Oscillator Discussion Thread

[dvgrn]

WLOG we can take the white cell to be ON in generation 0 and OFF in generation 2. Then we search for such a patch and find that it does not exist. Thus a period p phoenix does not exist. (I'm not sure how apg chooses the patch but I assume it's along the lines of start with 25x25, if there is a solution expand?)

Just while we're waiting for a more official writeup on this: here's an example pattern that APG posted on Discord to explain why 25x25 was chosen. The patch has to be centered on the key ON at T=0, OFF at T=2 cell, so its dimensions will be odd numbers. At 23x23 a SAT solver can still find solutions for a partly-period-4 patch of possible phoenix:

(pattern rotated to match EvinZL's diagram)

Code: Select all

x = 23, y = 23, rule = LifeHistory
4BCBC5BC9BC$C7BC3BCBCBCBCBCB$4BC3BCBC9BC$B2C7BC5BC3B$4BCBCBC5BC3BC3.A
$B2C7BCBC3BCB$6BCBC3BCBC2B3.2A$2BC5BCBC5B$4BC7BCBC5.A$4BC3BCBC3BA3.A$
2BC3BCBC4B3.A3.A$C5BC4BE6.A3.A$BCBC6B7.A3.A$5BCBCB.2A$2B2C4B5.A.A.A.A
.A$7BA.A.A.A$BC4B13.A.A$BCBCB4.A11.A$3BC$3B2.A3.A.A$BC.A.A$B6.A.A2.2A
$4.A!

But at 25x25 there apparently aren't any such patches that could theoretically be part of a larger p4 phoenix -- if you set up that SAT problem, you get UNSAT. It sounds like 25x25 was a big enough patch that all higher periods up to 69 have also returned zero solutions.

... Now I'm wondering whether there are any periods above 4 where 23x23 is a big enough patch after all -- i.e., maybe the odd periods actually get gradually easier to prove UNSAT for. Or if 25x25 is always both sufficient and necessary for periods 4 through 69, that would be interesting too!

[confocaloid]

[...]
Example of a mess : H to B + G + Tub

Code: Select all

x = 70, y = 68, rule = LifeHistory
7$35.2A$35.A$32.A4.A2.2A$32.5A.A2.A$18.2A16.B.2A.A.2A$19.A10.4AB3AB2.
A2.A$19.A.AB7.A2.A.A3B2A.A$20.2AB.3B4.7B2.A.2A$22.7B3.7B.A$22.16B.2A
14.2D$23.15B16.2B2D$22.16B15.2BDB$20.18B14.4B$18.19B14.4B$18.2BE15B
14.4B$17.3BEBE4B.7B6.2C6.4B$18.2B3E4B2.7B3.2B2CB4.4B$17.5BE4B2.9B.4B
4.4B$16.10B4.15B.4B$15.4B10.20B$15.3B11.19B$13.4B12.18B$13.2CB13.18B$
14.C13.20B$11.3C15.19B$11.C17.19B$30.17B$31.17B$34.14B$30.2B.15B$28.
19B$27.22B$24.2B.22B$21.23BD4B$20.2D21BDBD4B$19.2D23BD4B$20.2D27B$21.
D25B$25.22B$27.20B$27.15B3.2B.BC$28.3B3.6B4.BC2BC.C$28.3B5.3B5.C.C2BC
$29.B15.CB.B!

p311 oscillator, prime period

Code: Select all

x = 177, y = 130, rule = LifeHistory
169.A.2A$169.2A.A2$167.5A$167.A4.A2.2A$169.BAB.A2.A$169.B2A.A.A$167.A
4B.A.2A$166.ABAB3.A$166.A2BA2.2A$164.3B2A$160.7B$158.9B$157.10B$156.
11B$157.14B$157.14B$156.16B$155.17B$155.4B2A11B$150.9B2A10B$147.24B$
146.25B$146.24B$145.24B$144.26B$143.26B$142.29B$141.4B2A21B.2A$141.3B
A2BA18B3.A$141.4B2A8B.9B5.3A$142.6B2.4B3.8B7.A$146.B2.4B5.5B$148.4B5.
6B$147.4B5.7B$146.4B5.4B.2B$145.4B5.4B2.4B$144.4B5.4B5.2A$143.4B5.4B
6.A$113.2A27.4B5.4B8.3A$113.A27.4B5.4B11.A$110.A4.A2.2A20.4B5.4B$110.
5A.A2.A19.4B5.4B$96.2A16.B.2A.A.2A15.4B5.4B$78.2A17.A10.4AB3AB2.A2.A
14.4B5.4B$79.A17.A.AB7.A2.A.A3B2A.A15.4B5.4B$78.A19.2AB.3B4.7B2.A.2A
13.4B5.4B$50.B.BA15.B8.2A20.7B3.7B.A15.4B5.4B$49.A2BA.A5.3B5.3B8.B20.
16B.2A14.4B5.4B$48.A.A2BAB4.6B3.3B8.3B19.15B16.4B5.4B$49.AB.2B3.15B6.
6B16.16B15.4B5.4B$52.20B5.10B11.18B14.4B5.4B$52.22B3.11B3.2B2.20B14.
4B5.4B$52.11BA17B2A15BA15B14.4B5.4B$50.6B2A4BABA16B2A15BABA4B.7B6.2A
6.3AB5.4B$50.5BA2BA6BA32B3A4B2.7B3.2B2AB4.3BA5.4B$49.6BA2BA2BA2BA35BA
4B2.9B.4B4.3BA5.4B$50.6B2A3B3A40B4.15B.4B5.4B$50.22B.2B4.13B.4B10.20B
5.4B$50.22B7.7B.B4.4B11.19B5.4B$52.19B20.4B12.18B5.4B$51.15B.2B21.4B
13.18B4.A3B$50.15B24.4B13.20B2.BABA$49.19B20.4B15.19B.2B2A$48.21B19.
3B16.23B$47.23B16.3B19.21B$46.2A2B.19B15.4B20.19B$45.ABAB2.20B13.4B
24.15B$44.3BA4.18B13.4B21.2B.15B$43.4B5.18B12.4B20.19B$42.4B5.19B11.
4B4.B.7B7.22B$41.4B5.20B10.4B.13B4.2B.22B$40.4B5.4B.15B4.40B3A3B2A6B$
39.4B5.A3B4.4B.9B2.4BA35BA2BA2BA2BA6B$38.4B5.A3B4.B2A2B3.7B2.4B3A32BA
6BA2BA5B$37.4B5.B3A6.2A6.7B.4BABA15B2A16BABA4B2A6B$36.4B5.4B14.15BA
15B2A17BA11B$35.4B5.4B14.20B2.2B3.11B3.22B$34.4B5.4B14.18B11.10B5.20B
$33.4B5.4B15.16B16.6B6.15B3.2B.BA$32.4B5.4B16.15B19.3B8.3B3.6B4.BA2BA
.A$31.4B5.4B14.2A.16B20.B8.3B5.3B5.A.A2BA$30.4B5.4B15.A.7B3.7B20.2A8.
B15.AB.B$29.4B5.4B13.2A.A2.7B4.3B.B2A19.A$28.4B5.4B15.A.2A3BA.A2.A7.B
A.A17.A$27.4B5.4B14.A2.A2.B3AB4A10.A17.2A$26.4B5.4B15.2A.A.2A.B16.2A$
25.4B5.4B19.A2.A.5A$24.4B5.4B20.2A2.A4.A$11.A11.4B5.4B27.A$11.3A8.4B
5.4B27.2A$14.A6.4B5.4B$13.2A5.4B5.4B$13.4B2.4B5.4B$15.2B.4B5.4B$14.7B
5.4B$14.6B5.4B$14.5B5.4B2.B$4.A7.8B3.4B2.6B$4.3A5.9B.8B2A4B$7.A3.18BA
2BA3B$6.2A.21B2A4B$6.29B$8.26B$7.26B$8.24B$7.24B$6.25B$6.24B$6.10B2A
9B$5.11B2A4B$5.17B$5.16B$6.14B$6.14B$10.11B$10.10B$10.9B$10.7B$8.2A3B
$3.2A2.A2BA$3.A3.BABA$2A.A.4BA$.A.A.2AB$A2.A.BAB$2A2.A4.A$5.5A2$4.A.
2A$4.2A.A!

palindromium

[Tawal]

...
palindromium

Thanks a lot
It's a pleasure to see beautiful construction, especially from a useless semblance.

What means "palindromium" ?

Edit:
Ok I understand, in french it calls "vice versa"

[C28]

Is this p3 known?

Code: Select all

x = 9, y = 8, rule = B3/S23
2bo3b2o$bobobo2bo$ob2ob3o$o3bo$b2o2b3o$2bobo2bo$2bo2bo$3b2o!

[Sokwe]

Is this p3 known?

Code: Select all

x = 9, y = 8, rule = B3/S23
2bo3b2o$bobobo2bo$ob2ob3o$o3bo$b2o2b3o$2bobo2bo$2bo2bo$3b2o!

This is a stator variant of stillater. Back in 2021 Extrementhusiast enumerated the p3 rotors fitting in a 5x5 box.

[Sokwe]

Surely this [trivial p10] is completable!

Code: Select all

x = 27, y = 37, rule = B3/S23
4b2o9bob2o$3bo2bo6b2o3bo2b2o$2bo2bo11bo3bo2b2o$bob2o3b2o5bo6b2obo$b2o
2b4obo4bo7bo$4bo5bo6bo5bo$b2obo2b2o3b2obobo2b2obobo$b2ob4obo4bo2bo3bo
2b2o$15bo3bobo$6b2ob2o5bo2b2o$7bob2o2bob2o$7bobo2b2ob2o$4b2obobobo3bo
3b2o$4b2obobo3b2o2bo2bo$7bo3bo3b2ob2o$7b4o3bo3bo$10bo7bo$4b2o3b2obo3bo
b2o$3bo2bo2bobo3bo3b2o$4b2obobobo3bobo2bobo$7b2obo5b2o2bo3bo$8b3o7bobo
4bo$5bobo8b3o2bo3bo$3b2o2b2o2b2o3bo4bob2o$4b2obo5bo3b2o2bo$5bo6b2o5b4o
$4bo2b2o14bo$3b2ob3o7bob3o$2b3ob2obo6bob4obob2o$6bo2b2o10b3obo$2b2o2bo
b3o6bo7bo$b3o5bo7bob2obo2bo$4b5obo5b2obo3bo$2bobobo3bo8b2o3bo$5o10b2o
5bob2o$bo2bo2b3o$2bob2o3b2o!

Sadly, LLSSS is not doing very well at p5 searches.

It's easy with JLS if you don't care about the size of the solution. I produced the following in a few minutes:

Code: Select all

x = 49, y = 54, rule = B3/S23
5b2o$5bo15b2o5b2o4b2o$6bo14bo5bo2bo4bo$3b4o8b2ob2obo5b2obo4bob2o3b2obo
$3bo12bobo2b2o7b2o2b2obobo2bob2o2bo$6b3o6bo4bo2bob4o4bo3bo2bobo3b3o$6b
o2bo6b5o2bobo3b3o3b2obobo2b2o$8b2o8bobo2b2o3bo7bo4bobob2o$2o12b3o6b2o
2b2obo3bo4b2o2bobobo$obo2b3o5bo3bo2b3o4bobobobo3b2o3bobo3bo$9b3o2bo2bo
b2obo2bob2o5bo3bo8b2o$o2b2obobob3obo4b2ob5obo2b2obob5o3bo$bo5bo5bobo8b
o6bo2bobo4bo2b5o$bo4bo3b2obo18bobo2b4o7bo$6bo4bo5bo11b3o2bo6b5o$12bobo
3b2o9bo4b2o3bo2bo2bo$4b2o3b2o4b3o2b2o17b2o$3bo3bob5obob3obo3b2o$3b2obo
8bo4b2o3bo2bo$4bob2ob7o3b2ob2obob2o$4bo2bobo12b2obo$5b2o5b2o4bobo4bo$
12bo7b5ob2o$9b2obo3b2o3bo2bobo$10bob2obo4bo2bo2bo$9bo3bobo2bo3b2obo$
10b3o2bobo2bo2bob2o$12bobo2bo3bobo2bo$14b4o2b3obo$13bo3b2o5b2o$12bo2bo
6bo$13b2obo6b3o$14bo6b2o3bo$14bob2o4bobo2bo$11b2obo4bob2ob4o$12bob2obo
bo3bo$12bo4b4obo2bo$13b3o6bob2o$15b2o3bobo$18bo2b2o$15b4obo2b2o$15bo2b
o2b2o2bo$16bobo4bobo$15b2obo2b3ob2o$15bo2b2obo2bo$13bobob2o2b2obo$13b
2o2b2o4bo$17b2o2b2o$18bo2bo$19bobo$18b2ob2o$19bobo$19bobo$20bo!

[qqd]

Surely this [trivial p10] is completable!

Code: Select all

RLE

Sadly, LLSSS is not doing very well at p5 searches.

It's easy with JLS if you don't care about the size of the solution. I produced the following in a few minutes:

Code: Select all

RLE

For those who can't recognize the p2 and p5 parts:

Code: Select all

x = 49, y = 54, rule = LifeSuper
5.2A$5.A15.2A5.2A4.2A$6.A14.A5.A2.A4.A$3.4A8.2A.2A.A5.2A.A4.A.2A3.2A.
A$3.A12.A.A2.2A7.2A2.2A.A.A2.A.2A2.A$6.3A6.A4.A2.A.4A4.A3.A2.A.A3.3A$
6.A2.A6.5A2.A.A3.3A3.2A.A.A2.2A$8.2A8.A.A2.2A3.A7.A4.A.A.2A$2G12.3A6.
2A2.2A.A3.A4.2A2.A.A.A$G.G2.3A5.A3.A2.3A4.A.A.A.A3.2A3.A.A3.A$9.3A2.A
2.A.2A.A2.A.2A5.A3.A8.2A$G2.GA.A.A.3A.A4.2A.5A.A2.2A.A.5A3.A$.G5.A5.A
.A8.A6.A2.A.A4.A2.5A$.G4.A3.2A.A18.A.A2.4A7.A$6.A4.A5.A11.3A2.A6.5A$
12.A.A3.2A9.A4.2A3.A2.A2.A$4.2A3.2A4.3A2.2A17.2A$3.A3.A.5A.A.3A.A3.2A
$3.2A.A8.A4.2A3.A2.A$4.A.2A.7A3.2A.2A.A.2A$4.A2.A.A12.2A.A$5.2A5.2A4.
A.A4.A$12.A7.5A.2A$9.2A.A3.2A3.A2.A.A$10.A.2A.A4.A2.A2.A$9.A3.A.A2.A
3.2A.A$10.3A2.A.A2.A2.A.2A$12.A.A2.A3.A.A2.A$14.4A2.3A.A$13.A3.2A5.2A
$12.A2.A6.A$13.2A.A6.3A$14.A6.2A3.A$14.A.2A4.A.A2.A$11.2A.A4.A.2A.4A$
12.A.2A.A.A3.A$12.A4.4A.A2.A$13.3A6.A.2A$15.2A3.A.A$18.A2.2A$15.4A.A
2.2A$15.A2.A2.2A2.A$16.A.A4.A.A$15.2A.A2.3A.2A$15.A2.2A.A2.A$13.A.A.
2A2.2A.A$13.2A2.2A4.A$17.2A2.2A$18.A2.A$19.A.A$18.2A.2A$19.A.A$19.A.A
$20.A!

[pzq_alex]

For those who can't recognize the p2 and p5 parts:

Code: Select all

rle

(alternatively, use Pattern -> Identify, then click Map on the right)

[b-engine]

(alternatively, use Pattern -> Identify, then click Map on the right)

For those Golly users, remember to do this ONLY in LifeViewer, by clicking SHOW IN VIEWER before performing the step above.

Code: Select all

#Click for example
3o!

[JP21]

Surely this [trivial p10] is completable!

Code: Select all

rle

Sadly, LLSSS is not doing very well at p5 searches.

It's easy with JLS if you don't care about the size of the solution. I produced the following in a few minutes:

Code: Select all

rle

Trivial p15 (p3 part found with WLS):

Code: Select all

x = 66, y = 54, rule = B3/S23
11bo2bo7b2o$11bo2bo7bo15b2o5b2o4b2o$8bob2o2b2o7bo14bo5bo2bo4bo$7bobo5b
3o2b4o8b2ob2obo5b2obo4bob2o3b2obo$8bo11bo12bobo2b2o7b2o2b2obobo2bob2o
2bo$b2o20b3o6bo4bo2bob4o4bo3bo2bobo3b3o$2bo2b2o5b2o2b3o4bo2bo6b5o2bobo
3b3o3b2obobo2b2o$2bobob3o2bobo11b2o8bobo2b2o3bo7bo4bobob2o$2o2bobo2bo
2b2obo15b3o6b2o2b2obo3bo4b2o2bobobo$bobo3b2o2bo2b6o2b3o5bo3bo2b3o4bobo
bobo3b2o3bobo3bo$bob3o2bob2o2bobo9b3o2bo2bob2obo2bob2o5bo3bo8b2o$2obo
2bobobo7bob2obobob3obo4b2ob5obo2b2obob5o3bo$bob2obobobo4b2o7bo5bobo8bo
6bo2bobo4bo2b5o$bobo2bo2bo7b2o4bo3b2obo18bobo2b4o7bo$2bo2b2o7b2obo5bo
4bo5bo11b3o2bo6b5o$11bo5bo11bobo3b2o9bo4b2o3bo2bo2bo$9bobobo2bo4b2o3b
2o4b3o2b2o17b2o$13bo6bo3bob5obob3obo3b2o$8bob3ob3o3b2obo8bo4b2o3bo2bo$
8bo12bob2ob7o3b2ob2obob2o$9b2ob2o7bo2bobo12b2obo$10bob2o8b2o5b2o4bobo
4bo$10bo18bo7b5ob2o$9b2o15b2obo3b2o3bo2bobo$27bob2obo4bo2bo2bo$26bo3bo
bo2bo3b2obo$27b3o2bobo2bo2bob2o$29bobo2bo3bobo2bo$31b4o2b3obo$30bo3b2o
5b2o$29bo2bo6bo$30b2obo6b3o$31bo6b2o3bo$31bob2o4bobo2bo$28b2obo4bob2ob
4o$29bob2obobo3bo$29bo4b4obo2bo$30b3o6bob2o$32b2o3bobo$35bo2b2o$32b4ob
o2b2o$32bo2bo2b2o2bo$33bobo4bobo$32b2obo2b3ob2o$32bo2b2obo2bo$30bobob
2o2b2obo$30b2o2b2o4bo$34b2o2b2o$35bo2bo$36bobo$35b2ob2o$36bobo$36bobo$
37bo!

[amling]

Surely this [trivial p10] is completable!

Code: Select all

rle

Sadly, LLSSS is not doing very well at p5 searches.

It's easy with JLS if you don't care about the size of the solution. I produced the following in a few minutes:

Code: Select all

rle

Trivial p15 (p3 part found with WLS):

Code: Select all

(snip)

An analogous p4 side is easy enough and with a slight resolve of one of the p5 branches provides both a trivial p12 and p20:

Code: Select all

x = 84, y = 72, rule = B3/S23
9$24bob2ob2o$24b2ob2o2bo$30bo$24b5ob2o$23bo4b2o3b2o$23b4o4b2obo$32bo$
25bo6bo5b2o18b2ob2o$25b7ob2o3bobo2bo11bo3bobo$33bobo2b7o9bo3bo2bo$27b
3o3bob4o4b2o10bo2bobo$34b2o2bobobo7b6ob2ob2o$26bo2bo6b3obob2o2b2o6bo4b
o2bo$23b4o2bo10bobo2b2o3bo10b2o$23b3ob6o2bob3o2bo5bobobo2bo$30bobo4bo
4b2o10b2o$31bo3b2o$28bobo4b2obobo$28b3obo4bob2o$29bobobobobo$29bobob2o
2bo$26b2o3bobobobob2o$27bo3b5ob2obo$27bob2obobobo$28b2obo6b2o$33bobob
2o$28b2o10bo$30bob2o3b4o$33b5o$15b2o11b2obobob6o$12bob4o10b2obo5bo2bo$
11bo15bobob2o4bo$10bo3bo2bobo12bo5b2o$11b2o6b2o6bobo2bo3bo$4b2o13b2o8b
2ob2o2bo2bo$5bo2bo6bo4b2o4b2ob4o3bobobo$5bobob2obobob2o11bobo2b3ob2o$
3b2o2bobo2bobo17bo2bobo$4bobo4bo5b2o2b2o2b2o2bobob3obo$4bo2b2o2bob2o3b
2obo4bo2b2o5bo$3b2obo2bobobo5bob5o3b2o$4bob2obobobo4b2o2bo2bo3b2o15b2o
$4bobo2bo2bo6bo2bo2bob2obo13bo2bo$5bo2b2o6b3obo5b2obo2bo2b2ob2o4b2o$
14bo4bo7bobob2ob2o3bo$12b3ob4o7bo2bo3b2ob2o3b4o$12bobobobo12bob3o5bobo
2bobo$11b3obo3bo8b4obo3b2o3bo2bob2o$11bo6bo14b2obobo2bo2b2o$12b2obo18b
obo6bobo$13bob2o18bob8o$13bo23bo$12b2o23bob2o2b4o$38bobo2bo2bo!

Code: Select all

x = 97, y = 99, rule = B3/S23
7$50bob2ob2o$50b2ob2o2bo$56bo$50b5ob2o$49bo4b2o3b2o$49b4o4b2obo$58bo$
51bo6bo5b2o18b2ob2o$51b7ob2o3bobo2bo11bo3bobo$59bobo2b7o9bo3bo2bo$53b
3o3bob4o4b2o10bo2bobo$60b2o2bobobo7b6ob2ob2o$52bo2bo6b3obob2o2b2o6bo4b
o2bo$49b4o2bo10bobo2b2o3bo10b2o$49b3ob6o2bob3o2bo5bobobo2bo$56bobo4bo
4b2o10b2o$57bo3b2o$54bobo4b2obobo$54b3obo4bob2o$55bobobobobo$55bobob2o
2bo$52b2o3bobobobob2o$53bo3b5ob2obo$53bob2obobobo$54b2obo6b2o$59bobob
2o$54b2o10bo$42b2o12bob2o3b4o$42bo16b5o$45b4o5b2obobob6o$18b2o4b2o5b2o
11b3obo5b2obo5bo2bo$18bo4bo2bo5bo11b3o6bobob2o4bo$8bob2o3b2obo4bob2o5b
ob2ob2o19bo5b2o$5bo2b2obo2bobob2o2b2o7b2o2bobo15bobo2bo3bo$5b3o3bobo2b
o2bo5b4obo2bobo2bo7b2o7b2ob2o2bo2bo$9b2o2b3o2bo3b3o3bobo2bob3o6bo2bo4b
2ob4o3bobobo$7b2obobo5bo3bo2b2obo2bo12bo2bo7bobo2b3ob2o$6bo3bob3o7b2o
2b4o7b3o5bobo10bo2bobo$5bob2obo2bo5b2o4bo2b3ob2o2bo3bo6b2o2b2o2bobob3o
bo$5b2obobo6bo7bo2bobo5bob2o4b2o6bo2b2o5bo$9b2o2b2o2bobobo2bo3bo5bo3b
2o8b4o3b2o$5b5o2bo4bobo2bo11bo3bob5o3bo2bo3b2o15b2o$5bo7b4o2bobo17b2ob
ob3obo2bob2obo13bo2bo$8b5o6bo2b3o10bo3bo4bo2bo4b2obo2bo2b2ob2o4b2o$8bo
2bo2bo3b2o4bo8b3o3bob2o10bobob2ob2o3bo$13b2o17bo3bob2obo3b2ob2o3bo2bo
3b2ob2o3b4o$27b2o6bo2b2o3b3o4bo6bob3o5bobo2bobo$25bo2bo4bo4bo8bob2o3b
4obo3b2o3bo2bob2o$25b2obob5o3b7ob2obo9b2obobo2bo2b2o$28bob2o12bobo2bo
10bobo6bobo$28bo6bo4b2o5b2o12bob8o$26b2ob2ob4o5bo21bo$27bobo2b2ob3o3bo
b2o18bob2o2b4o$27bo2bob2o4bob2obo20bobo2bo2bo$28bobobo3bobobo3bo$27b2o
bob3obobo2b3o$27bo2bo2b4o2bobo$29bob2obo2b3o$28b2obo3b2o3bo$31bo3b4o2b
o$28b3obo6b2o$27bo3b3o5bo$26bo2bo3bo2b2obo$26b4ob3o2bo2bob2o$30bo3bobo
b2obo$28bo2bob2o6bo$28b2obobob2ob3o$31bo3bob2o$31bo$29b2o2bobob2o$28bo
2b3obo2bo$28bobo4bobo$27b2ob2obobob2o$29bo4bo3bo$29bob4o3bobo$30bo3bo
4b2o$31b2obo$32bobo$32bo3bo$31b2ob2o$32bobo$32bobo$33bo!

[carsoncheng]

I realized that the general-case phoenix problem proof (which is the non-existence of non-p2 finite phoenices in Life) has not made it to the forums yet (it's already been on the discord since yesterday), and so I'll summarize apgoucher's proof here:

Yes... at a high level the proof proceeds as follows:
1. prove that no 2x2 square of a finite phoenix (of any period) can contain more than 2 live cells;
2. deduce the correctness of wwei23's table at https://conwaylife.com/wiki/User_talk:P ... ransitions
3. suppose that we have a finite phoenix of some period other than 2, and consider the first (by diagonal reading order) cell that's not vacuum or p2;
4. there must be some time T such that the cell is off at generation T and on at generation T+2;
5. run a SAT solver on the 29x29x32 spacetime cuboid that's spatially centred on that 'first non-p2 cell' and consists of generations [T-17, T+14] to determine all possible 39-cell patches that are locally consistent with these constraints in this cuboid;
6. for each of the 20 different patches that arise in this manner, set up a new SAT problem to find all 39-cell patches that can be the grandparent of each of these patches;
7. keep repeating this until we obtain the set of all possible 39-cell patches that can occur at any time T-2*k (k >= 0) in the history;
8. note that all 197 of these patches have the central cell OFF, so can't match generation T+2 which has central cell ON;
9. as such, it can't be periodic at all (because even if the phoenix had odd period p, then it would also be periodic with period 2p, which is ruled out).

This also means that all finite phoenices in Life are of constant population:

As a corollary, we establish the conjecture on https://conwaylife.com/wiki/Phoenix that every (finite) phoenix has constant population: if you consider the arrangement of red and blue cells, corresponding to cells that are live in odd and even generations, then every red cell has 3 blue neighbours and every blue cell has 3 red neighbours, so there are equally many of each colour. (Every infinite phoenix technically has constant population too -- because its population is aleph_0 in every generation -- but there are examples of higher-period phoenix agars where the population density is non-constant.)

He said that a cp4space article on the phoenix proof will be written up soon.
EDIT: The cp4space article is on https://cp4space.hatsya.com/2024/01/20/every-finite-phoenix-has-period-2/ now

[hotcrystal0]

Is a completion of this oscillator partial from 2020 possible?

If it were not those pesky 2 cells...

Code: Select all

x = 12, y = 12, rule = LifeHistory
2.2C$3.C$C2.4C2.2C$3C2.3C.2C$2.C6.C$2.2C5.2C$2.2C6.C$3.C7.C2$2.4C$2.
2C.2C$7.C!

[JP21]

Is a completion of this oscillator partial from 2020 possible?

If it were not those pesky 2 cells...

Code: Select all

x = 12, y = 12, rule = LifeHistory
2.2C$3.C$C2.4C2.2C$3C2.3C.2C$2.C6.C$2.2C5.2C$2.2C6.C$3.C7.C2$2.4C$2.
2C.2C$7.C!

yes

Code: Select all

x = 29, y = 29, rule = B3/S23
2b2o$3bo$o2b4o2b2o$3o2b3ob2o$2bo6bo7bo$2b2o5b2o4b3o$2b2o6bo3bo$3bo7bo
3b5o$13b2o3bobob2o$2b4o4bo2bob2o2b2obobo$2b2ob2o2bobo3b2o3bobo2bo$7bo
2bo2bo4b2o3bobo$14b4obob3ob2o$8b2obo5bobo6bo$6bobo3bo3b10o$5bobob2obo
3bo5bo5bo$5bobob2obob2o2b3o4b4o$4b2obo4b3o3b2o4bo$7b2o2bo2bob2obob2obo
2b2o$7bobob4ob3o2b4o3bo$8b3o3bobo8b3o$12bobo3b2o2b2obo$8b3obob2o2b2obo
2bo$8bo2b2obo4bobobo$9bo4bo2b3o2bo$10b3obobo3b2o$12b2o2bo3bo$16bobobo$
15b2ob2o!

[Bullet51]

Is a completion of this oscillator partial from 2020 possible?

If it were not those pesky 2 cells...

Code: Select all

yes

Code: Select all

This is meant to be completed as a strictly-volatile p4 instead of just a p4.

[JP21]

This is meant to be completed as a strictly-volatile p4 instead of just a p4.

I realized that when I saw the partial, and even motivated me to try finding a smaller strictly volatile p4 hours earlier, but I got nothing.

At least a part of that partial were included four times in the strictly volatile p4:

Strictly volatile p4 oscillator, I think.
Might be reduced.

Code: Select all

x = 70, y = 70, rule = B3/S23
35bo$24bo10bo$24bobo2b3o2b3o$9b2o9bo3bo4b3o$12bo6bobo2b4ob2o$7bo2bo3bo
2bo8bo5b2o4b2o9bo$7bobo4bob4o2bobo7b10o5bobo$13bo5bo3bo10b2o4b2o7bo3bo
9b2o$8bo8bobo23b2ob4o2bobo6bo$11bo7bo22b3o2bo8bo2bo3bo2bo$9b2o26b3o2b
3o4bobo2b4obo4bobo$38bo11bo3bo5bo$10bo27bo15bobo8bo$9b2obo41bo7bo$10bo
52b2o$8bob4o$7bo55bo$8bo52bob2o$10bo52bo$11bo48b4obo$5b4obo55bo$8bo56b
o$6bob2o53bo$8bo53bo$63bob4o$8b3o54bo$8b3o53b2obo$9b2o54bo$6b2o$6b2o
57b3o$5b2o3bo54b3o$5b2o3b3o53b2o$6bo3bo52b2o$2bo3bo56b2o$3o3b2o54b2o3b
o$2bo3b2o54b2o3b3o$5b2o56bo3bo$5b2o52bo3bo$2b2o53b3o3b2o$2b3o54bo3b2o$
2b3o57b2o$62b2o$4bo54b2o$2bob2o53b3o$4bo54b3o$b4obo$7bo53bo$6bo53b2obo
$4bo56bo$3bo55bob4o$4bob4o48bo$6bo52bo$5b2obo52bo$6bo55bo$56b4obo$5b2o
52bo$7bo7bo41bob2o$4bo8bobo15bo27bo$9bo5bo3bo11bo$3bobo4bob4o2bobo4b3o
2b3o26b2o$3bo2bo3bo2bo8bo2b3o22bo7bo$8bo6bobo2b4ob2o23bobo8bo$5b2o9bo
3bo7b2o4b2o10bo3bo5bo$20bobo5b10o7bobo2b4obo4bobo$20bo9b2o4b2o5bo8bo2b
o3bo2bo$39b2ob4o2bobo6bo$38b3o4bo3bo9b2o$33b3o2b3o2bobo$34bo10bo$34bo!

And today I decided I'll briefly explain this (since I didn't before):

It's very close, but not close enough.

Code: Select all

x = 42, y = 24, rule = B3/S23
23bo5bo$22bobo4bo$12bo12b2ob2obob2o$12bo6b2o9b2o3bo$7b2obob2o2bob2o2b
2obo4b2o$6bo3b2o9b2o6bo4bo2bo$10b2o3b2o12b2o4b2o$4bo2bo4bo4bobo9bo7b2o
$5b2o4b2o5bo19bo$3b2o7bo21b3ob2o$3bo30b2o4b2o$2b2ob3o25b2obobo$2o4b2o
28bobobo$3bobob2o$bobobo22bobo7bo$23bo4bo2bo6bo$3bo7bobo9bobo5bo3b3o$
3bo6bo2bo5bo3bo11bo$4b3o3bo7bobo2b4ob2ob3o$6bo9bo8bo2b3o2bo$8b3ob2ob4o
2bobo4b3o$8bo2b3o4bo3bo$11b3o2bobo$18bo!

The quoted post contains an almost-strictly-volatile p4, in which there are only four cells that are oscillating with p2 instead of p4.
I found all the statorless parts using Nicolay Beluchenko's WLS modification, downloadable at viewtopic.php?p=98433#p98433

[dbell]

Here is a kickback-based oscillator.

Code: Select all

#C A period 4284 oscillator based on kickbacks.
#C This uses reactions between two phase-changing period 56 glider
#C streams produced by four period 28 glider guns.  Pairs of gliders
#C alternately perform kickbacks and annihilations.  A wave of
#C reactions travels down the glider streams from one pair of glider
#C guns to the other, reversing direction whenever the guns are reached.
#C The period can be increased by separating the pair of guns further.
#C David I. Bell, 22 January 2024
x = 242, y = 245
6boo8boo33bobbo$4bobbo8boo9bo18boo3b6o$4booboboo15bobo18bo9bo$5bobobbo
11bob3obo18bob7obo$bb3obbo14boo4boo14boobobobbobboboboo$bo23boo3bo14b
oobo7boboo$boboobobo13boobob4o12bo3bo9bo3bo$oobo4boo12bobbobo15b4ob3o
3b3ob4o$bobo5bo15bobbo20booboboo$boboobobbo19bo15boobb7obboo$oobo5bo6b
3o5boboboo9boo4boo4b3o4boo$3bo4boo4booboo4boo8bo6bo$3boobobo5b3o6bo7b
3o6bobo$23bo6bo10boo7bo$b4obbo15bo5bobboo11boo3b3o$bo3bobobbo12boobbo
bboobo10boo4b3ob3o$4booboboo10b3oboo4bo28boo$4bobbo23bo12b3ob3o4boo3b
oo$6boo9bobo7b3oboo15b3o3boo$12boo4boo6bobbo20bo$13bo4bo7booboboo6bo$
10b3o16bobbo5bo$10bo18boo7b3o3boob3o4booboo$45bob5obboobo$48boboo6bo$
24bobo18boo3b3ob3obo$25boo14boob3o6bobboboo$25bo15boboo7boboo4bo$43boo
6bobobob3o$39b5o3bo3boobbobo$39bo6bobo6boo$41bob4obbo$31bobo6boobo3bob
o$32boo12booboo$32bo12$45bobo$46boo$46bo12$59bobo$60boo$60bo12$73bobo$
74boo$74bo12$87bobo$88boo$88bo12$101bobo$102boo$102bo12$115bobo$116boo
$116bo$$115boo$114boo$116bo12$129boo$128boo$130bo12$143boo$142boo$144b
o12$157boo$156boo$158bo12$171boo$170boo$172bo3$224boo8boo$214bo8bobo8b
obbo$213bobo15booboboo$213bob3obo11boobobo$212boo4boo15bob3o$211bo3boo
5boo10bobo3bo$211b4oboboo12b3obboobo$214boboboo12b3o3boboo$213bobo15b
oo5bobo$185boo25bobobo6bo3boobb3o3boobo$184boo26boobb3o3bobobobboboo5b
oboo$186bo21bo7b3obbo7bobb3o3bo$208b3o7boobobbobobo3b3obboo$211bo5b3o
bboo3bo6bobo$208boobbo5boo15bob4o$208boboo3boo14boobobo3bo$210bo4boob
oo4bo6booboboo$210bobb3o3bo4bobo7bobbo$209boob3o9boo8boo$212bobbo12boo
$209booboboo12bo$209bobbo16b3o$211boo18bo$199boo16bo$198boo17bobo$200b
o16boo5$206b3obo13booboo$205booboobbo5boobo3bobo$207bobobo7bob4obbo$
217bo6bobo6boo$217b5o3bo3boobbobo$221bo7bobobob3o$219bobobbo7boo4bo$
213boo4boobbo5bo4boboo$212boo9bo7b4obo$214bo9bo3boo6bo$223b6o4bobo$
223bo8booboo$223bo$$220boo$219boo7boo$221bo6boo8boo$227bobo8boo$227boo
$227boo$219boo$218bobo$218bo$217boo4boo11boo$223bo4b5o4bo$227boo3boo$
221b5o9b5o$221bo5bobbobbo5bo$223boo11boo$222boobobobbobboboboo$225bob
7obo$225bo9bo$224boo3b6o$229bobbo!

BCNU,
-dbell

[glider_rider]

P37 loop I'm surprised wasn't found until now:

Code: Select all

x = 90, y = 90, rule = B3/S23
67bo$66bobob2o$66bob2obo$65b2o$64bo3b6o$65b3o6bo$67bob2obo2bo$68bobob
2obo$71bo3bob2o$72b2obo2bo$73bobobo$72bo2bob2o$66b3o4b2o4bo$66bo2bo4bo
b3o$67b2o5bobo$57bo17bo$55b2o$56b2o$60b2o$61bo10bo$58b3o10b2o$58bo12bo
bo2$68b2o$47bo21bo$46bo22bobo$46b3o21b2o3$85bo$76b3o5bobo$76b3o5bob3o$
75bo3bo3b2o4bo$75bob2o3bo2bob2o$37bobo36b3o4bobobo$37b2o30b2o11b2obo2b
o$38bo31b2o9bo3bob2o$69bo8bobob2obo$77bob2obo2bo$75b3o6bo$74bo3b6o$75b
2o$76bob2obo$28bo47bobob2o$28bobo29b2o15bo$12bo15b2o29bobo$8b2obobo47b
o$8bob2obo$13b2o$6b6o3bo$5bo6b3o$4bo2bob2obo$4bob2obobo8bo$b2obo3bo9b
2o31bo$bo2bob2o11b2o30b2o$2bobobo4b3o36bobo$b2obo2bo3b2obo$o4b2o3bo3bo
$b3obo5b3o$3bobo5b3o$4bo3$18b2o21b3o$18bobo22bo$20bo21bo$20b2o2$16bobo
12bo$17b2o10b3o$17bo10bo$28b2o$32b2o$33b2o$14bo17bo$13bobo5b2o$11b3obo
4bo2bo$10bo4b2o4b3o$11b2obo2bo$12bobobo$11bo2bob2o$11b2obo3bo$14bob2ob
obo$14bo2bob2obo$15bo6b3o$16b6o3bo$23b2o$18bob2obo$18b2obobo$22bo!

[confocaloid]

IMO categorifying these reactions as oscillators ("dependent reflector loops") does not tell the whole story. The most interesting part is the dependent reflector itself, and those components deserve to be a separate category of discoveries, not necessarily presented in a completed oscillator form.

[glider_rider]

That's fair, especially for the 0-degree ones or the 180-degree ones that can't be looped. I just like looping them when possible.

Speaking of loops, here's a p20:

Code: Select all

x = 33, y = 33, rule = B3/S23
16bo$16b3o$12b2o5bo$12bo5b2o$4bob2ob2obo14b2o$4b2obobobo11bo3bo$10bo
11b2o4bo$17b2o8b2o$7bobo6b3o$5bo2b2o7b4obo4b2o$5bo2b2o8bo4b2obobo$19bo
3b2o2bo$20bo7b3o$2b2o26bo$bobo$bo7bo$2o8bo20b2o$8b3o20bo$24bo4bobo$2bo
20bobo3b2o$2b3o17bo3bo$5bo11b2o3bo3bo$4bobo3bo7b2o2b2ob2o$4b2o4b2o5bo$
12bo$4b2o4b2o$4bo5bo11bo$5bo15bobobob2o$4b2o14bob2ob2obo$13b2o5bo$13bo
5b2o$14b3o$16bo!

[confocaloid]

That's fair, especially for the 0-degree ones or the 180-degree ones that can't be looped. I just like looping them when possible.

Actually, shifters can be "looped" too, if you are willing to loop the entire universe into a torus:

Code: Select all

#C p20 dependent glider shifter by carsoncheng
#C https://conwaylife.com/forums/viewtopic.php?p=163501#p163501
x = 40, y = 37, rule = B3/S23:T42,39
bo$2bo$3o3$6bo$7bo$5b3o3$11bo$12bo$10b3o3$16bo$17bo$15b3o12bo$28b3o$
27bo$17b3o7b2o$16bo3bo$15bo5bo$10b2o3bo5bo$10b2o3b3ob3o6bo$29bo$27b3o
2$14bo$13bobo17bo$14bo19bo$32b3o3$38bo$39bo$37b3o!

Code: Select all

#C p77 dependent glider shifter by carsoncheng
#C https://conwaylife.com/forums/viewtopic.php?p=163501#p163501
x = 61, y = 60, rule = B3/S23:T76,76
14b2o$obo11b2o$b2o$bo8$3b2o2b2ob2o$3b2ob2o3b2o$7b2ob2o$8b3o$9bo2$6b2o
15bo$7bo13bobo$4b3o15b2o$4bo16$41bo$42b2o$41b2o$51b2o$51b2o6b2o$59bo$
52bo4bobo$51b3o3b2o$51bob2o$54b2o$51bob2o$51b3o$52bo2$40b2o$40b2o6$58b
o$59bo$57b3o!

Also, If I remember correctly, when this was discussed on the forums, there was no observable consensus to describe those oscillators "loops" without adding the word 'dependent'.
I agree the oscillators visually resemble loops, but I still believe they are different enough from the actual glider loops. (And hence deserve a different description.) The gliders belong to the rotor and cannot be removed without breaking the oscillator.

[...]

4) is it okay to rename the p26 glider shuttle, p31 glider shuttle, and p59 glider shuttle to call them all "loops" instead, with a redirect?

NO, they are just oscillators with a rotor composed partially of glider streams. If you touch the rotor, the oscillator is destroyed. If you want to call them "loops", the word "dependent" should be used.

5) is it okay to rename the p71 glider shuttle to "p71 dependent reflector loop" while we're at it, with a redirect?

YES, it fulfills the criteria used so far. A DR-LOOP, something that visually resembles a "true" glider loop.

[...]
Time for a minor nitpick on terminology, I think: it doesn't seem like any of these should be referred to as "glider loops", without the word "dependent" in there somewhere at least. "Dependent" would give a good hint that you can't remove one of the gliders from the "loop" and expect the thing to still work.

However, there isn't actually any kind of signal loop at all in these things -- it's two or four separate segments. So any use of "loop" seems like not such a good idea. You wouldn't call something like this a "glider loop", right? [...]

You could argue that the signals are sub-lightspeed, it's just that the signal corresponding to each glider is actually the first one that wouldn't appear if it weren't there. I do think "dependent glider loop" is a good clarification to make, though: [...]

[Period1GliderGun]

That's fair, especially for the 0-degree ones or the 180-degree ones that can't be looped. I just like looping them when possible.

Speaking of loops, here's a p20:

Code: Select all

x = 33, y = 33, rule = B3/S23
16bo$16b3o$12b2o5bo$12bo5b2o$4bob2ob2obo14b2o$4b2obobobo11bo3bo$10bo
11b2o4bo$17b2o8b2o$7bobo6b3o$5bo2b2o7b4obo4b2o$5bo2b2o8bo4b2obobo$19bo
3b2o2bo$20bo7b3o$2b2o26bo$bobo$bo7bo$2o8bo20b2o$8b3o20bo$24bo4bobo$2bo
20bobo3b2o$2b3o17bo3bo$5bo11b2o3bo3bo$4bobo3bo7b2o2b2ob2o$4b2o4b2o5bo$
12bo$4b2o4b2o$4bo5bo11bo$5bo15bobobob2o$4b2o14bob2ob2obo$13b2o5bo$13bo
5b2o$14b3o$16bo!

Another p20 by combining it with the p20 dependent glider shifter:

Code: Select all

x = 54, y = 54, rule = B3/S23
25bo$25b3o$18b2o8bo$18b2o7b2o$36b2o$13bo16bo5bo$12bobo14b3o5bo$13bo14b
2obo4b2o$18b2o7b2o$18bobo7b2obo4b2o$20bo8b3o3bobo$18bobo9bo5bo$18b2o17b
3o7bo$30b2o7bo6bobo$12b2o16bobo14bo$12bo17bo8bo$4bob2ob2obo29bo$4b2ob
obobo24b2o5bo$10bo6bobo15bo6b2ob3o2b2o$10b2o5b2o3b2o11bo4bo9b2o$10b2o
6bo3bobo10b2obo3b2ob3o$5b2o2bobo12bo12b2obo$5b2o3bo13b2o7b2o2b2o$34bo
$10bo20b3o$2b2o7bo19bo20b2o$bobo3bo44bo$bo8bo39bobo$2o5b3o12bo27b2o$20b
3o22bo$19bo23b2ob2o$9b3o7b2o7b2o7b2o4b2ob2o$8bo3bo16bo8b2o$7bo5bo15bo
bo5bo$2b2o3bo5bo16b2o$2b2o3b3ob3o6bo22bo$21bo20bobobob2o$19b3o12bo6bo
b2ob2obo$33b3o5bo$6bo25bo2b2o3b2o$5bobo6bo17b3obo$6bo7b3o13bo4b2o$17b
o11bo2bo$16bobo2bo7bobo$16b2o2bobo7b2o$22bo6b3o3b2o$16b2o3bo9b4obo3bo
$16bo4bo10bo2b2o2bobo$17bo15bo2bo3bo$16b2o18bo$25b2o6bo2bo$25bo8b2o$26b
3o$28bo!

[hotcrystal0]

Does there exist a toaster variant with this frontend? I have been using WLS on it for around two weeks, but so far nothing, even though WLS shows it's promising.

Code: Select all

x = 10, y = 11, rule = B3/S23
4bo2bo2$3bo$b3ob2ob2o$o3b2o2b2o$4obo3bo$3bobo3bo$2bo2bobobo$2bobobobo
$3b2obobo$7bo!

[dbell]

Here is an attempt to create an oscillator out of period multiplying kickback streams.

Code: Select all

#C A failed oscillator built using kickbacks.
#C This uses many period 80 glider guns.
#C David I. Bell, 26 January 2024
x = 827, y = 829
58boobb3o$58bobobo6boo$59bo10bo$60bobo7bobo3bobboo$65bo5boo3boobbo$60b
ob3obo7bobb3o$59bobboobbo7boo$60boobo10bobb3o$62bo12boobbo$63bobo12bo$
60bo18b3o$59bobo19bo$60bo$47boo19b3o$47bo19bo3bo$48bo17bo5bo$35bo11boo
18bo3bo$bbo32b3o11boo12boo3b3o5boo$bb3o10bo22bo8boobbo10bobo11bobo$5bo
7b3o21boo9bobo11bo15bo$4boo6bo19boo7bo4boboboo9boo15boo$12boo17bobo6bo
bo3boo$29b3obobo4bobbo$28bo5boo5boo$28boo$70bo$43boo6bo10bo6bobo$43bob
o5b3o8bobo5bo7boo$18booboo20bo10bo7boo12boboo$16boo4bo9boo19boo12bo7bo
$9bo13boo7boo32bobo9bo$7bo3bo4bo4boboo41bobbo4boobo$6bo4bo5boobboboo
42bobo4boo$11bo6bobbo45b3o$oo7boo29bo27boo$oobbo34bobo26boo$33boo4bobo
4boo15boo3boo$33bobbo3bo3bobbo8boo5bobo$4boboo26b3o7b3o9boo7bo42bo$8bo
12boo42boo36boo3bo$5bo3bo11bobo8b7o3b7o54bobobbo5boo$5bobbo14bo8bo6bob
o6bo3bo51bobo8bo$5bobbobboo10boo8boboboo3boobobo3boboboo48b3o7bobo6boo
$5bobbobbobo20boobo5boboo4bobobobo49bobbo5boobb3obbo$5bobboobboo25bobo
8boobobobobbo44b3obobo10b3o$4bo3bobbo26booboo8bobboob4o44bo4boo7boo$7b
obboo39bo4bo48boobboo8boob3o$4boo4bo41b3obobboo47b3o10bobbo$54boo3boo
47boo13bo$105bo18b3o$104bobo19bo$105bo$92boo19boo$14bo77bo19bobboo$12b
obo78bo18booboo$13boo65bo11boo18booboo$47bo32b3o11boo12boo4bo6boo$47b
3o10bo22bo8boobbo10bobo11bobo$50bo7b3o21boo9bobo11bo15bo$49boo6bo19boo
7bo4boboboo9boo15boo$57boo17bobo6bobo3boo$74b3obobo4bobbo$73bo5boo5boo
$73boo$115bo$54b3o39bo10bobo4bobo6bo$54bobbo24b3o11b3o8bobo5bo$53bo3bo
20bo20bo9bo11b3obo$53boboboo18bobo18boo13bo6boboo$54booboo18boboo7b3o
22boo5boobo$55b3o20bobbobo5boo10bo12bobobob3o$82boo4bo11b3o$53bo45b5o
16bo$34bo10boo4b5o42boo3boo$32bobo10boo4bobbo29b3o12b5o9boo$33boo15boo
bb3o21boo11boo7b3o5boo3boo$50b3obboo21bo13bo8bo6bobo$56bo22boo3b3o3boo
18bo$53boboo9boo15bo3bo22boo36boobb3o$53b3o10bobo8b7o3b7o54bobo8boo$
54bo13bo8bo6bobo6bo3bo51bo10bo$68boo8boboboo3boobobo3boboboo48boo8bobo
6boo$79boobo5boboo4bobobobo48booboo5boobboo3bo$84bobo8boobobobobbo45bo
4bo8bob3o$83booboo8bobboob4o44bo4bo8boo$96bo4bo48boo3bo9bob3o$97b3obo
bboo48bo11bobbo$99boo3boo47boo13bo$150bo18b3o$149bobo19bo$150bo$137boo
19boo$137bo19bobbo$54bo83bo18booboo$52bobo70bo11boo19bobo$53boo37bo32b
3o11boo12boo4bo6boo$92b3o10bo22bo8boobbo10bobo11bobo$95bo7b3o21boo9bob
o11bo15bo$94boo6bo19boo7bo4boboboo9boo15boo$102boo17bobo6bobo3boo$119b
3obobo4bobbo$118bo5boo5boo$67bobo48boo$68boo83bo6bo7boo$68bo72bo10bo6b
obo$133b3o5b3o8b3o5bo6bo3bo$133bo10bo21bo4bo$108bob3o9boo10bo8boo12bo
7bobobo$106boobo3bo8boo32bobo5bobobo$99bo7bo4boo42bobbobbo4bo$97booboo
6b4obo43b3obbo3bo$97bo3bo$90boo4bobboo29bo33boo$74bo15boo3bobbo30bobo
26boo$72bobo20bobbo24boo4bobo4boo15boo3boo$73boo20bo27bobbo3bo3bobbo8b
oo5bobo$95boo27b3o7b3o9boo7bo42bo$98bo12boo42boo36boo3bo$97boo12bobo8b
7o3b7o54bo4bo5boo$95bobo15bo8bo6bobo6bo3bo51boo9bo4bo$95boo16boo8bobob
oo3boobobo3boboboo58bobo6boo$100b3o21boobo5boboo4bobobobo48booboo5boo
3bo3bo$87bobo5b3o4bo26bobo8boobobobobbo45boobobo8b5o$88boo8b3obo25boob
oo8bobboob4o47b3o9bo$88bo5bo3bobo40bo4bo48boobo11bob3o$94boo4bo41b3obo
bboo44booboo11bobbo$99bo44boo3boo45b3o14bo$98bo96bo18b3o$194bobo19bo$
195bo$103bo78boo19boo$104bo77bo19bobbo$102b3o78bo19bobo$94bo75bo11boo
19b3o$92bobo42bo32b3o11boo12boo11boo$93boo42b3o10bo22bo8boobbo10bobo
11bobo$140bo7b3o21boo9bobo11bo15bo$139boo6bo19boo7bo4boboboo9boo15boo$
147boo17bobo6bobo3boo$164b3obobo4bobbo$163bo5boo5boo$163boo$107bobo89b
o5bo7bo$108boo76bo10boo5bobo6boo$108bo35b3o25boo3bobo6b3o9boo5bo6boobo
$143bobbo24bobo15bo12bo8bobb3o$143bo3bo19boobobbo6bo7boo10bo3bo5bobobo
$144b4o19boo4bo3bobbo23bo4bobobo$146bo24boo6bo20bo3bobb3obbo$173bo3boo
11boo16boboo$123bo18boo45bobboo15boo$124bo10boo5b3o44booboo16bo$122b3o
10boo4bobbo44booboo9boo$114bo26boboo23boo4b3o4boo8bo6boo3boo$112bobo
26boboboo21bobboob3oboobbo15bobo$113boo27boobbo22b3o7b3o18bo42bo$143b
3o10boo42boo36boob3o$144bo11bobo8b7o3b7o54bob3o6boo$158bo8bo6bobo6bo3b
o51boo9bo5bo$158boo8boboboo3boobobo3boboboo58bobobobobboo$169boobo5bob
oo4bobobobo49boboo5boobo5bo$174bobo8boobobobobbo45boobobo9b4o$127bobo
43booboo8bobboob4o43bo5bo9bo$128boo56bo4bo48boobo11bob3o$128bo58b3obo
bboo45b4o11bobbo$189boo3boo62bo$240bo18b3o$239bobo19bo$240bo$227boo19b
oo$143bo83bo19bobbo$144bo83bo19b3o$142b3o70bo11boo20bo$134bo47bo32b3o
11boo12boo11boo$132bobo47b3o10bo22bo8boobbo10bobo11bobo$133boo50bo7b3o
21boo9bobo11bo15bo$184boo6bo19boo7bo4boboboo9boo15boo$192boo17bobo6bob
o3boo$209b3obobo4bobbo$157bo50bo5boo5boo$158boo48boo$157boo84bo6bo$
147bobo81bo11bobo3bobo5b3o$148boo74boo5b3o9boo5bo9bo$148bo75bobo7bo21b
o3bo$198boobboo8boo10bo8boo20bobobbo$197b3obboo8boo32boo5bobbobo$198b
oobb3o42bobo3bo3bo$189boo8bobboo44boo3bo$187boobo63b3o$163bo16boo4bo3b
o29bo$164bo15boo4bo32bobo26boo$162b3o22bo25boo4bobo4boo15boo3boo$154bo
31bo26bobbo3bo3bobbo8boo5bobo$152bobo31bo27b3o7b3o9boo7bo$153boo29boob
oo12boo42boo$184booboo12bobo8b7o3b7o$185bo17bo8bo6bobo6bo3bo$185bo17b
oo8boboboo3boobobo3boboboo$177bo8bo3boo22boobo5boboo4bobobobo$178boo7b
o3bo27bobo8boobobobobbo$177boo6bobbobbo26booboo8bobboob4o$167bobo15bo
4bo40bo4bo$168boo15booboo42b3obobboo$168bo19boo44boo3boo4$193bo$191bob
o$183bo8boo$184bo$182b3o$174bo$172bobo$173boo4$197bo$198boo$197boo$
187bobo$188boo$188bo4$213bo$211bobo$203bo8boo$204bo$202b3o$194bo$192bo
bo$193boo4$217bo$218boo$217boo$207bobo$208boo$208bo4$233bo$231bobo$
223bo8boo$224bo$222b3o$214bo$212bobo$213boo4$237bo$238boo$237boo$227bo
bo$228boo$228bo4$253bo$251bobo$243bo8boo$244bo$242b3o$234bo$232bobo$
233boo4$257bo$258boo$257boo$247bobo$248boo$248bo4$273bo$271bobo$263bo
8boo$264bo$262b3o$254bo$252bobo$253boo4$277bo$278boo$277boo$267bobo$
268boo$268bo4$293bo$291bobo$283bo8boo$284bo$282b3o$274bo$272bobo$273b
oo4$297bo$298boo$297boo$287bobo$288boo$288bo4$313bo$311bobo$303bo8boo$
304bo$302b3o$294bo$292bobo$293boo4$317bo$318boo$317boo$307bobo$308boo$
308bo4$333bo$331bobo$323bo8boo$324bo$322b3o$314bo$312bobo$313boo4$337b
o$338boo$337boo$327bobo$328boo$328bo4$353bo$351bobo$343bo8boo$344bo$
342b3o$334bo$332bobo$333boo4$357bo$358boo$357boo$347bobo$348boo$348bo
4$373bo$371bobo$363bo8boo$364bo$362b3o$354bo$352bobo$353boo4$377bo$
378boo$377boo$367bobo$368boo$368bo4$393bo$391bobo$383bo8boo$384bo$382b
3o$374bo$372bobo$373boo4$397bo$398boo$397boo$387bobo$388boo$388bo4$
413bo$411bobo$403bo8boo$404bo$402b3o$394bo$392bobo$393boo4$417bo$418b
oo$417boo$407bobo$408boo$408bo4$433bo$431bobo$423bo8boo$424bo$422b3o$
414bo$412bobo$413boo4$437bo$438boo$437boo$427bobo$428boo$428bo4$453bo$
451bobo$443bo8boo$444bo$442b3o$434bo$432bobo$433boo4$457bo$458boo$457b
oo$447bobo$448boo$448bo4$473bo$471bobo$463bo8boo$464bo$462b3o$454bo$
452bobo$453boo4$477bo$478boo$477boo$467bobo$468boo$468bo4$493bo$491bob
o$483bo8boo$484bo$482b3o$474bo$472bobo$473boo4$497bo$498boo$497boo$
487bobo$488boo$488bo4$513bo$511bobo$503bo8boo$504bo$502b3o$494bo$492bo
bo$493boo4$517bo$518boo$517boo$507bobo$508boo$508bo4$533bo$531bobo$
532boo3$514bo$512bobo$513boo3$542bo$537bo3boo$538boobobo$537boo15$564b
3o$564bo$565bo18$584b3o$584bo$585bo18$604b3o$604bo$605bo18$624b3o$624b
o$625bo18$644b3o$644bo$645bo18$664b3o$664bo$665bo18$684b3o$684bo$685bo
18$704b3o$704bo$705bo18$724b3o$724bo$725bo18$744b3o$744bo$745bo18$764b
3o$764bo$765bo18$784b3o$784bo$785bo7$764boo4boo4boo4boo40boo$764bo5bo
5bo5bo31bo8bobo$765b3o3b3o3b3o3b3o27boboboo4bo$767bo5bo5bo5bo19bo8bob
3oboo$805b3o8bo3boo$808bo7b4o4b3o$807boo8bob3o$794boo23bobo$794b3o23bo
$795boo$789boo4boo16boo$789boo3boo3bo4b3o6booboo6bo$798bobo3bo4bo5bo6b
3o$799bo5bo4bo10bo$821boo$793b3o11bobo$792bo28boo$792bo3bo21boo$792bo
bbobo9boo8bobboboo$794bobobbo8bo9bobo$795bo3bo5b3o8bobobo$799bo5bo9bob
oobobo$796b3o16bo5boo$814boo!

A slower gun at the lower right could fix this, but I fear that its period would be related to the glider stream period, so to make the whole thing pointless.

Still, it's pretty while it works.

EDIT: Well, this works.

Code: Select all

#C A period 480  oscillator built using kickbacks.
#C This uses many period 80 glider guns.
#C One of the downward gliders is used to delete
#C an upward glider to prevent the reaction failing.
#C David I. Bell, 26 January 2024
x = 830, y = 832
58boobb3o$58bobo8boo$59bo10bo5bo$60boo8bobob3obboo$61booboo5booboo4bo$
61bo4bo9b4o$60bo4bo10bo$60boo3bo9bob3o$64bo11bobbo$63boo13bo$60bo18b3o
$59bobo7bo11bo$60bo7b3o$47boo18b5o$47bo18boo3boo$48bo16b3o3b3o$35bo11b
oo16b3o3boo$bbo32b3o11boo12b3ob5o4boo$bb3o10bo22bo8boobbo10bobo3b3o5bo
bo$5bo7b3o21boo9bobo11bo6bo8bo$4boo6bo19boo7bo4boboboo9boo15boo$12boo
17bobo6bobo3boo$29b3obobo4bobbo$28bo5boo5boo$9b3o16boo$9bobbo57bo$8bo
42bo17bobo6bo$11boo24b3o11b3o14bobbo5b3o$7bo3boo20boo19bo21bob3o$7bo
24bobo18boo12bobbo4bo3bo$8b3o21bobbo31bo6bo3bo$32bo3bo21bo8bobo3b3obo$
10boo21bo4bo20bo8boo4b3o$10boo22bobbo14boobbobboo14bo$oo7bobbo23bo3bo
10b3obobob3o$oo6b3o28bobo10boobbobboo7boo$7boboobo20boo4bobo4boo5bo5bo
3boo3boo$6b3o24bobo4bo4bobo6b5o4bobo$5bo28boo9boo8b3o7bo42bo$6bo14boo
14bo5bo12bo8boo36boo3bo$6boo13bobo8b4obo5bob4o54bo4bo5boo$7bobboo11bo
8bo5bo3bo5bo3bo51boo9bo$8b3o12boo8boboboo3boobobo3boboboo58boboob3oboo
$9bo24boobo5boboo4bobobobo48booboo5bo3bo4bo$39bobo8boobobobobbo45boobo
bo10b3o$38booboo8bobboob4o47b3o10bo$51bo4bo48boobo9bo3b3o$52b3obobboo
44booboo10boobbo$54boo3boo45b3o14bo$105bo18b3o$104bobo19bo$105bo7b3o$
92boo18bo3bo$92bo18bo5bo$93bo17bo5bo$80bo11boo17bo5bo$47bo32b3o11boo
12boobbo3bo4boo$47b3o10bo22bo8boobbo10bobo3b3o5bobo$50bo7b3o21boo9bobo
11bo15bo$49boo6bo19boo7bo4boboboo9boo15boo$57boo17bobo6bobo3boo$74b3ob
obo4bobbo$73bo5boo5boo$73boo$23bobo89bo$24boo61b3o6bo10bo6bobo6bo$24bo
62bo8b3o7bo8bo6bobo$62boobboo20bo10bo6b3o12bo3bo$66b3o8boo19boo12bo7bo
3bo$61bo15boo32bobo5bo3bo$55bo12bobo39boobboobbo3bo$55bobo3bobbob4o41b
ooboo3bobo$57bo4b3ob3o42b3oboo3bo$45boo38bo28b3o$45boo37bobo26bobo$78b
oo4bobo4boo15boo3boo$78bobbo3bo3bobbo8boo5bobo$52boo25b3o7b3o9boo7bo
42bo$51bobbo11boo42boo36boob3o$49bo16bobo8b7o3b7o54bob3o6boo$49bo18bo
8bo6bobo6bo3bo51boo9bo$48bo7boo10boo8boboboo3boobobo3boboboo58bobo3boo
boo$48bo9bo20boobo5boboo4bobobobo49boboo5b3oboo3bo$49bo34bobo8boobobob
obbo45boobobo6boobb3o$43bobo6bo30booboo8bobboob4o43bo5bo7b4o$44boo7boo
bbo38bo4bo48boobo10bobb3o$44bo9bobo40b3obobboo45b4o10boobbo$99boo3boo
62bo$150bo18b3o$149bobo19bo$150bo8bo$137boo19b3o$59bo77bo19b5o$60bo77b
o17boo3boo$58b3o64bo11boo18b5o$92bo32b3o11boo12boo3b3o5boo$92b3o10bo
22bo8boobbo10bobo4bo6bobo$95bo7b3o21boo9bobo11bo15bo$94boo6bo19boo7bo
4boboboo9boo15boo$102boo17bobo6bobo3boo$119b3obobo4bobbo$118bo5boo5boo
$118boo$99b3o58bo$63bobo32bobbo39bo17bobo$64boo32bo3bo24b3o11b3o10bo5b
o6b3o$64bo32boobbo21boo19bo9bo4bo7b3o$99bo22bobbo8bo8boo13bobo6b3o$
100boo20bo12bo8b3o10bo6b3o$100b3o20bobbobo6bo9b3o10bobo3b3o$99b4o21b5o
15b5o10bo4b3o$143boo3boo$79bo10boo50b3o3b3o$80bo9boo7bobo27b3o11boo3b
oo8boo$78b3o17booboo20boo4b3o4boo6b5o4boo3boo$97boboboo20bobo9bobo7b3o
5bobo$96boob4o21bo11bo9bo8bo$98b5o8boo13bo7bo20boo36boobb3o$97boobbo9b
obo8b6o5b6o54bobobo6boo$98b3o12bo8bo6bobo6bo3bo51bo10bo$99bo13boo8bobo
boo3boobobo3boboboo48bobo7bobo3bobboo$124boobo5boboo4bobobobo52bo5boo
3boobbo$129bobo8boobobobobbo44bob3obo7bobb3o$128booboo8bobboob4o43bobb
oobbo7boo$83bobo55bo4bo48boobo10bobb3o$84boo56b3obobboo46bo12boobbo$
84bo59boo3boo47bobo12bo$195bo18b3o$194bobo19bo$195bo$182boo19b3o$182bo
19bo3bo$99bo83bo17bo5bo$100bo69bo11boo18bo3bo$98b3o36bo32b3o11boo12boo
3b3o5boo$137b3o10bo22bo8boobbo10bobo11bobo$140bo7b3o21boo9bobo11bo15bo
$139boo6bo19boo7bo4boboboo9boo15boo$147boo17bobo6bobo3boo$164b3obobo4b
obbo$163bo5boo5boo$113bo49boo$114boo89bo$113boo63boo6bo10bo6bobo$103bo
bo72bobo5b3o8bobo5bo7boo$104boo47booboo20bo10bo7boo12boboo$104bo46boo
4bo9boo19boo12bo7bo$144bo13boo7boo32bobo9bo$142bo3bo4bo4boboo41bobbo4b
oobo$141bo4bo5boobboboo42bobo4boo$146bo6bobbo45b3o$135boo7boo29bo27boo
$119bo15boobbo34bobo26boo$120bo47boo4bobo4boo15boo3boo$118b3o47bobbo3b
o3bobbo8boo5bobo$139boboo26b3o7b3o9boo7bo42bo$143bo12boo42boo36boo3bo$
140bo3bo11bobo8b7o3b7o54bobobbo5boo$140bobbo14bo8bo6bobo6bo3bo51bobo8b
o$140bobbobboo10boo8boboboo3boobobo3boboboo48b3o7bobo6boo$140bobbobbob
o20boobo5boboo4bobobobo49bobbo5boobb3obbo$133bo6bobboobboo25bobo8boobo
bobobbo44b3obobo10b3o$134boo3bo3bobbo26booboo8bobboob4o44bo4boo7boo$
133boo7bobboo39bo4bo48boobboo8boob3o$123bobo13boo4bo41b3obobboo47b3o
10bobbo$124boo63boo3boo47boo13bo$124bo115bo18b3o$239bobo19bo$240bo$
227boo19boo$149bo77bo19bobboo$147bobo78bo18booboo$139bo8boo65bo11boo
18booboo$140bo41bo32b3o11boo12boo4bo6boo$138b3o41b3o10bo22bo8boobbo10b
obo11bobo$185bo7b3o21boo9bobo11bo15bo$184boo6bo19boo7bo4boboboo9boo15b
oo$192boo17bobo6bobo3boo$209b3obobo4bobbo$208bo5boo5boo$208boo$153bo
96bo$154boo33b3o39bo10bobo4bobo6bo$153boo34bobbo24b3o11b3o8bobo5bo$
143bobo42bo3bo20bo20bo9bo11b3obo$144boo42boboboo18bobo18boo13bo6boboo$
144bo44booboo18boboo7b3o22boo5boobo$190b3o20bobbobo5boo10bo12bobobob3o
$217boo4bo11b3o$188bo45b5o16bo$169bo10boo4b5o42boo3boo$167bobo10boo4bo
bbo29b3o12b5o9boo$159bo8boo15boobb3o21boo11boo7b3o5boo3boo$160bo24b3o
bboo21bo13bo8bo6bobo$158b3o30bo22boo3b3o3boo18bo$188boboo9boo15bo3bo
22boo$188b3o10bobo8b7o3b7o$189bo13bo8bo6bobo6bo3bo$203boo8boboboo3boob
obo3boboboo$214boobo5boboo4bobobobo$219bobo8boobobobobbo$173bo44booboo
8bobboob4o$174boo55bo4bo$173boo57b3obobboo$163bobo68boo3boo$164boo$
164bo4$189bo$187bobo$179bo8boo$180bo$178b3o5$202bobo$203boo$193bo9bo$
194boo$193boo$183bobo$184boo$184bo4$209bo$207bobo$199bo8boo$200bo$198b
3o$$201boo$200boo$202bo$222bobo$223boo$213bo9bo$214boo$213boo4$231bo$
231bo$230bo$228bo$227b3o$228boo13$254boo$253boo$255bo17$243bobo$244boo
28boo$244bo28boo$275bo5$259bo$260bo$258b3o7$273bo$274boo$273boo$263bob
o$264boo28boo$264bo28boo$295bo3$289bo$287bobo$279bo8boo$280bo$278b3o7$
293bo$294boo$293boo$283bobo$284boo$284bo6$299bo$300bo$298b3o10$303bobo
$304boo28boo$304bo28boo$335bo18$354boo$353boo$355bo18$374boo$373boo$
375bo17$363bobo$364boo28boo$364bo28boo$395bo5$379bo$380bo$378b3o7$393b
o$394boo$393boo$383bobo$384boo28boo$384bo28boo$415bo3$409bo$407bobo$
399bo8boo$400bo$398b3o7$413bo$414boo$413boo$403bobo$404boo$404bo6$419b
o$420bo$418b3o10$423bobo$424boo28boo$424bo28boo$455bo18$474boo$473boo$
475bo18$494boo$493boo$495bo17$483bobo$484boo28boo$484bo28boo$515bo5$
499bo$500bo$498b3o7$513bo$514boo$513boo$503bobo$504boo28boo$504bo28boo
$535bo3$529bo$527bobo$519bo8boo$520bo$518b3o7$533bo$534boo$533boo$523b
obo$524boo$524bo6$539bo$540bo$538b3o10$543bobo$544boo28boo$544bo28boo$
575bo18$594boo$593boo$595bo18$614boo$613boo$615bo17$603bobo$604boo28b
oo$604bo28boo$635bo5$619bo$620bo$618b3o7$633bo$634boo$633boo$623bobo$
624boo28boo$624bo28boo$655bo3$649bo$647bobo$639bo8boo$640bo$638b3o7$
653bo$654boo$653boo$643bobo$644boo$644bo6$659bo$660bo$658b3o10$663bobo
$664boo28boo$664bo28boo$695bo18$714boo$713boo$715bo18$734boo$733boo$
735bo17$723bobo$724boo28boo$724bo28boo$755bo5$739bo$740bo$738b3o7$753b
o$754boo$753boo$743bobo$744boo28boo$744bo28boo$775bo3$769bo$767bobo$
759bo8boo$760bo$758b3o$$755boo4boo4boo$755bo5bo5bo$756b3o3b3o3b3o$758b
o5bo5bo$$772boo$772boobboo$776bobo$777bo$780b3o11boo$774boo3bo13boo$
775bo3bo3bo11bo$772b3o4bobbobo42boo$772bo8bobobbo30bo8bobo$782bo3bo29b
oboboo4bo$786bo21bo8bob3oboo$783b3o22b3o8bo3boo$811bo7b4o4b3o$810boo8b
ob3o$804boo16bobo$803boo8boo8bo$797b3o5bo7boo$792boobbo4bo11boobbo$
792boobboo4bo11boo3bo7bo$799bo3bo11boobbo5b3o$801boo13b3o5bo$824boo$
797bo$796b3o25boo$795b3obo21bobboo$796bo3bo9boo8bobooboo$797bo3bo9bo9b
obo$798bob3o5b3o8bobobo$799b3o6bo9boboobobo$800bo17bo5boo$817boo!

I hope looping the stream back on itself doesn't count as cheating.

BCNU,
-dbell

[dbell]

Here is a larger example of my new oscillator pattern.

Code: Select all

#C A period 880 oscillator based on kickback reactions.
#C This uses many streams produced by period 80 glider guns.
#C The base glider stream period here is multiplied by 11.
#C Adding or removing glider guns at the top left will change the
#C multiplication factor, which is one more than the number of guns.
#C If such a change is made, simply adding eaters if necessary and
#C running the pattern will eventually result in the new oscillator.
#C David I. Bell, 26 January 2024
x = 1052, y = 1024
58boobb3o$58bobo8boo$59bo10bo$60boo8bobo3booboo$61booboo5b3oboo3bo$61b
o4bo6boobb3o$60bo4bo7b4o$60boo3bo8bobb3o$64bo10boobbo$63boo13bo$60bo
18b3o$59bobo19bo$60bo$47boo18bobo$47bo18bobbo$48bo19boo$35bo11boo$bbo
32b3o11boo12boo11boo$bb3o10bo22bo8boobbo10bobo11bobo$5bo7b3o21boo9bobo
11bo15bo$4boo6bo19boo7bo4boboboo9boo15boo$12boo17bobo6bobo3boo$29b3obo
bo4bobbo$28bo5boo5boo$28boo35bo$63boo5bo$51bo12boo3bobo$51b3o16bo6b3o$
20bo24boo7bo14bo7b3o$19boboo9boo10boo7boo13bobo6b3o$18bo4bo8boo12bo20b
o6b3o$19bo48bobo3b3o$20b4o45bo4b3o$9boo$oo4boobo30bo$oo4bobbo29bobo26b
oo$33boo4bobo4boo15boo3boo$33bobbo3bo3bobbo8boo5bobo35boobb3o$4bobboo
25b3o7b3o9boo7bo35bobobo6boo$4bobo14boo42boo35bo10bo$5bo15bobo8b7o3b7o
54bobo7bobo3bobboo$23bo8bo6bobo6bo3bo55bo5boo3boobbo$6boo15boo8boboboo
3boobobo3boboboo46bob3obo7bobb3o$6bobo25boobo5boboo4bobobobo44bobboobb
o7boo$5booboboo27bobo8boobobobobbo42boobo10bobb3o$5boobobbo26booboo8bo
bboob4o44bo12boobbo$5boobobo40bo4bo49bobo12bo$8boo42b3obobboo42bo18b3o
$54boo3boo41bobo19bo$103bo$90boo19b3o$11bo78bo19bo3bo$12boo77bo17bo5bo
$11boo65bo11boo18bo3bo$45bo32b3o11boo12boo3b3o5boo$45b3o10bo22bo8boobb
o10bobo11bobo$48bo7b3o21boo9bobo11bo15bo$47boo6bo19boo7bo4boboboo9boo
15boo$55boo17bobo6bobo3boo$72b3obobo4bobbo$71bo5boo5boo$71boo$53bo59bo
$52b3o26bo12bo17bobo$51boobbo25bo12b3o10boo4bo7boo$51bo3bo20bo4bo15bo
8bo12boboo$51bobo21boboo8bo8boo13boo5bo$75boboo7bobo22b3o7bo$52booboo
19b4obo6bo9b3o10b3o3boobo$54bo25boo5bo9bo3bo15boo$51bo44bo5bo$31bo11b
oo4bo3bo29bo12bo5bo$32boo9boo9bo28bo12bo5bo8boo$31boo18boobo21boo5bo5b
oo6bo3bo4boo3boo$48bobobobbo20bobo4bo4bobo7b3o5bobo$49boobobbo21bo4b3o
4bo18bo$51bobbo9boo15bobobo22boo$51bobbo9bobo8b8ob8o55boobb3o$51b3o12b
o8bo6bobo6bo3bo51bobobo6boo$66boo8boboboo3boobobo3boboboo48bo10bo5bo$
77boobo5boboo4bobobobo48bobo7bobob3obboo$82bobo8boobobobobbo50bo5boob
oo4bo$81booboo8bobboob4o45bob3obo9b4o$94bo4bo48bobboobbo9bo$95b3obobb
oo45boobo11bob3o$97boo3boo47bo13bobbo$152bobo12bo$149bo18b3o$148bobo
19bo$149bo$136boo19boo$51bo84bo19bobbo$52boo83bo19b3o$51boo71bo11boo$
91bo32b3o11boo12boo11boo$91b3o10bo22bo8boobbo10bobo11bobo$94bo7b3o21b
oo9bobo11bo15bo$93boo6bo19boo7bo4boboboo9boo15boo$101boo17bobo6bobo3b
oo$118b3obobo4bobbo$67bo49bo5boo5boo$65bobo49boo$66boo84bobo4bo$140bo
11boo4bobo6bo$134bo5b3o10bo3bobbo5b3o$108bobbo21boo8bo21bob3o$107bo3bo
9boo10bobo6boo12bobbo4bo3bo$107bo4bo8boo33bo6bo3bo$107bo4bo43bobo3b3ob
o$98bo9bo3bo44boo4b3o$96b4o9bobo52bo$71bo17boo4bo3bo29bo$72boo15boo4bo
bo30bobo26boo$71boo23bo25boo4bobo4boo15boo3boo$122bobbo3bo3bobbo8boo5b
obo$94bobo26b3o7b3o9boo7bo36boobb3o$93bobbo13boo42boo35bobo8boo$94bobo
13bobo8b7o3b7o54bo10bo$94b3o15bo8bo6bobo6bo3bo51boo8bobo6boo$95b3o14b
oo8boboboo3boobobo3boboboo48booboo5boobboo3bo$87bo9b3o23boobo5boboo4bo
bobobo47bo4bo8bob3o$85bobo8booboo27bobo8boobobobobbo43bo4bo8boo$86boo
6bobbobbo26booboo8bobboob4o43boo3bo9bob3o$94boo3bo40bo4bo51bo11bobbo$
95b4o42b3obobboo46boo13bo$97bo45boo3boo43bo18b3o$192bobo19bo$193bo$
180boo19boo$100bobo77bo19bobbo$101boo78bo18booboo$91bo9bo66bo11boo19bo
bo$92boo41bo32b3o11boo12boo4bo6boo$91boo42b3o10bo22bo8boobbo10bobo11bo
bo$138bo7b3o21boo9bobo11bo15bo$137boo6bo19boo7bo4boboboo9boo15boo$145b
oo17bobo6bobo3boo$162b3obobo4bobbo$161bo5boo5boo$161boo$107bo88bo6bo7b
oo$105bobo35bo40bo10bo6bobo$106boo34b3o25boo12b3o8b3o5bo6bo3bo$141bobb
oo23boboo14bo9bo11bo4bo$141bo3bo19b3o3boo13boo13bo6bobobo$142boobo19b
3obobo5boo22b3o3bobobo$144boo24boo3bobo27bo4bo$170bo5bo11b3o14bo3bo$
140bobo44bo3bo$120bobo10boo4bobbo43bo5bo14boo$121boo10boo4bo3bo29bo13b
o3bo9boo$111bo9bo16boobo24boo3booboo3boo7b3o5boo3boo$112boo25bo3boo21b
obb4ob4obbo15bobo$111boo31bo22b4obbobb4o18bo$140bobbo10boo42boo$141b3o
10bobo8b7o3b7o55boobb3o$156bo8bo6bobo6bo3bo51bobo8boo$156boo8boboboo3b
oobobo3boboboo48bo10bo$167boobo5boboo4bobobobo48boo8bobo3booboo$172bob
o8boobobobobbo46booboo5b3oboo3bo$127bo43booboo8bobboob4o46bo4bo6boobb
3o$125bobo56bo4bo49bo4bo7b4o$126boo57b3obobboo45boo3bo8bobb3o$187boo3b
oo49bo10boobbo$242boo13bo$239bo18b3o$238bobo19bo$239bo$226boo18bobo$
140bobo83bo18bobbo$141boo84bo19boo$131bo9bo72bo11boo$132boo47bo32b3o
11boo12boo11boo$131boo48b3o10bo22bo8boobbo10bobo11bobo$184bo7b3o21boo
9bobo11bo15bo$183boo6bo19boo7bo4boboboo9boo15boo$191boo17bobo6bobo3boo
$156bo51b3obobo4bobbo$157bo49bo5boo5boo$155b3o49boo35bo$147bo94boo5bo$
145bobo82bo12boo3bobo$146boo82b3o16bo6b3o$199bo24boo7bo14bo7b3o$198bob
oo9boo10boo7boo13bobo6b3o$197bo4bo8boo12bo20bo6b3o$198bo48bobo3b3o$
199b4o45bo4b3o$188boo$160bobo16boo4boobo30bo$161boo16boo4bobbo29bobo
26boo$151bo9bo50boo4bobo4boo15boo3boo$152boo58bobbo3bo3bobbo8boo5bobo
35boobb3o$151boo30bobboo25b3o7b3o9boo7bo35bobobo6boo$183bobo14boo42boo
35bo10bo$184bo15bobo8b7o3b7o54bobo7bobo3bobboo$202bo8bo6bobo6bo3bo55bo
5boo3boobbo$176bo8boo15boo8boboboo3boobobo3boboboo46bob3obo7bobb3o$
177bo7bobo25boobo5boboo4bobobobo44bobboobbo7boo$175b3o6booboboo27bobo
8boobobobobbo42boobo10bobb3o$167bo16boobobbo26booboo8bobboob4o44bo12b
oobbo$165bobo16boobobo40bo4bo49bobo12bo$166boo19boo42b3obobboo42bo18b
3o$233boo3boo41bobo19bo$282bo$269boo19b3o$190bo78bo19bo3bo$191boo77bo
17bo5bo$190boo65bo11boo18bo3bo$180bobo41bo32b3o11boo12boo3b3o5boo$181b
oo41b3o10bo22bo8boobbo10bobo11bobo$171bo9bo45bo7b3o21boo9bobo11bo15bo$
172boo52boo6bo19boo7bo4boboboo9boo15boo$171boo61boo17bobo6bobo3boo$
251b3obobo4bobbo$250bo5boo5boo$250boo$196bo35bo59bo$197bo33b3o26bo12bo
17bobo$195b3o32boobbo25bo12b3o10boo4bo7boo$187bo42bo3bo20bo4bo15bo8bo
12boboo$185bobo42bobo21boboo8bo8boo13boo5bo$186boo66boboo7bobo22b3o7bo
$231booboo19b4obo6bo9b3o10b3o3boobo$233bo25boo5bo9bo3bo15boo$230bo44bo
5bo$210bo11boo4bo3bo29bo12bo5bo$211boo9boo9bo28bo12bo5bo8boo$210boo18b
oobo21boo5bo5boo6bo3bo4boo3boo$200bobo24bobobobbo20bobo4bo4bobo7b3o5bo
bo$201boo25boobobbo21bo4b3o4bo18bo42bo$191bo9bo28bobbo9boo15bobobo22b
oo36boo3bo$192boo36bobbo9bobo8b8ob8o54bobobbo5boo$191boo37b3o12bo8bo6b
obo6bo3bo51bobo8bo$245boo8boboboo3boobobo3boboboo48b3o7bobo6boo$256boo
bo5boboo4bobobobo49bobbo5boobb3obbo$261bobo8boobobobobbo44b3obobo10b3o
$216bo43booboo8bobboob4o44bo4boo7boo$217bo55bo4bo48boobboo8boob3o$215b
3o56b3obobboo47b3o10bobbo$207bo68boo3boo47boo13bo$205bobo119bo18b3o$
206boo118bobo19bo$327bo$314boo19boo$314bo19bobboo$230bo84bo18booboo$
231boo69bo11boo18booboo$230boo37bo32b3o11boo12boo4bo6boo$220bobo46b3o
10bo22bo8boobbo10bobo11bobo$221boo49bo7b3o21boo9bobo11bo15bo$211bo9bo
49boo6bo19boo7bo4boboboo9boo15boo$212boo65boo17bobo6bobo3boo$211boo83b
3obobo4bobbo$295bo5boo5boo$246bo48boo$244bobo90bo$236bo8boo64bo6bo10bo
bo4bobo6bo$237bo72boo6b3o8boo6bo$235b3o50bo21bobo8bo8bo12b3obo$227bo
56b6o9boo19boo12bo7boboo$225bobo55booboobbo8boo32bobo6boobo$226boo47b
3o5boo3boboo41bobbo3bob3o$274b5o6b4obo43b3o$273boo3bo7boo47bo6bo$267b
oo4b5o29bo$250bo16boo3b4o30bobo26boo$251boo18b3o26boo4bobo4boo15boo3b
oo$250boo19boo27bobbo3bo3bobbo8boo5bobo$240bobo29boo27b3o7b3o9boo7bo$
241boo30bobo12boo42boo36boobb3o$231bo9bo31b3o12bobo8b7o3b7o54bobo8boo$
232boo38boboo14bo8bo6bobo6bo3bo51bo10bo$231boo39boo4bo11boo8boboboo3b
oobobo3boboboo48boo8bobo6boo$274bo3boo21boobo5boboo4bobobobo48booboo5b
oobboo3bo$266bo6b3o3boo25bobo8boobobobobbo45bo4bo8bob3o$264bobo5boobob
o27booboo8bobboob4o44bo4bo8boo$256bo8boo4boobbobo40bo4bo48boo3bo9bob3o
$257bo13boo4bo41b3obobboo48bo11bobbo$255b3o18bo44boo3boo47boo13bo$247b
o124bo18b3o$245bobo123bobo19bo$246boo124bo$359boo19boo$279bobo77bo19bo
bbo$280boo78bo18booboo$270bo9bo66bo11boo19bobo$271boo41bo32b3o11boo12b
oo4bo6boo$270boo42b3o10bo22bo8boobbo10bobo11bobo$260bobo54bo7b3o21boo
9bobo11bo15bo$261boo53boo6bo19boo7bo4boboboo9boo15boo$251bo9bo62boo17b
obo6bobo3boo$252boo87b3obobo4bobbo$251boo87bo5boo5boo$340boo$286bo88bo
6bo7boo$284bobo35bo40bo10bo6bobo$276bo8boo34b3o25boo12b3o8b3o5bo6bo3bo
$277bo42bobboo23boboo14bo9bo11bo4bo$275b3o42bo3bo19b3o3boo13boo13bo6bo
bobo$267bo53boobo19b3obobo5boo22b3o3bobobo$265bobo55boo24boo3bobo27bo
4bo$266boo81bo5bo11b3o14bo3bo$319bobo44bo3bo$299bobo10boo4bobbo43bo5bo
14boo$300boo10boo4bo3bo29bo13bo3bo9boo$290bo9bo16boobo24boo3booboo3boo
7b3o5boo3boo$291boo25bo3boo21bobb4ob4obbo15bobo$290boo31bo22b4obbobb4o
18bo42bo$280bobo36bobbo10boo42boo36boo3bo$281boo37b3o10bobo8b7o3b7o54b
o4bo5boo$271bo9bo53bo8bo6bobo6bo3bo51boo9bo4bo$272boo61boo8boboboo3boo
bobo3boboboo58bobo6boo$271boo73boobo5boboo4bobobobo48booboo5boo3bo3bo$
351bobo8boobobobobbo45boobobo8b5o$306bo43booboo8bobboob4o47b3o9bo$304b
obo56bo4bo48boobo11bob3o$296bo8boo57b3obobboo44booboo11bobbo$297bo68b
oo3boo45b3o14bo$295b3o119bo18b3o$287bo128bobo19bo$285bobo129bo$286boo
116boo19boo$404bo19bobbo$319bobo83bo19bobo$320boo70bo11boo19b3o$310bo
9bo38bo32b3o11boo12boo11boo$311boo46b3o10bo22bo8boobbo10bobo11bobo$
310boo50bo7b3o21boo9bobo11bo15bo$300bobo58boo6bo19boo7bo4boboboo9boo
15boo$301boo66boo17bobo6bobo3boo$291bo9bo84b3obobo4bobbo$292boo41bo49b
o5boo5boo$291boo43bo48boo$334b3o84bo5bo7bo$326bo81bo10boo5bobo6boo$
324bobo74boo5b3o9boo5bo6boobo$316bo8boo73boo9bo21bobb3o$317bo56bobobb
oo8boo11bo7boo20bobobo$315b3o56bobboo10boo32b3o5bobobo$307bo66bobboobb
o41boobobb3obbo$305bobo57b3o7boobbobo43boo3boboo$306boo56booboo62boo$
357boo4bobbo30bo34bo$339bobo15boo4boo31bobo26boo$340boo21boo25boo4bobo
4boo15boo3boo$330bo9bo22boo25bobbo3bo3bobbo8boo5bobo$331boo30bo27b3o7b
3o9boo7bo42bo$330boo29bo3bo12boo42boo36boob3o$320bobo41boo12bobo8b7o3b
7o54bob3o6boo$321boo39bo17bo8bo6bobo6bo3bo51boo9bo5bo$311bo9bo40boo16b
oo8boboboo3boobobo3boboboo58bobobobobboo$312boo41bo7bo3boo22boobo5bob
oo4bobobobo49boboo5boobo5bo$311boo43bo6boo3boo26bobo8boobobobobbo45boo
bobo9b4o$354b3o6bo3boo26booboo8bobboob4o43bo5bo9bo$346bo14booboobo40bo
4bo48boobo11bob3o$344bobo15b4obo41b3obobboo45b4o11bobbo$336bo8boo17b3o
44boo3boo62bo$337bo124bo18b3o$335b3o123bobo19bo$327bo134bo$325bobo41bo
79boo19boo$326boo42boo77bo19bobbo$369boo79bo19b3o$359bobo75bo11boo20bo
$360boo42bo32b3o11boo12boo11boo$350bo9bo43b3o10bo22bo8boobbo10bobo11bo
bo$351boo54bo7b3o21boo9bobo11bo15bo$350boo54boo6bo19boo7bo4boboboo9boo
15boo$340bobo71boo17bobo6bobo3boo$341boo88b3obobo4bobbo$331bo9bo88bo5b
oo5boo$332boo41bo54boo$331boo43bo88bo6bo$374b3o76bo11bobo3bobo5b3o$
366bo45bo26boo3boo7b3o9boo5bo9bo$364bobo44b3o24bobo3b3o9bo21bo3bo$356b
o8boo43boobbo19boobboo5bobo7boo11b3o6bobobbo$357bo54b3o19boobboo5boo
20b5o3bobbobo$355b3o81bo5boo20boobbo3bo3bo$347bo92booboo12boo16bo$345b
obo41bo20bo45bobbo16b3o$346boo42boo10boo5boo45booboo$389boo11boo6bo46b
obo10boo$379bobo26b3o6bo17boo3booboo3boo8bo6boo3boo$380boo26bo3boo3bo
17bobbo3bo3bobbo15bobo$370bo9bo28bo3bo22b3o7b3o18bo$371boo37b3o10boo
42boo$370boo51bobo8b7o3b7o$360bobo62bo8bo6bobo6bo3bo$361boo62boo8bobob
oo3boobobo3boboboo$351bo9bo74boobo5boboo4bobobobo$352boo41bo45bobo8boo
bobobobbo$351boo43bo43booboo8bobboob4o$394b3o56bo4bo$386bo67b3obobboo$
384bobo69boo3boo$376bo8boo$377bo$375b3o$367bo$365bobo41bo$366boo42boo$
409boo$399bobo$400boo$390bo9bo$391boo$390boo$380bobo$381boo42bo$371bo
9bo41bobo$372boo41bo8boo$371boo43bo$414b3o$406bo$404bobo$396bo8boo$
397bo$395b3o$387bo$385bobo41bo$386boo42boo$429boo$419bobo$420boo$410bo
9bo$411boo$410boo$400bobo$401boo42bo$391bo9bo41bobo$392boo41bo8boo$
391boo43bo$434b3o$426bo$424bobo$416bo8boo$417bo$415b3o$407bo$405bobo
41bo$406boo42boo$449boo$439bobo$440boo$430bo9bo$431boo$430boo$420bobo$
421boo42bo$411bo9bo41bobo$412boo41bo8boo$411boo43bo$454b3o$446bo$444bo
bo$436bo8boo$437bo$435b3o$427bo$425bobo41bo$426boo42boo$469boo$459bobo
$460boo$450bo9bo$451boo$450boo$440bobo$441boo42bo$431bo9bo41bobo$432b
oo41bo8boo$431boo43bo$474b3o$466bo$464bobo$456bo8boo$457bo$455b3o$447b
o$445bobo41bo$446boo42boo$489boo3$470bo16boo$471boo13boo$470boo16bo$
460bobo$461boo42bo$451bo9bo41bobo$452boo50boo$451boo4$476bo$477bo38b3o
$475b3o38bo$467bo49bo$465bobo$466boo7$480bobo$481boo$471bo9bo$472boo$
471boo5$536b3o$536bo$487bo49bo$485bobo$486boo9$491bo$492boo$491boo5$
556b3o$556bo$557bo18$576b3o$576bo$577bo18$596b3o$596bo$597bo11$551bo$
552boo$551boo5$616b3o$616bo$567bo49bo$565bobo$566boo7$580bobo$581boo$
571bo9bo$572boo$571boo4$596bo$597bo38b3o$595b3o38bo$587bo49bo$585bobo$
586boo4$610bo$611boo$610boo$600bobo$601boo$591bo9bo$592boo$591boo$$
626bo$624bobo$616bo8boo$617bo38b3o$615b3o38bo$607bo49bo$605bobo$606boo
$$639bobo$640boo$630bo9bo$631boo$630boo$620bobo$621boo$611bo9bo$612boo
41bo$611boo43bo$654b3o$646bo$644bobo$636bo8boo$637bo$635b3o$627bo$625b
obo41bo$626boo42boo$669boo$659bobo$660boo$650bo9bo$651boo$650boo$640bo
bo$641boo$631bo9bo$632boo41bo$631boo43bo$674b3o$666bo$664bobo$656bo8b
oo$657bo38b3o$655b3o38bo$647bo49bo$645bobo$646boo$$679bobo$680boo$670b
o9bo$671boo$670boo$660bobo$661boo$651bo9bo$652boo$651boo$$686bo$684bob
o$676bo8boo$677bo38b3o$675b3o38bo$667bo49bo$665bobo$666boo4$690bo$691b
oo$690boo$680bobo$681boo$671bo9bo$672boo$671boo4$696bo$697bo38b3o$695b
3o38bo$687bo49bo$685bobo$686boo7$700bobo$701boo$691bo9bo$692boo$691boo
5$756b3o$756bo$707bo49bo$705bobo$706boo9$711bo$712boo$711boo5$776b3o$
776bo$777bo18$796b3o$796bo$797bo18$816b3o$816bo$817bo11$771bo$772boo$
771boo5$836b3o$836bo$787bo49bo$785bobo$786boo7$800bobo$801boo$791bo9bo
$792boo$791boo4$816bo$817bo38b3o$815b3o38bo$807bo49bo$805bobo$806boo4$
830bo$831boo$830boo$820bobo$821boo$811bo9bo$812boo$811boo$$846bo$844bo
bo$836bo8boo$837bo38b3o$835b3o38bo$827bo49bo$825bobo$826boo$$859bobo$
860boo$850bo9bo$851boo$850boo$840bobo$841boo$831bo9bo$832boo41bo$831b
oo43bo$874b3o$866bo$864bobo$856bo8boo$857bo$855b3o$847bo$845bobo41bo$
846boo42boo$889boo$879bobo$880boo$870bo9bo$871boo$870boo$860bobo$861b
oo$851bo9bo$852boo41bo$851boo43bo$894b3o$886bo$884bobo$876bo8boo$877bo
38b3o$875b3o38bo$867bo49bo$865bobo$866boo$$899bobo$900boo$890bo9bo$
891boo$890boo$880bobo$881boo$871bo9bo$872boo$871boo$$906bo$904bobo$
896bo8boo$897bo38b3o$895b3o38bo$887bo49bo$885bobo$886boo4$910bo$911boo
$910boo$900bobo$901boo$891bo9bo$892boo$891boo4$916bo$917bo38b3o$915b3o
38bo$907bo49bo$905bobo$906boo7$920bobo$921boo$911bo9bo$912boo$911boo5$
976b3o$976bo$927bo49bo$925bobo$926boo9$931bo$932boo$931boo5$996b3o$
996bo$997bo8$947boo4boo4boo4boo4boo4boo4boo4boo$947bo5bo5bo5bo5bo5bo5b
o5bo$948b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o$950bo5bo5bo5bo5bo5bo5bo5bo$$
994boo$994boobboo$998bobo$999bo$$996boo4b3o11b3o$997bo4b3o11bo$994b3o
5b3o12bo31boo$994bo10b3o31bo8bobo$1005b3o30bobobb3obobo$1005b3o22bo8bo
3boboboo$1030b3o12b3o$1033bo7boo6b3o$1032boo7b3obo$1038bo3b3obo$1026b
3o7boobo4boo$1026bo8bo$1014boo3b3o5bo7boboobbo$1014boo3b3obbo11bobbobb
o6bo$1019boobbobo14boo5b3o$1024bo21bo$1046boo$$1018boo23b3o$1018boobo
20bobo$1022bo9boo8bo3boo$1019bo13bo9boboo$1020boboo6b3o8bobobo$1022boo
6bo9boboobobo$1040bo5boo$1039boo!

I am amazed by this pattern. It's not easy to see how adding another stream at the left edge of the existing stream can change the period of the rightmost stream.

BCNU,
-dbell