo32bo3b2o3bo16b2o7b2o$
53bo31bobobo4bo6b2o8bo8bo$86bo3bo3bo6bobo5bobo$87b2obob2o7bo7b2o$88bob
obo12bo8b2o$86bobobobo13bo6bobo5b2o$85bobobobo10b2o2bo6bo7b2o$85bobobo
13b3o6b2o$84b2obob2o13bo$83bo3bo3bo34bo$82bobobo4bo30b2obobo$82bo3b2o
3bo29bobobobo$67bo15b2obo4bo26bo2bobobobob2o$66b2o19bo3bo26b4ob2o2bo2b
o$66bobo12b5obob2o31bo4b2o$81bo2bo2bobo18b2o10bobo$86bo2bo18b2o10b2o$
87b2o$94bo$81bo10b2o23b2o$81b3o9b2o21bo2bo$84bo31bobo2bo2bo$83b2o30b2o
bob5o$106b2o7bo2bo$116bo2b4o$96b2o8b2o7bo2b2o3bo$80b2o15bo18bo2b3obo$
80bobo14bobo7bobo5bo2bo3bo$80bo17b2o8bo6b2obob2o$93b2o13bo7bobobo$86b
2o5bobo20bobobobo$86bobo6bo21bobobobo$88bo6b2o22bobobo$86bo21bo9b2obob
2o$82bo24bobo8bo2bo3bo$81bobobo23bo9bo2b3obo$81bob4o18bo2b2o8bo2b2o3bo
$78b2obobo3bo2bo13bo6bob2o4bo2b4o$78bo2bo2b2ob4o9bo4bobobobob2o3bo2bo$
80b2o4bo11bo4bo2bob2o3bo4b2obob5o$86bobo8bo5bo4bo3bo6bobo2bo2bo$87b2o
14bo5bobo7bo2bo$98bo2bo18b2o$99b3o7$97b2o$98bo24bo$95b3o26bo$95bo26b3o
!

The first two 2G-to-H converters work at p54. I'm not sure which one would be best to use. The p54 construction is likely more difficult, so I'm not going to do it.

[77topaz]

Hmm... in that p52 construction, would it be possible to avoid needing a 3G->4G reaction by replacing the eater 2 with some welded object that can also eat those first natural gliders?

[dvgrn]

Hmm... in that p52 construction, would it be possible to avoid needing a 3G->4G reaction by replacing the eater 2 with some welded object that can also eat those first natural gliders?

Unfortunately not -- or at least, I think the welded object would have to be something unlikely like an eater2 plus p13/p26/p52 oscillator with a nice spark. (And I haven't checked to see if p13 and p26 would really work anyway).

Look at the incoming gliders at the time that they suppress the FNGs -- the location is so close to the Herschel's reaction envelope that nothing stable can be placed there without interacting. The mechanism has to reach in there somehow and remove the FNG very early on, and then get back out of the way.

[77topaz]

Ah, I see what you mean now. I had mistakenly believed, due to the evolution of the incomplete pattern Sokwe posted, that suppressing the FNGs was only necessary to avoid them colliding with the eater 2 (which occurs relatively far from the reaction envelope), but from testing in Golly I see that the FNGs would also interfere with the converting reaction when that is in process.

However, now that I think about it, isn't there a complete database of all three-glider collisions? Shouldn't we already know whether or not a 3G->4G reaction exists? (Then again, I suppose this gun wouldn't require it to be a "pure" 3G->4G reaction, just something that converts 3G to 4G.)