Thread for your miscellaneous posts and discussions

[confocaloid]

LuveelVoom's 8yr old sister made it

came from discord

That is still unclear, because you did not explain what "came from discord", and who created, discovered, suggested what.
(The CA? The name? The patterns and reactions?)

Please be careful to make it clear where is the line between your stuff and contributions from people other than yourself. Your starting a new thread does not automatically become a significant contribution to the topic, without further efforts from you to contribute something of interest to others.

[hotdogPi]

"Blockus" gets zero results on the Discord server.

I can also rule out CARuler and LuveelVoom's 8-year-old sister being the same person.

[CARuler]

"Blockus" gets zero results on the Discord server.

I can also rule out CARuler and LuveelVoom's 8-year-old sister being the same person.

I didn't make it, and yes I did just name it

[confocaloid]

It is better to leave naming to the person who made the CA. Both in general, and in this particular case.
In general, it is traditional to leave naming to the discoverer or inventor.
In this case, the character string '(blockus or whatever)' does not feel like a particularly good name. What do you mean "or whatever"? Sounds like someone not really caring much about good naming.

[CARuler]

It is better to leave naming to the person who made the CA. Both in general, and in this particular case.
In general, it is traditional to leave naming to the discoverer or inventor.
In this case, the character string '(blockus or whatever)' does not feel like a particularly good name. What do you mean "or whatever"? Sounds like someone not really caring much about good naming.

the name is not very important, most people just leave their rules without a name

[confocaloid]

the name is not very important, most people just leave their rules without a name

Sure. You could leave the topic basically unnamed, too. You could just put the rulestring, without appending "(blockus or whatever)".

That wouldn't excuse posting a new low-effort thread before there is any observable evidence of the topic being interesting to the community.

However, that would avoid the problem with the title of the thread being disrespectful to the person who made the CA in an obvious way.

[wwei47]

I agree with "nearly" as an informal description, however, "totalistic" would mean that the middle cell is counted along with its neighbours in a single count. So for example B36/S25 is totalistic ("a cell lives in the next generation iff its neighbourhood currently contains =3 or =6 alive cells"), but B3/S237 is not totalistic.

You have a good point there. I'm pointing out here that "INT" is often used to mean "isotropic non-totalistic", so I do wonder why this usage became so widespread.

[confocaloid]

Yes, and also "isotropic non-totalistic" is used on the forums interchangeably to mean either of the following:

• "isotropic, not outer-totalistic"
• "isotropic, not necessarily outer-totalistic"
• "two-state isotropic, not outer-totalistic"
• "two-state isotropic, not necessarily outer-totalistic"
• "isotropic on the square tiling, not outer-totalistic"
• "isotropic on the square tiling, not necessarily outer-totalistic"
• "two-state isotropic on the square tiling, not outer-totalistic"
• "two-state isotropic on the square tiling, not necessarily outer-totalistic"
• ...

These are all different. There are multistate isotropic CA, and multistate outer-totalistic CA, and there are such CA on the hexagonal tiling and on other tessellations.

Having some experience with being confused by some of these incomplete descriptions, I'm trying to be explicit about what are the assumptions. Hence e.g. "two-state isotropic with range-1 Moore neighbourhood" explicitly, when someone else would just write "INT" instead. That is longer, but avoids the confusion.)

[b-engine]

Here's an encoding method of large patterns (often macro spaceships) with "linear chains" of repetitive small patterns:

RULE;A=RLE,B=RLE2,...;X,Y,DISX,DISY,ROT,TYPE,RPT;...

RULE is the rulestring or ruletable name, e.g. B3/S23.

A=RLE, appends A as alias of RLE. B=RLE2 is also the same.

X and Y, is where a "chain" starts, relative to the bottom corner of the entire pattern.

DISX and DISY, is the displacement of each object in a chain; each object has its bottom-left as position.

ROT, is the rotation of all the objects in the chain. Possible values are 0 to 7, as any asymmetric pattern (like glider) in a square grid can point at one of the 8 directions. If applied to symmetric patterns, the lower value that leads to the same intended rotation is chosen, but other possible values are acceptable.

TYPE, the type of all the objects in the chain, appended to a symbol.

RPT, the length of the chain, means how many copy of the objects exist in the chain.

The encoding always ends with "&".



Example: B3/S23,A=bo$2bo$3o!,B=2o$2o!,20,10,5,-8,2,A,25;50,2,-1,1,5,B,55&

[CARuler]

why is viewtopic.php?f=12&t=4068 locked?

[unname4798]

why is viewtopic.php?f=12&t=4068 locked?

Someone messed this game up.

[CARuler]

why is viewtopic.php?f=12&t=4068 locked?

Someone messed this game up.

who
and why did it have to be locked

[hotdogPi]

Post 200000 is coming soon. This is 198959, for reference.

1: January 17, 2009
10000: December 6, 2013
20000: May 29, 2015
30000: April 14, 2016
40000: January 29, 2017
50000: August 27, 2017
60000: May 14, 2018
70000: February 7, 2019
80000: July 23, 2019
90000: February 21, 2020
100000: July 3, 2020
110000: November 10, 2020
120000: January 22, 2021
130000: May 10, 2021
140000: January 9, 2022
150000: August 22, 2022
160000: April 2, 2023
170000: October 8, 2023
180000: March 9, 2024
190000: July 17, 2024

[confocaloid]

Code: Select all

x = 34, y = 24, rule = B2i3ai4cei5c6c7/S2-ae3acein4-t5-aq6cei7c8

edit:

Code: Select all

x = 40, y = 39, rule = B2i3ai4cei5c6c7/S2-ae3acein4-t5-aq6cei7c8

Please add sufficiently detailed human-readable descriptions to your posts. The forum rule 5b says

Readers of your post should have a rough idea of what to expect when they open your RLE in LifeViewer or copy it into another program. Outside of the Sandbox forum, at least briefly describe (or quote another post that describes) what pattern(s) you're posting. Descriptions also make it much easier to find patterns by searching the forums.

[get_Snacked]

hmm... if i had to rank people who are the best at finding interesting patterns without the usage of search programs, i would go:
1. JP21
2. Period1GliderGun
3. hotcrystal0
4. erRoR_6o6
5. pipsqueek
EDIT: replaced myself at #5 with pipsqueek (bro is gone now)

[b-engine]

hmm... if i had to rank people who are the best at finding interesting patterns without the usage of search programs, i would go:

If I have to rank 5 people here who are the best at finding interesting OCA without usage of any search programs. I would go (expect that blanks may be filled with something else):

1. islptng (?)
2. b-engine (myself)
3. R2INT
4.
5. CARuler (?)

[get_Snacked]

If I have to rank 5 people here who are the best at finding interesting OCA without usage of any search programs. I would go (expect that blanks may be filled with something else):

1. islptng (?)
2. b-engine (myself)
3. R2INT
4.
5. CARuler (?)

what about H.H.P.M.P. Cole?

[confocaloid]

As for how to obtain this "phase 1" pattern, I have only rough idea. [...]

Certain kinds of buggy/incorrect implementations will fail on the following input pattern (a p552 glider gun), or on some variant of this input pattern:

Code: Select all

x = 218, y = 168, rule = B3/S23
108bo$107bobo$107bobo$106b2ob2o$105bo2bo3bo$104bobo2b4o$105bob2o$106bo
2b4o$107b2o3bo$109b2o$109bo$110bo$109b2o$69b2o44b2o$69bobo44bo29bo$71b
o4b2o35b3o25b2o2bobo$67b4ob2o2bo2bo33bo27bobo2bobo$67bo2bobobobob2o20b
2o5b2o10b2o23b2o2bo$70bobobobo23b2o5b2o11bo24bobo$71b2obobo40b3o22bo2b
ob2o$75bo41bo23bobobo$142bo2b4o$61b2o80b2o3bo$62bo7b2o74bo$62bobo5b2o
71b2ob2o$63b2o78b2o$146b2o$78bo56b2o10bo$79bo21bo5bo18b2o7b2o9bo$28b2o
5b2o40b3o20b3o3b3o18bo18b2o$28b2o5b2o62b2o2bobo2b2o17bobo$98bob4ob4obo
17b2o$73b2o25b3o3b3o$73bo25b3o5b3o$74b3o$76bo71b2o$148b2o2$28b3o3b3o
70bo$27bo2bo3bo2bo68bobo$27b2obo3bob2o67b2ob2o$105b2ob2o23bo$132bobo$
106b3o23bobo$85b3o8bo3b2o5bo25bo$71b2o11bo4bo4b2o4b2o5bo22b3o$71b2o10b
o5bo4bo2bo32bo$84bo8bo3bo$85b2o8b2o$35bo$33b2ob2o47b2o8b2o$33b2ob2o46b
o8bo3bo$71b2o10bo5bo4bo2bo$32bobobobo32b2o11bo4bo4bo2bo$85b3o7b2o$33b
2ob2o$28b2o4b3o$28b2o5bo3$96b2o5bo$96b2o4b3o$101b2ob2o$17b3o7b2o$3b2o
11bo4bo4bo2bo70bobobobo$3b2o10bo5bo4bo2bo$16bo8bo3bo71b2ob2o$17b2o8b2o
72b2ob2o$103bo$17b2o8b2o37bo$16bo8bo3bo34b3o$3b2o10bo5bo4bo2bo33bo$3b
2o11bo4bo4b2o4b2o5bo23b2o$17b3o8bo3b2o5bo$38b3o$71b2o$37b2ob2o30bo$37b
2ob2o16bobo11bob2o19b2obo3bob2o$38bobo18b2o3b2o4b3o2bo19bo2bo3bo2bo$
39bo19bo4b2o3bo3b2o21b3o3b3o$69b4o$55b2o15bo$54bobo12b3o$4bo49bo13bo$
4b3o24b3o5b3o11b2o14b5o$7bo24b3o3b3o32bo$6b2o15b2o5bob4ob4obo28bo$22bo
bo6b2o2bobo2b2o29b2o23b2o5b2o$2b2o14b2o2bo9b3o3b3o55b2o5b2o$bo2bo13bob
ob2o9bo5bo$bob2o14b2obo2bo$2o22b2o$o2b2o$b2o2bo$3b2obo15b2o$b2o2bo5bo
10b2o$o2bo6bobo$b2o7bobo$11bo$21b2o9b2o5b2o$22bo9b2o5b2o$5b2o12b3o$5b
2o12bo$20b2o$21bo$20bo$20b2o2$25bo$25b3o$28bo$27b2o7$37b2o$30b2o5bobo$
30b2o7bo$39b2o2$26bo$25bobob2o$25bobobobo$22b2obobobobo2bo$22bo2bo2b2o
b4o$24b2o4bo$30bobo$31b2o30$216b2o$216b2o4$216bo$209b2o6bo$209b2o4b3o!

Specifically, consider the following generation:

Code: Select all

x = 241, y = 200, rule = LifeHistory
127.2B$126.5B$123.8B$122.10B$122.15B$120.19B$119.22B$119.24B$108.A9.
28B$107.A.A8.29B$107.A.A7.30B$106.2A.2A2.34B$105.A2.A2.BA34B$104.A.A
2.4A34B$105.A.2A3.B.33B$106.A2.4A2B2.30B$107.2A2.BAB2.31B$109.2A5.20B
.10B$109.A6.19B4.8B$110.A6.20B4.6B$109.2A4.23B4.4B$69.2A44.2A2.19B$
69.A.A44.A3.18B8.A$71.A4.2A35.3A5.8B.8B3.2A2.A.A$67.4A.2A2.A2.A33.A5.
5B7.7B3.A.A2.A.A$67.A2.A.A.A.A.2A20.2A5.2A10.2A10.7B4.B.2A2.A$69.BABA
BA.A21.2B2AB3.B2A2B9.A11.6B3.2B2.A.A$70.B2ABA.A21.4B5.4B6.3A12.7B.2BA
B.A.2A$71.2B.BA22.6B.6B6.A14.9BA.A.A$70.3B25.6B.6B22.8B.A2.4A$61.2A6.
4B27.4B.4B24.6B4.2A3.A$62.A6.B2A3B24.5B.5B22.6B6.B.A$62.A.AB3.B2A3B
24.5B.5B22.7B3.B2AB2A$63.2AB.10B21.6B.6B22.8B.B2A$65.13B21.5B.5B23.
10B3.2A$65.14B19.3BA2B.2BA3B21.3B2A6B4.A$65.15B18.2B3AB.B3A2B15.2A5.
2B2A6B3.A$28.2A5.2A30.8B2.4B17.2BAB2A.2ABA2B16.A5.10B3.2A$26.2B2AB3.B
2A2B28.6B5.4B16.4B2A.2A4B16.A.AB2.11B$26.4B5.4B27.9B4.4B15.4B2A.2A4B
17.2AB.12B$26.6B.6B26.4B4.2A5.4B14.4B2A.2A4B19.15B$26.6B.6B25.4B5.A7.
4B13.6B.6B19.16B$28.4B.4B26.4B7.3A5.4B12.6B.6B19.16B.2B$27.5B.5B24.4B
10.A6.4B11.6B.6B19.18B2A$27.5B.5B23.4B19.4B11.5B.5B19.17B.B2A$26.2B3A
B.B3A2B21.4B21.4B9.13B17.4B2.8B.4B.B$27.BA2BA.A2BAB21.4B23.4B9.7B3A2B
16.4B4.7B$26.BA3BA.A3BAB19.4B25.4B8.7B3A2B15.4B5.6B$26.B4AB.B4AB18.4B
27.4B8.4B.5B15.4B6.4B$26.2BA3B.3BA2B17.4B29.4B5.7B2AB2AB13.4B5.A3B$
26.6B.6B16.4B31.4B4.6B.A3BA13.4B5.A.AB$26.6B.6B15.4B14.4B3.B.4B2A3B.
5B2.4B2.2B3A2B11.4B6.A.A$26.6B.6B14.4B15.4B.7BA9B3A.2B2AB.3BA3B10.4B
8.A$26.6B.6B13.4B15.2A10BA2B2A5BA4B2.2A2.7B9.4B6.3A$26.6B.6B12.4B16.
2A10BA2BA6BA3BA8.3B10.4B7.A$26.6B.6B11.4B18.B.9BABA7BA3BAB7.3B9.4B$
27.5B.2BA2B11.4B21.10B2A9B2A3B7.B9.4B$26.8B3A2B9.4B40.9B15.4B$27.6BA
3BAB8.4B23.10B2A9B2A5B13.4B$27.6B2AB2AB7.4B22.B.9BABA7B2A3BA3BC11.4B$
28.4B.2AB2A7.4B22.2A10BA2BA6BA4BABCBCB9.4B$26.13B5.4B23.2A10BA2B2A5B
2A3BA2B2C2B7.4B$26.6B.2AB2A5.4B25.4B.7BA10B2A9B5.4B$26.4B2.B2AB2AB3.
4B26.4B3.B.4B2A3B.8B2.6B3.4B$26.2B2AB.BA3BA2B.4B48.5B4.6B.4B$28.2A2.
2B3A7B52.B6.9B$34.BA7B59.9B$34.9B59.BA7B$28.B6.9B52.2A2.2B3A7B$25.5B
4.6B.4B49.2B2AB.BA3BA2B.4B$4.4B3.B.4B2A3B.8B2.6B3.4B48.4B2.B2AB2AB3.
4B$4.4B.7BA10B2A9B5.4B47.6B.2AB2A5.4B$3.2A10BA2B2A5B2A3BA6B7.4B46.13B
5.4B$3.2A10BA2BA6BA4BA5B9.4B47.4B.2AB2A7.4B$4.B.9BABA7B2A3BA4B11.4B
45.6B2AB2AB7.4B$6.10B2A9B2A5B13.4B44.6BA3BAB8.4B$24.9B15.4B42.8B3A2B
9.4B$6.10B2A9B2A3B7.B9.4B13.A28.5B.2BA2B11.4B$4.B.9BABA7BA3BAB7.3B9.
4B10.3A27.6B.6B11.4B$3.2A10BA2BA6BA3BA8.3B10.4B8.A30.6B.6B12.4B$3.2A
10BA2B2A5BA4B2.2A2.7B9.4B7.2A29.6B.6B13.4B$4.4B.7BA9B3A.2B2AB.3BA3B
10.4B3.5B29.6B.6B14.4B$4.4B3.B.4B2A3B.5B2.4B2.2B3A2B11.4B2.3B31.6B.6B
15.4B$22.4B4.6B.A3BA13.9B7.2A21.6B.6B16.4B$21.4B5.7B2AB2AB13.8B8.A21.
2BA3B.3BA2B17.4B$20.4B8.4B.5B15.10B3.B.A.2A18.B4AB.B4AB18.4B$19.4B8.
7B3A2B14.7B2A2B.B3A2.A18.BA3BA.A3BAB19.4B$18.4B9.7B3A2B14.7B2A3BAB2.
2A20.BA2BA.A2BAB21.4B$17.4B9.13B14.12B4A21.2B3AB.B3A2B21.4B$16.4B11.
5B.5B13.2AB.7B3.2B.A22.5B.5B23.4B$15.4B11.6B.6B11.A.AB.7B2.B3A23.5B.
5B24.4B$4.A9.4B12.6B.6B11.A5.4B4.A27.4B.4B26.4B$4.3A6.4B13.6B.6B10.2A
5.4B5.5A20.6B.6B25.4B$7.A4.4B14.4B2A.2A4B16.4B10.A20.6B.6B26.4B$6.2A
3.4B8.2A5.4B2A.2A4B15.4B9.A22.4B5.4B27.4B$6.8B8.A.A5.4B2A.2A4B14.4B
10.2A21.2B2AB3.B2A2B28.4B$2.2A4.5B5.2A2.A7.2BAB2A.2ABA2B13.4B36.2A5.
2A31.4B$.A.BAB.5B6.A.A.2A6.2B3AB.B3A2B12.4B78.4B$.A.2AB2.5B6.2A.A2.A
4.3BA2B.2BA3B11.4B80.4B$2A.B.B3.5B3.3B.B2.2A5.5B.5B11.4B82.4B$A2.2A2B
2.5B3.4B9.6B.6B9.4B84.4B$.2A2.AB.13B.B8.5B.5B9.4B86.4B$3.2ABA13B.B2A
7.5B.5B8.4B88.4B$.2A2.A5BA10B2A8.4B.4B8.4B90.4B$A2.A2.4BABA7B.2B7.6B.
6B5.4B92.4B$.2A3.4BABA7B10.6B.6B4.4B94.4B$7.4BA7B11.4B5.4B3.4B96.4B$
9.9B3.2A7.2B2AB3.B2A2B2.BA2B98.4B$6.B.10B.B2.A9.2A5.2A3.2A2B100.4B$5.
2A12B3A21.2B2A102.4B$5.2AB.8B.BA22.4B104.4B$6.B3.6B4.2A19.4B106.4B$
11.4B6.A18.4B108.4B$12.4B4.A18.4B110.4B$13.4B3.2A16.4B112.4B$14.4B19.
4B114.4B$15.4B6.A10.4B116.4B$16.4B5.3A7.4B118.4B$17.4B7.A5.4B120.4B$
18.4B5.2A4.4B122.4B$19.4B4.9B124.4B$20.4B5.6B126.4B$21.4B2.8B127.4B$
22.15B126.4B$23.14B127.4B$24.13B128.4B$25.10B.B2A127.4B$27.3B2AB3.BA.
A127.4B$27.3B2AB6.A128.4B$29.4B6.2A128.4B$29.3B138.4B$26.AB.2B140.4B$
25.A.AB2AB140.4B$25.A.ABABAB140.4B$22.2A.A.A.A.A2.A139.4B$22.A2.A2.2A
.4A140.4B$24.2A4.A145.4B$30.A.A144.4B$31.2A145.4B$179.4B$180.4B$181.
4B$182.4B$183.4B$184.4B$185.4B$186.4B$187.4B$188.4B$189.4B$190.4B$
191.4B$192.4B$193.4B$194.4B$195.4B$196.4B$197.4B$198.4B$199.4B$200.4B
$201.4B$202.4B$203.4B$204.4B$205.4B$206.4B$207.4B$208.4B4.2A$209.4B3.
2A$210.4B$211.4B$212.4B$213.4B$209.2A3.4B$209.2A4.4B$216.4B$217.4B$
218.4B$219.4B$220.4B$221.4B$222.4B$223.4B$224.4B$225.4B$226.4B$227.4B
$228.4B$229.4B$230.4B$231.4B$232.4B$233.4B$234.4B$235.4B$236.4B$237.
3BC$238.CBC$239.2C!

Remove gliders one-by-one from this phase, each time checking whether the removal of the leading glider changes anything in the pattern 552 ticks later (apart from the expected disappearance of the leading glider translated by 138 cells diagonally).

The first "white glider" in the lower-right corner passes the test, and apparently can be safely removed.
After that, second "white glider" also passes the test, and apparently also can be removed.
After that, there are no other removable gliders in this phase.

The first error already happened, because second "white glider" is necessary for the large spark in the top right corner to occur. Removal of that glider will cause incorrect bounding box computation.

Ignore that error for now, and evolve the remaining pattern (with both "white gliders" removed) 1 tick, to get the next generation:

Code: Select all

x = 218, y = 176, rule = LifeHistory
127.2B$126.5B$123.8B$122.10B$122.15B$120.19B$119.22B$119.24B$108.A9.
28B$107.A.A8.29B$107.A.A7.30B$106.2A.2A2.34B$105.A2.A2.BA34B$104.A.A
2.4A34B$105.A.2A3.B.33B$106.A2.4A2B2.30B$107.2A2.BAB2.31B$109.2A5.20B
.10B$109.A6.19B4.8B$110.A6.20B4.6B$109.2A4.23B4.4B$69.2A44.2A2.19B$
69.A.A44.A3.18B8.A$71.A4.2A35.3A5.8B.8B3.2A2.A.A$67.4A.2A2.A2.A33.A5.
5B7.7B3.A.A2.A.A$67.A2.A.A.A.A.2A20.2A5.2A10.2A10.7B4.B.2A2.A$69.BABA
BA.A21.2B2AB3.B2A2B9.A11.6B3.2B2.A.A$70.B2ABA.A21.4B5.4B6.3A12.7B.2BA
B.A.2A$71.2B.BA22.6B.6B6.A14.9BA.A.A$70.3B25.6B.6B22.8B.A2.4A$61.2A6.
4B27.4B.4B24.6B4.2A3.A$62.A6.B2A3B24.5B.5B22.6B6.B.A$62.A.AB3.B2A3B
24.5B.5B22.7B3.B2AB2A$63.2AB.10B21.6B.6B22.8B.B2A$65.13B21.5B.5B23.
10B3.2A$65.14B19.2B3AB.B3A2B21.3B2A6B4.A$65.15B18.2BA2BA.A2BA2B15.2A
5.2B2A6B3.A$28.2A5.2A30.8B2.4B17.2BA3B.3BA2B16.A5.10B3.2A$26.2B2AB3.B
2A2B28.6B5.4B16.6B.6B16.A.AB2.11B$26.4B5.4B27.9B4.4B15.3BA2B.2BA3B17.
2AB.12B$26.6B.6B26.4B4.2A5.4B14.4B2A.2A4B19.15B$26.6B.6B25.4B5.A7.4B
13.6B.6B19.16B$28.4B.4B26.4B7.3A5.4B12.6B.6B19.16B.2B$27.5B.5B24.4B
10.A6.4B11.6B.6B19.18B2A$27.2BA2B.2BA2B23.4B19.4B11.5B.5B19.17B.B2A$
26.2B3AB.B3A2B21.4B21.4B9.9BA3B17.4B2.8B.4B.B$27.2A2BA.A2B2A21.4B23.
4B9.7BABA2B16.4B4.7B$26.BA3BA.A3BAB19.4B25.4B8.7BABA2B15.4B5.6B$26.BA
B2AB.B2ABAB18.4B27.4B8.4B.A3BA15.4B6.4B$26.B2A3B.3B2AB17.4B29.4B5.7B
2AB2AB13.4B5.A3B$26.6B.6B16.4B31.4B4.6B.A3BA13.4B5.A.AB$26.6B.6B15.4B
14.4B3.B.4BA4B.4BA2.4B2.2B3A2B11.4B6.A.A$26.6B.6B14.4B15.4B.7BA2BA6B
2AB.2B2AB.2B3A2B10.4B8.A$26.6B.6B13.4B15.2A10B5A5BAB2AB2.2A2.7B9.4B6.
3A$26.6B.6B12.4B16.2A9B2AB3A4B3A3B8.3B10.4B7.A$26.6B.6B11.4B18.B.9BAB
2A7BA2BAB7.3B9.4B$27.5B.B3AB11.4B21.10B2A10BA3B7.B9.4B$26.8B3A2B9.4B
40.9B15.4B$27.6BA3BAB8.4B23.10B2A8B2A6B13.4B$27.5BA5BA7.4B22.B.9BAB2A
6B3ABA5B11.4B$28.4B.2AB2A7.4B22.2A9B2AB3A4BA4B3A4B9.4B$26.13B5.4B23.
2A10B5A5B3ABA7B7.4B$26.6B.2AB2A5.4B25.4B.7BA2BA6B2A10B5.4B$26.4B2.A5B
A3.4B26.4B3.B.4BA4B.8B2.6B3.4B$26.2B2AB.BA3BA2B.4B48.5B4.6B.4B$28.2A
2.2B3A7B52.B6.9B$34.3A6B59.9B$34.9B59.3A6B$28.B6.9B52.2A2.2B3A7B$25.
5B4.6B.4B49.2B2AB.BA3BA2B.4B$4.4B3.B.4BA4B.8B2.6B3.4B48.4B2.A5BA3.4B$
4.4B.7BA2BA6B2A10B5.4B47.6B.2AB2A5.4B$3.2A10B5A5B3ABA7B7.4B46.13B5.4B
$3.2A9B2AB3A4BA4B3A4B9.4B47.4B.2AB2A7.4B$4.B.9BAB2A6B3ABA5B11.4B45.5B
A5BA7.4B$6.10B2A8B2A6B13.4B44.6BA3BAB8.4B$24.9B15.4B42.8B3A2B9.4B$6.
10B2A10BA3B7.B9.4B13.A28.5B.B3AB11.4B$4.B.9BAB2A7BA2BAB7.3B9.4B10.3A
27.6B.6B11.4B$3.2A9B2AB3A4B3A3B8.3B10.4B8.A30.6B.6B12.4B$3.2A10B5A5BA
B2AB2.2A2.7B9.4B7.2A29.6B.6B13.4B$4.4B.7BA2BA6B2AB.2B2AB.2B3A2B10.4B
3.5B29.6B.6B14.4B$4.4B3.B.4BA4B.4BA2.4B2.2B3A2B11.4B2.3B31.6B.6B15.4B
$22.4B4.6B.A3BA13.9B7.2A21.6B.6B16.4B$21.4B5.7B2AB2AB13.8B8.A21.B2A3B
.3B2AB17.4B$20.4B8.4B.A3BA15.10B3.B.A.2A18.BAB2AB.B2ABAB18.4B$19.4B8.
7BABA2B14.7B2A2B.B3A2.A18.BA3BA.A3BAB19.4B$18.4B9.7BABA2B14.7B2A3BAB
2.2A20.2A2BA.A2B2A21.4B$17.4B9.9BA3B14.12B4A21.2B3AB.B3A2B21.4B$16.4B
11.5B.5B13.2AB.7B3.2B.A22.2BA2B.2BA2B23.4B$15.4B11.6B.6B11.A.AB.7B2.B
3A23.5B.5B24.4B$4.A9.4B12.6B.6B11.A5.4B4.A27.4B.4B26.4B$4.3A6.4B13.6B
.6B10.2A5.4B5.5A20.6B.6B25.4B$7.A4.4B14.4B2A.2A4B16.4B10.A20.6B.6B26.
4B$6.2A3.4B8.2A5.3BA2B.2BA3B15.4B9.A22.4B5.4B27.4B$6.8B8.A.A5.6B.6B
14.4B10.2A21.2B2AB3.B2A2B28.4B$2.2A4.5B5.2A2.A7.2BA3B.3BA2B13.4B36.2A
5.2A31.4B$.A.BAB.5B6.A.A.2A6.2BA2BA.A2BA2B12.4B78.4B$.A.2AB2.5B6.2A.A
2.A4.2B3AB.B3A2B11.4B80.4B$2A.B.B3.5B3.3B.B2.2A5.5B.5B11.4B82.4B$A2.
2A2B2.5B3.4B9.6B.6B9.4B84.4B$.2A2.AB.13B.B8.5B.5B9.4B86.4B$3.2ABA13B.
B2A7.5B.5B8.4B88.4B$.2A2.A5BA10B2A8.4B.4B8.4B90.4B$A2.A2.4BABA7B.2B7.
6B.6B5.4B92.4B$.2A3.4BABA7B10.6B.6B4.4B94.4B$7.4BA7B11.4B5.4B3.4B96.
4B$9.9B3.2A7.2B2AB3.B2A2B2.A3B98.4B$6.B.10B.B2.A9.2A5.2A3.A3B100.4B$
5.2A12B3A21.B3A102.4B$5.2AB.8B.BA22.4B104.4B$6.B3.6B4.2A19.4B106.4B$
11.4B6.A18.4B108.4B$12.4B4.A18.4B110.4B$13.4B3.2A16.4B112.4B$14.4B19.
4B114.4B$15.4B6.A10.4B116.4B$16.4B5.3A7.4B118.4B$17.4B7.A5.4B120.4B$
18.4B5.2A4.4B122.4B$19.4B4.9B124.4B$20.4B5.6B126.4B$21.4B2.8B127.4B$
22.15B126.4B$23.14B127.4B$24.13B128.4B$25.10B.B2A127.4B$27.3B2AB3.BA.
A127.4B$27.3B2AB6.A128.4B$29.4B6.2A128.4B$29.3B138.4B$26.AB.2B140.4B$
25.A.AB2AB140.4B$25.A.ABABAB140.4B$22.2A.A.A.A.A2.A139.4B$22.A2.A2.2A
.4A140.4B$24.2A4.A145.4B$30.A.A144.4B$31.2A145.4B$179.4B$180.4B$181.
4B$182.4B$183.4B$184.4B$185.4B$186.4B$187.4B$188.4B$189.4B$190.4B$
191.4B$192.4B$193.4B$194.4B$195.4B$196.4B$197.4B$198.4B$199.4B$200.4B
$201.4B$202.4B$203.4B$204.4B$205.4B$206.4B$207.4B$208.4B4.2A$209.4B3.
2A$210.4B$211.4B$212.4B$213.4B$209.2A3.4B$209.2A4.3B!

Second error can be seen by XORing this pattern with the result of evolving it for one full cycle (552 ticks). The expected result of XOR is one glider (an output glider) and no other changes. The actual result of XOR is this, and can be taken as indication that the pattern is broken and is no longer a gun:

Code: Select all

x = 5, y = 3, rule = LifeHistory
C.C$C2.2C$C.2C!
#C [[ VIEWONLY ]]

[b-engine]

what about H. H. P. M. P. Cole?

I doesn't see that (s)he made many rules; I would place Cole at 6th place.

[wwei47]

(s)he

Friendly reminder that people can and do use other pronouns.

[Vort]

... Certain kinds of buggy/incorrect implementations will fail on the following input pattern (a p552 glider gun), or on some variant of this input pattern: ...

... Remove gliders one-by-one from this phase, each time checking whether the removal of the leading glider changes anything in the pattern 552 ticks later (apart from the expected disappearance of the leading glider translated by 138 cells diagonally). ...

I did not said how to perform "parallel universes" check exactly. (I even did not tried to implement it yet)

From your example it looks like such check should take into account every generation (not only 552 ticks later).
It will produce loop inside of the loop unfortunately.
But, first, lifelib should advance already known states pretty fast.
Second, it may be possible to eliminate some parts of computation.

upd: Idea of going back in time allows to focus on checking of single glider, while also limiting range of generations, which need checking.
In most of the cases, "parallel universe" check will succeed right away (or in few generations) after that single glider was born.

[confocaloid]

From your example it looks like such check should take into account every generation (not only 552 ticks later).
It will produce loop inside of the loop unfortunately.
But, first, lifelib should advance already known states pretty fast.
Second, it may be possible to eliminate some parts of computation.

Probably the best idea I was able to imagine so far, in order to guarantee correctness, would be to build a directed graph out of statements of the following form:

A glider g is a visible object (can be identified as a glider) in such-and-such location in phase t,
and the 1-tick successor of g is a visible object (can be identified as a glider) in the same location in phase (t + 1) mod period,
and presence or absence of g in phase t causes presence or absence of the 1-tick successor of g in phase (t+1) mod period and no other changes apart from that.

Then, instead of deleting escaping output gliders one-by-one, hopefully it would become possible to detect and trim the entire chain of escaping output gliders at once.

It might be tricky to write a good fast provably-correct implementation of this.
On the other hand, as soon as there are "shortcuts" to avoid dealing with causalities, there is a risk that someone will invent a counterexample pattern that will cause another damaged not-a-gun on Catagolue.

[Vort]

... Then, instead of deleting escaping output gliders one-by-one, hopefully it would become possible to detect and trim the entire chain of escaping output gliders at once. ...

I don't think "chain" is a problem really.
When converting "phase 1" to "phase 2", removal is perfectly controlled and can be easily done.

As for obtaining "phase 1", I think trimming some gliders very far away (without precise checks) (I forgot about this part yesterday) and going back in time allows to focus on single glider without any problems.

[confocaloid]

... Then, instead of deleting escaping output gliders one-by-one, hopefully it would become possible to detect and trim the entire chain of escaping output gliders at once. ...

I don't think "chain" is a problem really.
When converting "phase 1" to "phase 2", removal is perfectly controlled and can be easily done.

As for obtaining "phase 1", I think trimming some gliders very far away (without precise checks) (I forgot about this part yesterday) and going back in time allows to focus on single glider without any problems.

There might be a problem with doing the removals quickly enough. It sounds like "focusing on a single glider" would need repeatedly iterating over all phases of the gun many times, at the same time removing gliders from them one-by-one.

Suppose you already reached this pattern (p25 glider gun):

Code: Select all

x = 35, y = 26, rule = B3/S23
11b2o4b2o$11bobo2bobo$13bo2bo$12bo4bo$12b2o2b2o$14b2o$6b2o$7bo$7bobo$
5b2ob3ob4o$4bobo3b3ob4ob2o$4bobo3b2o2bo2b4o$2b2obob2ob2o3b2o4bo$3bobo
3bo2bo3bob3o$3bobobobo8b3o$2obo$o2bobo21bo$2bo5bo19bo$3b5o18b3o2$2bob
2o$2b2obo2$32bobo$33b2o$33bo!

To be able to safely remove the leading glider in the lower-right corner, there must be a way to prove that presence or absence of that glider will never cause any kind of difference, either permanent or temporary, to the evolution of the pattern (of course apart from presence or absence of successors of that glider).
How to prove that? Since it's the leading glider, presumably all gliders after that point were already removed as escaping output gliders. Evolve the above pattern for 1 tick, then evolve the same pattern with the leading glider removed for 1 tick, and check that the only difference is disappearance of the 1-tick successor of the glider:

Code: Select all

x = 35, y = 26, rule = DoubleB3S23
11.2C4.2C$11.C.C2.C.C$13.C2.C$12.C4.C$12.2C2.2C$14.2C$6.2C$7.C$7.C.C$
5.2C.3C.4C$4.C.C3.3C.4C.2C$4.C.C3.2C2.C2.4C$2.2C.C.2C.2C3.2C4.C$3.C.C
3.C2.C3.C.3C$3.C.C.C.C8.3C$2C.C$C2.C.C21.C$2.C5.C19.C$3.5C18.3C2$2.C.
2C$2.2C.C2$32.A.A$33.2A$33.A!

However, once this leading glider is deleted from this phase, it seems like the algorithm must jump to a different phase of the gun. The algorithm cannot simply continue removing gliders from the same phase. It seems like, after deleting the leading glider, the algorithm must evolve the remainder for (24 = 25 - 1) ticks:

Code: Select all

x = 35, y = 26, rule = DoubleB3S23
11.2C4.2C$11.C.C2.C.C$13.4C$11.C2.2C2.C$11.C2.2C2.C$13.C2.C$6.2C$7.C$
7.C.C$5.2C.2C3.2C$4.C.C4.2C.2C3.C$4.C.C4.C4.5C$2.2C.C.2C2.C3.2C4.C$3.
C.C3.C2.2C5.2C$3.C.C.2C8.C.C$2C.C.C.2C7.C$C2.5C18.C$2.C4.C19.2C$3.5C
18.2C2$2.C.2C$2.2C.C$33.A$34.A$32.3A!

Then repeat the same check again ("presence or absence of the glider in this phase causes presence or absence of the 1-tick successor of the glider in the next phase, and no other changes apart from that"). If the check succeeds, remove the leading glider, and again evolve the remainder for 24 ticks. Repeat as long as the check succeeds.

It seems like the algorithm will eventually reach the following phase, which in this case does not contain any "detectable glider" in the expected location, so in this case it is impossible to perform the presence-or-absence check to begin with:

Code: Select all

x = 23, y = 22, rule = B3/S23
11b2o4b2o$11bobo2bobo$13bo2bo$12b2o2b2o$11b3o2b3o$13bo2bo$6b2o$7bo6bo$
7bobo$5b2ob2o2b3o$4bobo5b2obo$4bobo8b3o2bobo$2b2obob2o3b2o3b2o3bo$3bob
o3bo5bo6bo$3bobob2o7bo4bo$2obobobo10b2o$o2b2obo$2bo4bo$3b5o2$2bob2o$2b
2obo!

I think this idea works (unless I'm missing some flaw, how about pseudo period guns?), but it might be tricky to make it work fast enough, hopefully also without consuming lots of memory.


EDIT: here is an example of a problem with pseudo period guns. The gun period is 57, the output glider stream period is 19. There are three different ways to "interpret" this gun as a period-57 gun that shoots glider triplets "xq4_456zy1562zy5247" (rather than single gliders):

Code: Select all

x = 500, y = 132, rule = B3/S23
24b2o3b2o5b2o62b2o5b2o3b2o80b2o3b2o5b2o62b2o5b2o3b2o80b2o3b2o5b2o62b2o
5b2o3b2o$19bo3bobo4bo5b2o62b2o5bo4bobo3bo70bo3bobo4bo5b2o62b2o5bo4bobo
3bo70bo3bobo4bo5b2o62b2o5bo4bobo3bo$18bobobo2bob3o78b3obo2bobobo68bobo
bo2bob3o78b3obo2bobobo68bobobo2bob3o78b3obo2bobobo$19b2ob3o2bo82bobob
2ob2o70b2ob3o2bo82bobob2ob2o70b2ob3o2bo82bobob2ob2o$26bo89bo79bo89bo
79bo89bo$17b5ob2o32bob2o2b2o45bo2b8o66b5ob2o32bob2o2b2o45bo2b8o66b5ob
2o32bob2o2b2o45bo2b8o$16bo8b2o30bobo3bo2bo43bo3bo6bo64bo8b2o30bobo3bo
2bo43bo3bo6bo64bo8b2o30bobo3bo2bo43bo3bo6bo$15bob3o2bo2bob2o27bo2b3o3b
2o45b3o2bob2obo62bob3o2bo2bob2o27bo2b3o3b2o45b3o2bob2obo62bob3o2bo2bob
2o27bo2b3o3b2o45b3o2bob2obo$15bobobob2o35b2o49b2ob2obo2bo3bo62bobobob
2o35b2o49b2ob2obo2bo3bo62bobobob2o35b2o49b2ob2obo2bo3bo$14b2o2b2ob2obo
3bo27bo2b2o2bo38b2o8b2obo3bo2b2o60b2o2b2ob2obo3bo27bo2b2o2bo38b2o8b2ob
o3bo2b2o60b2o2b2ob2obo3bo27bo2b2o2bo38b2o8b2obo3bo2b2o$17b2o4b2ob2o24b
2ob2obo41b5o4bobo3bo3bo67b2o4b2ob2o24b2ob2obo41b5o4bobo3bo3bo67b2o4b2o
b2o24b2ob2obo41b5o4bobo3bo3bo$18bo7bobo23b3o7b2obo18bo13b3ob3o4bo2bo5b
2o68bo7bobo23b3o7b2obo18bo13b3ob3o4bo2bo5b2o68bo7bobo23b3o7b2obo18bo
13b3ob3o4bo2bo5b2o$16bobobo2bobob2o8bo13bo6bo3bo2bo11b2o3b5o10bo3bo8bo
3bo2bobobobo62bobobo2bobob2o8bo13bo6bo3bo2bo11b2o3b5o10bo3bo8bo3bo2bob
obobo62bobobo2bobob2o8bo13bo6bo3bo2bo11b2o3b5o10bo3bo8bo3bo2bobobobo$
9bo5bobo2b4obo2bo6b2obo15b3ob2o2bo3bo11bo2bo5bo8bo4bo5bo2b3ob4obob2obo
54bo5bobo2b4obo2bo6b2obo15b3ob2o2bo3bo11bo2bo5bo8bo4bo5bo2b3ob4obob2ob
o54bo5bobo2b4obo2bo6b2obo15b3ob2o2bo3bo11bo2bo5bo8bo4bo5bo2b3ob4obob2o
bo$7b3o3b3obobo5bo2bo6b2obo12b2ob3obo4b3o12bobob5o6bo2bobo2b2o4bo2b3o
7bo3bo52b3o3b3obobo5bo2bo6b2obo12b2ob3obo4b3o12bobob5o6bo2bobo2b2o4bo
2b3o7bo3bo52b3o3b3obobo5bo2bo6b2obo12b2ob3obo4b3o12bobob5o6bo2bobo2b2o
4bo2b3o7bo3bo$6bo5bo3bo2bo2b2obob2o7b2o18b2ob4o13b2o2bobobo11bo13bo3b
5obo3b3o49bo5bo3bo2bo2b2obob2o7b2o18b2ob4o13b2o2bobobo11bo13bo3b5obo3b
3o49bo5bo3bo2bo2b2obob2o7b2o18b2ob4o13b2o2bobobo11bo13bo3b5obo3b3o$5bo
bo5b3o3bobobob2obo24bob2o5bob2o9bobobobo2bo24bo2bobo2bo2b2o5bo47bobo5b
3o3bobobob2obo24bob2o5bob2o9bobobobo2bo24bo2bobo2bo2b2o5bo47bobo5b3o3b
obobob2obo24bob2o5bob2o9bobobobo2bo24bo2bobo2bo2b2o5bo$2bo2bobob4o7b2o
2bobo17b2o7b2obo4bo2bo2bo4bo2bo2b2o3bo13bo11bobobo5bo6bobo43bo2bobob4o
7b2o2bobo17b2o7b2obo4bo2bo2bo4bo2bo2b2o3bo13bo11bobobo5bo6bobo43bo2bob
ob4o7b2o2bobo17b2o7b2obo4bo2bo2bo4bo2bo2b2o3bo13bo11bobobo5bo6bobo$bob
obo2bo2bo2b4o4bobobob3o12bob2o6bo3bob2obobob2o3bobobo5b3o2bo4b2o2bobo
2bo6b5obobo4b5obobo42bobobo2bo2bo2b4o4bobobob3o12bob2o6bo3bob2obobob2o
3bobobo5b3o2bo4b2o2bobo2bo6b5obobo4b5obobo42bobobo2bo2bo2b4o4bobobob3o
12bob2o6bo3bob2obobob2o3bobobo5b3o2bo4b2o2bobo2bo6b5obobo4b5obobo$2b2o
bobo4b2o4bo3bo2bo5bo11bob2o6bo3bob2obobo6bobo2b4ob3o2bo5bo4bo8bo5bobob
o5bo2bo2bobo41b2obobo4b2o4bo3bo2bo5bo11bob2o6bo3bob2obobo6bobo2b4ob3o
2bo5bo4bo8bo5bobobo5bo2bo2bobo41b2obobo4b2o4bo3bo2bo5bo11bob2o6bo3bob
2obobo6bobo2b4ob3o2bo5bo4bo8bo5bobobo5bo2bo2bobo$4b2o7bo2b2o2bobo3b5o
13bo8b2obo4bo2bob2o4bobobo2bo3bo8bo3bo9b5obo3bo3b2o4bobob3o41b2o7bo2b
2o2bobo3b5o13bo8b2obo4bo2bob2o4bobobo2bo3bo8bo3bo9b5obo3bo3b2o4bobob3o
41b2o7bo2b2o2bobo3b5o13bo8b2obo4bo2bob2o4bobobo2bo3bo8bo3bo9b5obo3bo3b
2o4bobob3o$2b2obo2b3o2bobo2b3ob2o4bo24bob2o5bo4bo6b2o5bo2bo4b3ob3o14bo
bobob2o2bo7b2o3bo38b2obo2b3o2bobo2b3ob2o4bo24bob2o5bo4bo6b2o5bo2bo4b3o
b3o14bobobob2o2bo7b2o3bo38b2obo2b3o2bobo2b3ob2o4bo24bob2o5bo4bo6b2o5bo
2bo4b3ob3o14bobobob2o2bo7b2o3bo$bobob3o4b2ob2o39b2ob4ob2o8bo3bo3bobo4b
5o12b2o5b3o2bobo2b3o2bob2obo37bobob3o4b2ob2o39b2ob4ob2o8bo3bo3bobo4b5o
12b2o5b3o2bobo2b3o2bob2obo37bobob3o4b2ob2o39b2ob4ob2o8bo3bo3bobo4b5o
12b2o5b3o2bobo2b3o2bob2obo$o4bob3o7b2o32b2ob3obo4b2o5b2o2bo3bob2o8b2o
15bo9b2ob2o4b3obo2b2o35bo4bob3o7b2o32b2ob3obo4b2o5b2o2bo3bob2o8b2o15bo
9b2ob2o4b3obo2b2o35bo4bob3o7b2o32b2ob3obo4b2o5b2o2bo3bob2o8b2o15bo9b2o
b2o4b3obo2b2o$4o3b3obob2obo2bo34b3ob2ob2obo6bo3bo2bob2ob2o22bob2o4b2o
7b3obobobo37b4o3b3obob2obo2bo34b3ob2ob2obo6bo3bo2bob2ob2o22bob2o4b2o7b
3obobobo37b4o3b3obob2obo2bo34b3ob2ob2obo6bo3bo2bob2ob2o22bob2o4b2o7b3o
bobobo$10bo2b2o2b2obo30bo10bob3o4bob2obo2b3o24b2ob2o3bo2bob2obob3o5bo
47bo2b2o2b2obo30bo10bob3o4bob2obo2b3o24b2ob2o3bo2bob2obob3o5bo47bo2b2o
2b2obo30bo10bob3o4bob2obo2b3o24b2ob2o3bo2bob2obob3o5bo$2b2ob2obo3b4o2b
obo31b3o6b2o2bobo4bo6bo3bo15b2o12bob2o2b2o2bo6b2o40b2ob2obo3b4o2bobo
31b3o6b2o2bobo4bo6bo3bo15b2o12bob2o2b2o2bo6b2o40b2ob2obo3b4o2bobo31b3o
6b2o2bobo4bo6bo3bo15b2o12bob2o2b2o2bo6b2o$2bo5bob2o4b3ob2o12b2o16b2ob
2o3bo2bo3bo5b8o2bo15b2o5b2ob2o2bobo2b4o3bob2o43bo5bob2o4b3ob2o12b2o16b
2ob2o3bo2bo3bo5b8o2bo15b2o5b2ob2o2bobo2b4o3bob2o43bo5bob2o4b3ob2o12b2o
16b2ob2o3bo2bo3bo5b8o2bo15b2o5b2ob2o2bobo2b4o3bob2o$obo15bobo14bo20bob
o2b6o10bo28b2obobobob3o4b2obo44bobo15bobo14bo20bobo2b6o10bo28b2obobobo
b3o4b2obo44bobo15bobo14bo20bobo2b6o10bo28b2obobobob3o4b2obo$2o11b2o3bo
bo14bobo23bo13b2ob3obo28bobobo54b2o11b2o3bobo14bobo23bo13b2ob3obo28bob
obo54b2o11b2o3bobo14bobo23bo13b2ob3obo28bobobo$19bo16b2o12b2o6b2obob2o
11bobo3bo3b2o22b2obobo3b2o68bo16b2o12b2o6b2obob2o11bobo3bo3b2o22b2obob
o3b2o68bo16b2o12b2o6b2obob2o11bobo3bo3b2o22b2obobo3b2o$50b2o8bo2bobo
10bo3b2o4b2o26bo105b2o8bo2bobo10bo3b2o4b2o26bo105b2o8bo2bobo10bo3b2o4b
2o26bo$55b2o6bobo11b3o145b2o6bobo11b3o145b2o6bobo11b3o$13b3o11bo12bobo
12bo8bo14bo13b3o25b3o59b3o11bo12bobo12bo8bo14bo13b3o25b3o59b3o11bo12bo
bo12bo8bo14bo13b3o25b3o$12b4o11b3o11bobo9bobo39bo11b2o10b2o61b4o11b3o
11bobo9bobo39bo11b2o10b2o61b4o11b3o11bobo9bobo39bo11b2o10b2o$2o9b2o2b
2o13bo9b2obo9b2o32bo4bo15bo10bo3bo46b2o9b2o2b2o13bo9b2obo9b2o32bo4bo
15bo10bo3bo46b2o9b2o2b2o13bo9b2obo9b2o32bo4bo15bo10bo3bo$2o10bob2o13b
2o11bo6b2o6b2o4bo18b2o2bobo19bobo3b3obo2b2o9b2o36b2o10bob2o13b2o11bo6b
2o6b2o4bo18b2o2bobo19bobo3b3obo2b2o9b2o36b2o10bob2o13b2o11bo6b2o6b2o4b
o18b2o2bobo19bobo3b3obo2b2o9b2o$13b3o33bobo4bobo4b3o16b2obo2bo3bobo14b
2o6bo14b2o49b3o33bobo4bobo4b3o16b2obo2bo3bobo14b2o6bo14b2o49b3o33bobo
4bobo4b3o16b2obo2bo3bobo14b2o6bo14b2o$14bo20b2o13b2o3bo10bo19b2o26bo6b
o62bo20b2o13b2o3bo10bo19b2o26bo6bo62bo20b2o13b2o3bo10bo19b2o26bo6bo$
34bo2bo16bob2o7b2o54bo82bo2bo16bob2o7b2o54bo82bo2bo16bob2o7b2o54bo$34b
o2bo12b5o3bo22b2o3b2o27b2o3bo83bo2bo12b5o3bo22b2o3b2o27b2o3bo83bo2bo
12b5o3bo22b2o3b2o27b2o3bo$18bo15bo2bo12bo4b3o10b2o12bo4bo26bo3b2o68bo
15bo2bo12bo4b3o10b2o12bo4bo26bo3b2o68bo15bo2bo12bo4b3o10b2o12bo4bo26bo
3b2o$17b3o15b2o14b3obo4b2o6b2o9b3o4bo26bo73b3o15b2o14b3obo4b2o6b2o9b3o
4bo26bo73b3o15b2o14b3obo4b2o6b2o9b3o4bo26bo$17b2obo32bobo6bo16bo6b2o
25bo6bo66b2obo32bobo6bo16bo6b2o25bo6bo66b2obo32bobo6bo16bo6b2o25bo6bo$
16b2o2b2o37bo41bo4bo10bo68b2o2b2o37bo41bo4bo10bo68b2o2b2o37bo41bo4bo
10bo$17b4o34bob2o40b2o4bo6b2o2bob3o66b4o34bob2o40b2o4bo6b2o2bob3o66b4o
34bob2o40b2o4bo6b2o2bob3o$17b3o37bob2o39b2o4bo4bo3bo71b3o37bob2o39b2o
4bo4bo3bo71b3o37bob2o39b2o4bo4bo3bo$57bobo54b2o111bobo54b2o111bobo54b
2o$36b2o18b2o2bo50b3o92b2o18b2o2bo50b3o92b2o18b2o2bo50b3o$30b2o4bobo
11bo8b2o12bo126b2o4bobo11bo8b2o12bo126b2o4bobo11bo8b2o12bo$11bob2o3b2o
3b2obo3b2o5b2o12b2o19b2o46bo60bob2o3b2o3b2obo3b2o5b2o12b2o19b2o46bo60b
ob2o3b2o3b2obo3b2o5b2o12b2o19b2o46bo$11bo3bo6bo3bo23b2o20bobo7bo31b2o
3bobo59bo3bo6bo3bo23b2o20bobo7bo31b2o3bobo59bo3bo6bo3bo23b2o20bobo7bo
31b2o3bobo$11bo14bo7b2o46b3o34bobo59bo14bo7b2o46b3o34bobo59bo14bo7b2o
46b3o34bobo$11bobo2b6o2bobo8bo11bo15bob2o18bo23bob2o4b3ob2o58bobo2b6o
2bobo8bo11bo15bob2o18bo23bob2o4b3ob2o58bobo2b6o2bobo8bo11bo15bob2o18bo
23bob2o4b3ob2o$9bobob2o3b2o3b2obobo3b3o11bobo14bobo18b2o20b2obo3b4o2bo
bo2bo54bobob2o3b2o3b2obobo3b3o11bobo14bobo18b2o20b2obo3b4o2bobo2bo54bo
bob2o3b2o3b2obobo3b3o11bobo14bobo18b2o20b2obo3b4o2bobo2bo$6bo10bo2bo
11bo14bo13b2obobo36b2o6bo2b2o2b2o3b2o51bo10bo2bo11bo14bo13b2obobo36b2o
6bo2b2o2b2o3b2o51bo10bo2bo11bo14bo13b2obobo36b2o6bo2b2o2b2o3b2o$6bobob
o3bob2o2b2obo3bobo16bo14bo40bo5b3obob2obo2b3o53bobobo3bob2o2b2obo3bobo
16bo14bo40bo5b3obob2obo2b3o53bobobo3bob2o2b2obo3bobo16bo14bo40bo5b3obo
b2obo2b3o$6bobobo5b2o2b2o22b3o14bo2bo5b2o30bobobob3o7b2o2bo5bo47bobobo
5b2o2b2o22b3o14bo2bo5b2o30bobobob3o7b2o2bo5bo47bobobo5b2o2b2o22b3o14bo
2bo5b2o30bobobob3o7b2o2bo5bo$9bob3obo2b2o2bob2o3bobo16b3o11bobo5bobo
13bo13b2o2bob3o4b2ob2o3bo4b3o7bo42bob3obo2b2o2bob2o3bobo16b3o11bobo5bo
bo13bo13b2o2bob3o4b2ob2o3bo4b3o7bo42bob3obo2b2o2bob2o3bobo16b3o11bobo
5bobo13bo13b2o2bob3o4b2ob2o3bo4b3o7bo$5b2o2bob3obobo2bobob4o3bo40bo12b
3o13bob2obo2b3o2bobo2b2o4bo10b3o36b2o2bob3obobo2bobob4o3bo40bo12b3o13b
ob2obo2b3o2bobo2b2o4bo10b3o36b2o2bob3obobo2bobob4o3bo40bo12b3o13bob2ob
o2b3o2bobo2b2o4bo10b3o$5b3ob2ob2obo6bobobob3o13b3o25b2o11b2o14bo3b2o7b
o2b2o6b2o7b2o3bo35b3ob2ob2obo6bobobob3o13b3o25b2o11b2o14bo3b2o7bo2b2o
6b2o7b2o3bo35b3ob2ob2obo6bobobob3o13b3o25b2o11b2o14bo3b2o7bo2b2o6b2o7b
2o3bo$6bo2b2o2bobob4obo5bo17bob3o43b2o6b3obobo4b2o3bo14bo3bobo36bo2b2o
2bobob4obo5bo17bob3o43b2o6b3obobo4b2o3bo14bo3bobo36bo2b2o2bobob4obo5bo
17bob3o43b2o6b3obobo4b2o3bo14bo3bobo$5b2o2bo4bo8bobobo2b3o17bo36b2o5bo
bo7bobo2bo2bo2b3o4b3o8b5ob2o34b2o2bo4bo8bobobo2b3o17bo36b2o5bobo7bobo
2bo2bo2b3o4b3o8b5ob2o34b2o2bo4bo8bobobo2b3o17bo36b2o5bobo7bobo2bo2bo2b
3o4b3o8b5ob2o$5bo4bobobob7o5bobo2bo11bob3o5b3obo5bo21b2o7bo9bobob4o8bo
2bo8bo40bo4bobobob7o5bobo2bo11bob3o5b3obo5bo21b2o7bo9bobob4o8bo2bo8bo
40bo4bobobob7o5bobo2bo11bob3o5b3obo5bo21b2o7bo9bobob4o8bo2bo8bo$7bo6bo
bo3bobo2b2obo2b2o10b5o7b2o2b2o5bo29b2o8bobo5b2o6bo2bo7bobo3b4o34bo6bob
o3bobo2b2obo2b2o10b5o7b2o2b2o5bo29b2o8bobo5b2o6bo2bo7bobo3b4o34bo6bobo
3bobo2b2obo2b2o10b5o7b2o2b2o5bo29b2o8bobo5b2o6bo2bo7bobo3b4o$6b2o4b2o
4bobo4bo2bo14b3o9b2o2bobo2b3o40bo5bo2bo6bo2bo5b3ob3o4bo32b2o4b2o4bobo
4bo2bo14b3o9b2o2bobo2b3o40bo5bo2bo6bo2bo5b3ob3o4bo32b2o4b2o4bobo4bo2bo
14b3o9b2o2bobo2b3o40bo5bo2bo6bo2bo5b3ob3o4bo$17b2ob2o4b2o28b6o21bo24b
3o3b2o3b2o2bo2bo5bobo2b4obobo42b2ob2o4b2o28b6o21bo24b3o3b2o3b2o2bo2bo
5bobo2b4obobo42b2ob2o4b2o28b6o21bo24b3o3b2o3b2o2bo2bo5bobo2b4obobo$21b
o15b2o17b2o2b2o20bobob2o22bo12bobo5b2o9bobo46bo15b2o17b2o2b2o20bobob2o
22bo12bobo5b2o9bobo46bo15b2o17b2o2b2o20bobob2o22bo12bobo5b2o9bobo$21bo
b2o4b2o7bo17b5o8bo12bobobobo32b2obo7bob2o2bobo3b3o44bob2o4b2o7bo17b5o
8bo12bobobobo32b2obo7bob2o2bobo3b3o44bob2o4b2o7bo17b5o8bo12bobobobo32b
2obo7bob2o2bobo3b3o$9b2o4b2o3b2obo4bo2bo6bobo14b2obo11b2o7b2obobobobo
2bo27bobo9bobob3o4bo4bo2bo28b2o4b2o3b2obo4bo2bo6bobo14b2obo11b2o7b2obo
bobobo2bo27bobo9bobob3o4bo4bo2bo28b2o4b2o3b2obo4bo2bo6bobo14b2obo11b2o
7b2obobobobo2bo27bobo9bobob3o4bo4bo2bo$10bo4bobobo3bobo3bobo2b2o3b2o
15b2o11b2o8bo2bo2b2ob4o14bo10b3o2b2o7bo4bo4bo4bo3b3o27bo4bobobo3bobo3b
obo2b2o3b2o15b2o11b2o8bo2bo2b2ob4o14bo10b3o2b2o7bo4bo4bo4bo3b3o27bo4bo
bobo3bobo3bobo2b2o3b2o15b2o11b2o8bo2bo2b2ob4o14bo10b3o2b2o7bo4bo4bo4bo
3b3o$8bo4b3obob4ob2o2bo2bobo2bo44b2o4bo11b2o3b5o8b2o3b4o4b2o2bobo2bobo
bo2b2o5bo24bo4b3obob4ob2o2bo2bobo2bo44b2o4bo11b2o3b5o8b2o3b4o4b2o2bobo
2bobobo2b2o5bo24bo4b3obob4ob2o2bo2bobo2bo44b2o4bo11b2o3b5o8b2o3b4o4b2o
2bobo2bobobo2b2o5bo$8b2o3b2o2bo13bob3o6b2o43bobo10bo2bo5bo7bo3b2o2bo4b
2o2bob4obob3o3bob2obo23b2o3b2o2bo13bob3o6b2o43bobo10bo2bo5bo7bo3b2o2bo
4b2o2bob4obob3o3bob2obo23b2o3b2o2bo13bob3o6b2o43bobo10bo2bo5bo7bo3b2o
2bo4b2o2bob4obob3o3bob2obo$9bo3b4ob8obobo12b2o4b2o38b2o10bobob2ob2o8bo
5bobo4b2o2bo7bo3b3o5bo2bo21bo3b4ob8obobo12b2o4b2o38b2o10bobob2ob2o8bo
5bobo4b2o2bo7bo3b3o5bo2bo21bo3b4ob8obobo12b2o4b2o38b2o10bobob2ob2o8bo
5bobo4b2o2bo7bo3b3o5bo2bo$9bobo3bo2bobo2bobobobob3o14bobo7b2o38b2o2bob
obo11b2o10b2o2bob2o6bo5bobobobobo20bobo3bo2bobo2bobobobob3o14bobo7b2o
38b2o2bobobo11b2o10b2o2bob2o6bo5bobobobobo20bobo3bo2bobo2bobobobob3o
14bobo7b2o38b2o2bobobo11b2o10b2o2bob2o6bo5bobobobobo$8bo3bo5bobo2bobo
2bob2o2bo13bo9bo14bo23bobobo4bo10b4o10bo4bobo4b2ob2o4bobob2o20bo3bo5bo
bo2bobo2bob2o2bo13bo9bo14bo23bobobo4bo10b4o10bo4bobo4b2ob2o4bobob2o20b
o3bo5bobo2bobo2bob2o2bo13bo9bo14bo23bobobo4bo10b4o10bo4bobo4b2ob2o4bob
ob2o$8bo4bob2obo2b2o2bobo4b3o24b3o12bo19bo2bo2b2obo2b2o10b2o11bobobo2b
3o3bobo3bob2o24bo4bob2obo2b2o2bobo4b3o24b3o12bo19bo2bo2b2obo2b2o10b2o
11bobobo2b3o3bobo3bob2o24bo4bob2obo2b2o2bobo4b3o24b3o12bo19bo2bo2b2obo
2b2o10b2o11bobobo2b3o3bobo3bob2o$11bo3b2obo6bobo4bo28bo10b3o18bobobo5b
o2b2o4bobo5bo8b2ob2obobo3bo2bobo2bo2b2o2b2o23bo3b2obo6bobo4bo28bo10b3o
18bobobo5bo2b2o4bobo5bo8b2ob2obobo3bo2bobo2bo2b2o2b2o23bo3b2obo6bobo4b
o28bo10b3o18bobobo5bo2b2o4bobo5bo8b2ob2obobo3bo2bobo2bo2b2o2b2o$9b3ob
3o4b4o6b3o45bobo12bobo2b4obo2b2o4bo2b2o3bo7bo5bo2b2obo2b2ob4o3bo2bobo
20b3ob3o4b4o6b3o45bobo12bobo2b4obo2b2o4bo2b2o3bo7bo5bo2b2obo2b2ob4o3bo
2bobo20b3ob3o4b4o6b3o45bobo12bobo2b4obo2b2o4bo2b2o3bo7bo5bo2b2obo2b2ob
4o3bo2bobo$9bo2b2o2bo3b4o3bo2b2o3bo43b2o13bobobo2bobo2b2o4b4o3b2o8b5o
3bo3b2o6b2o3bobo2bo19bo2b2o2bo3b4o3bo2b2o3bo43b2o13bobobo2bobo2b2o4b4o
3b2o8b5o3bo3b2o6b2o3bobo2bo19bo2b2o2bo3b4o3bo2b2o3bo43b2o13bobobo2bobo
2b2o4b4o3b2o8b5o3bo3b2o6b2o3bobo2bo$12b3o14b3o3b3o41bo16bo4bo4bo7b2o2b
3o17b3o3b4o2bob2ob5o22b3o14b3o3b3o41bo16bo4bo4bo7b2o2b3o17b3o3b4o2bob
2ob5o22b3o14b3o3b3o41bo16bo4bo4bo7b2o2b3o17b3o3b4o2bob2ob5o$14bob2o8b
2obo8bo29b2o25bo4b3obobo9bobo10b3o9b2o6bo3b2o29bob2o8b2obo8bo29b2o25bo
4b3obobo9bobo10b3o9b2o6bo3b2o29bob2o8b2obo8bo29b2o25bo4b3obobo9bobo10b
3o9b2o6bo3b2o$16b12o9b2o29bo15bo7b2o3bobo2b2obo7bob2o5b2o5bo2bob2o2b2o
bo8b4o2b2o28b12o9b2o29bo15bo7b2o3bobo2b2obo7bob2o5b2o5bo2bob2o2b2obo8b
4o2b2o28b12o9b2o29bo15bo7b2o3bobo2b2obo7bob2o5b2o5bo2bob2o2b2obo8b4o2b
2o$13bob2obob4obob2obo39bo14bo7bobo9b2o5bobo7bo8b2ob2o3bo2b8obo5bo25bo
b2obob4obob2obo39bo14bo7bobo9b2o5bobo7bo8b2ob2o3bo2b8obo5bo25bob2obob
4obob2obo39bo14bo7bobo9b2o5bobo7bo8b2ob2o3bo2b8obo5bo$14bobo10bobo3b2o
5b2o8b2o14b5o12b3o7bobob4o2bobo5bo2bo2b2o4b3o13bobo2b4o9bobo24bobo10bo
bo3b2o5b2o8b2o14b5o12b3o7bobob4o2bobo5bo2bo2b2o4b3o13bobo2b4o9bobo24bo
bo10bobo3b2o5b2o8b2o14b5o12b3o7bobob4o2bobo5bo2bo2b2o4b3o13bobo2b4o9bo
bo$33b2o4bobo9bo13bo28bo4b3ob3o5bo2bo10bo5b2ob4obobo16b2o43b2o4bobo9bo
13bo28bo4b3ob3o5bo2bo10bo5b2ob4obobo16b2o43b2o4bobo9bo13bo28bo4b3ob3o
5bo2bo10bo5b2ob4obobo16b2o$22b2o15b2o10bobo12b3o26b4o3bobo7bo2bo15b2ob
o2bob2o51b2o15b2o10bobo12b3o26b4o3bobo7bo2bo15b2obo2bob2o51b2o15b2o10b
obo12b3o26b4o3bobo7bo2bo15b2obo2bob2o$21b5o26b2o3bo11bo33bo8bo2bo75b5o
26b2o3bo11bo33bo8bo2bo75b5o26b2o3bo11bo33bo8bo2bo$20bobo2bo6b2o22bo2bo
6b4o27b2ob5o8b3o29bobo4bo37bobo2bo6b2o22bo2bo6b4o27b2ob5o8b3o29bobo4bo
37bobo2bo6b2o22bo2bo6b4o27b2ob5o8b3o29bobo4bo$20bo3b3o4b2ob2o20bo2bo6b
o3b2o26bobo3bo18bo21bo4b2o38bo3b3o4b2ob2o20bo2bo6bo3b2o26bobo3bo18bo
21bo4b2o38bo3b3o4b2ob2o20bo2bo6bo3b2o26bobo3bo18bo21bo4b2o$21b3o2bo5bo
2bo21bobo7b3o2bo13bobo9bo3b2o18b3o20b3ob3o39b3o2bo5bo2bo21bobo7b3o2bo
13bobo9bo3b2o18b3o20b3ob3o39b3o2bo5bo2bo21bobo7b3o2bo13bobo9bo3b2o18b
3o20b3ob3o$23b4o5bo2bo33bob2o14b2o10b3o19b4o24b2o7b2o33b4o5bo2bo33bob
2o14b2o10b3o19b4o24b2o7b2o33b4o5bo2bo33bob2o14b2o10b3o19b4o24b2o7b2o$
16b2o8bo6b2o4b2o28bo17bo6bo6bo18b2o10b2o6bo7b2o9bo26b2o8bo6b2o4b2o28bo
17bo6bo6bo18b2o10b2o6bo7b2o9bo26b2o8bo6b2o4b2o28bo17bo6bo6bo18b2o10b2o
6bo7b2o9bo$14b2ob2o3b2o2b2o10bo2bo26b2o22bobo24b3o10b2o5bobo13bo28b2ob
2o3b2o2b2o10bo2bo26b2o22bobo24b3o10b2o5bobo13bo28b2ob2o3b2o2b2o10bo2bo
26b2o22bobo24b3o10b2o5bobo13bo$14b2o8b4o12b2o51b2o25b2o24bo3bo4bo2bo
25b2o8b4o12b2o51b2o25b2o24bo3bo4bo2bo25b2o8b4o12b2o51b2o25b2o24bo3bo4b
o2bo$11b4o8b2o14b2ob2o77b4o11b2o2b2o5b4o30b4o8b2o14b2ob2o77b4o11b2o2b
2o5b4o30b4o8b2o14b2ob2o77b4o11b2o2b2o5b4o$11b2o2b2o3b2ob2o14b2o3bo15b
2o60b3o11b4o5b2o2b2o30b2o2b2o3b2ob2o14b2o3bo15b2o60b3o11b4o5b2o2b2o30b
2o2b2o3b2ob2o14b2o3bo15b2o60b3o11b4o5b2o2b2o$12bo8b2o6b2o7b3o3bo15bo4b
2o30bobo23bo12bo3bo41bo8b2o6b2o7b3o3bo15bo4b2o30bobo23bo12bo3bo41bo8b
2o6b2o7b3o3bo15bo4b2o30bobo23bo12bo3bo$3b2o7b4o13b2o8b2o3bo16b3o2bo31b
2o30bo14bobo25b2o7b4o13b2o8b2o3bo16b3o2bo31b2o30bo14bobo25b2o7b4o13b2o
8b2o3bo16b3o2bo31b2o30bo14bobo$3b2o7bo2b3o21b2ob2o20b2o32bo30bo7b2o7bo
26b2o7bo2b3o21b2ob2o20b2o32bo30bo7b2o7bo26b2o7bo2b3o21b2ob2o20b2o32bo
30bo7b2o7bo$12b3o3bo21b2o6bo10b3o2bo63b2o6b2o44b3o3bo21b2o6bo10b3o2bo
63b2o6b2o44b3o3bo21b2o6bo10b3o2bo63b2o6b2o$13bo2bobo19bo2bo5b3o8bo3bob
o37b2o25b2o4b3ob3o41bo2bobo19bo2bo5b3o8bo3bobo37b2o25b2o4b3ob3o41bo2bo
bo19bo2bo5b3o8bo3bobo37b2o25b2o4b3ob3o$13b5o21b2o5bo2b2o7b5ob2o39bo24b
o4b2o4bo41b5o21b2o5bo2b2o7b5ob2o39bo24bo4b2o4bo41b5o21b2o5bo2b2o7b5ob
2o39bo24bo4b2o4bo$15b2o42bo42bobo29bo4bobo43b2o42bo42bobo29bo4bobo43b
2o42bo42bobo29bo4bobo$22b2obo2bob2o26bobo3b4o35bo18b2o68b2obo2bob2o26b
obo3b4o35bo18b2o68b2obo2bob2o26bobo3b4o35bo18b2o$21bobob4ob2o5bo19b3ob
3o4bo52bobo4b2o61bobob4ob2o5bo19b3ob3o4bo52bobo4b2o61bobob4ob2o5bo19b
3ob3o4bo52bobo4b2o$15b4o2bobo13b3o11bo5bobo2b4obobo25b3o23b2o5b2o3bobo
10bobo36b4o2bobo13b3o11bo5bobo2b4obobo25b3o9bo13b2o5b2o3bobo10bobo36b
4o2bobo13b3o11bo5bobo2b4obobo25b3o9bo13b2o5b2o3bobo10bobo$11bob8o2bo3b
2ob2o8bo8b2o5b2o9bobo25b6o31bob2obob4obob2obo31bob8o2bo3b2ob2o8bo8b2o
5b2o9bobo25b6o7b2o22bob2obob4obob2obo31bob8o2bo3b2ob2o8bo8b2o5b2o9bobo
25b6o7b2o22bob2obob4obob2obo$9b4o8bob2o2b2obo2bo5b2o2b3o2b3o6bob2o2bob
o3b2o27b2obo22b2o9b12o32b4o8bob2o2b2obo2bo5b2o2b3o2b3o6bob2o2bobo3b2o
27b2obo5b2o15b2o9b12o32b4o8bob2o2b2obo2bo5b2o2b3o2b3o6bob2o2bobo3b2o
27b2obo5b2o15b2o9b12o$5b2ob2o3bo6b2o9b3o9b2o2b3o6bobob3o4bo32bobo21bo
8bob2o8b2obo26b2ob2o3bo6b2o9b3o9b2o2b3o6bobob3o4bo32bobo21bo8bob2o8b2o
bo26b2ob2o3bo6b2o9b3o9b2o2b3o6bobob3o4bo32bobo21bo8bob2o8b2obo$4bob2ob
2obo2b4o3b3o19bo2bo8bo4bo4bo35bo22b3o3b3o14b3o23bob2ob2obo2b4o3b3o19bo
2bo8bo4bo4bo35bo22b3o3b3o14b3o23bob2ob2obo2b4o3b3o19bo2bo8bo4bo4bo35bo
22b3o3b3o14b3o$4bobobo3b2o6b2o3bo3b5o7bo2bo4bobo3b2o2bobo2bobobo33b2o
23bo3b2o2bo3b4o3bo2b2o2bo20bobobo3b2o6b2o3bo3b5o7bo2bo4bobo3b2o2bobo2b
obobo33b2o23bo3b2o2bo3b4o3bo2b2o2bo20bobobo3b2o6b2o3bo3b5o7bo2bo4bobo
3b2o2bobo2bobobo33b2o9bo13bo3b2o2bo3b4o3bo2b2o2bo$2b2o2bo2bo3b4ob2o2bo
b2o2bo5bo5bo2bobo3bo5b2o2bob4o2bobo60b3o6b4o4b3ob3o18b2o2bo2bo3b4ob2o
2bob2o2bo5bo5bo2bobo3bo5b2o2bob4o2bobo60b3o6b4o4b3ob3o18b2o2bo2bo3b4ob
2o2bob2o2bo5bo5bo2bobo3bo5b2o2bob4o2bobo41bobo16b3o6b4o4b3ob3o$3bob2o
2b2o2bo2bobo2bo3bobob2ob2o7bobo5b3o3b2o2bo5bobobo60bo4bobo6bob2o3bo21b
ob2o2b2o2bo2bobo2bo3bobob2ob2o7bobo5b3o3b2o2bo5bobobo60bo4bobo6bob2o3b
o21bob2o2b2o2bo2bobo2bo3bobob2ob2o7bobo5b3o3b2o2bo5bobobo42b2o16bo4bob
o6bob2o3bo$3bo5b2obo3bobo3b3o2bobobo23b2o2bob2o2bo2bo59b3o4bobo2b2o2bo
b2obo4bo18bo5b2obo3bobo3b3o2bobobo23b2o2bob2o2bo2bo59b3o4bobo2b2o2bob
2obo4bo18bo5b2obo3bobo3b3o2bobobo23b2o2bob2o2bo2bo59b3o4bobo2b2o2bob2o
bo4bo$4b3obobo4b2ob2o4bobo4bo24bo4bobobo62bo2b2obo2bobo2bobo5bo3bo19b
3obobo4b2ob2o4bobo4bo24bo4bobobo62bo2b2obo2bobo2bobo5bo3bo19b3obobo4b
2ob2o4bobo4bo24bo4bobobo62bo2b2obo2bobo2bobo5bo3bo$6bobobobo5bo6b2obo
2b2o23bobobo2b2o64b3obobobobo2bobo2bo3bobo22bobobobo5bo6b2obo2b2o23bob
obo2b2o64b3obobobobo2bobo2bo3bobo22bobobobo5bo6b2obo2b2o23bobobo2b2o
64b3obobobobo2bobo2bo3bobo$8bo5b3o3bo7bo2b2o3b3o5bobo7b2ob2obobo70bobo
b8ob4o3bo24bo5b3o3bo7bo2b2o3b3o5bobo7b2ob2obobo70bobob8ob4o3bo24bo5b3o
3bo7bo2b2o3b3o5bobo7b2ob2obobo70bobob8ob4o3bo$8bob2obo3b3obob4obo2b2o
5bo3bobo2bo5bo5bo2bo64b3obo13bo2b2o3b2o23bob2obo3b3obob4obo2b2o5bo3bob
o2bo5bo5bo2bo64b3obo13bo2b2o3b2o23bob2obo3b3obob4obo2b2o5bo3bobo2bo5bo
5bo2bo64b3obo13bo2b2o3b2o$9bo5b2o2bobobo2bobo2b2o3bobo4bo2bo7b5o3b2o
62bo2bobo2bo2b2ob4obob3o4bo24bo5b2o2bobobo2bobo2b2o3bobo4bo2bo7b5o3b2o
62bo2bobo2bo2b2ob4obob3o4bo24bo5b2o2bobobo2bobo2b2o3bobo4bo2bo7b5o3b2o
62bo2bobo2bo2b2ob4obob3o4bo$10b3o3bo4bo4bo4bo8bo2bo12bo70b2o2bobo3bobo
3bobobo4bo27b3o3bo4bo4bo4bo8bo2bo12bo70b2o2bobo3bobo3bobobo4bo27b3o3bo
4bo4bo4bo8bo2bo12bo70b2o2bobo3bobo3bobobo4bo$12bo2bo4bo4b3obobo6b3o2b
2o86bo2bo4bobo4b2o4b2o28bo2bo4bo4b3obobo6b3o2b2o86bo2bo4bobo4b2o4b2o
28bo2bo4bo4b3obobo6b3o2b2o86bo2bo4bobo4b2o4b2o$16b3o3bobo2b2obo6b3o2b
3o87b2o4b2ob2o43b3o3bobo2b2obo6b3o2b3o87b2o4b2ob2o43b3o3bobo2b2obo6b3o
2b3o87b2o4b2ob2o$18bobo9b2o5b2o149bobo9b2o5b2o149bobo9b2o5b2o$18bobob
4o2bobo5bo151bobob4o2bobo5bo151bobob4o2bobo5bo$19bo4b3ob3o158bo4b3ob3o
158bo4b3ob3o$20b4o3bobo160b4o3bobo160b4o3bobo$28bo12b2o155bo12b2o155bo
12b2o$22b2ob4obo161b2ob4obo161b2ob4obo$21bobobo2bob3o158bobobo2bob3o
158bobobo2bob3o$22bo3bobo4bo5bo2bo149bo3bobo4bo5bo2bo149bo3bobo4bo5bo
2bo$27b2o3b2o5b2o156b2o3b2o5b2o156b2o3b2o5b2o!

[Vort]

There might be a problem with doing the removals quickly enough. It sounds like "focusing on a single glider" would need repeatedly iterating over all phases of the gun many times, at the same time removing gliders from them one-by-one.

Suppose you already reached this pattern (p25 glider gun):

Code: Select all

x = 35, y = 26, rule = B3/S23
11b2o4b2o$11bobo2bobo$13bo2bo$12bo4bo$12b2o2b2o$14b2o$6b2o$7bo$7bobo$
5b2ob3ob4o$4bobo3b3ob4ob2o$4bobo3b2o2bo2b4o$2b2obob2ob2o3b2o4bo$3bobo
3bo2bo3bob3o$3bobobobo8b3o$2obo$o2bobo21bo$2bo5bo19bo$3b5o18b3o2$2bob
2o$2b2obo2$32bobo$33b2o$33bo!

...

I'll just explain my idea with this pattern as example.

1. Advance pattern forward in time;
2. Choose one of the gliders (yellow);
3. Go back in time until yellow glider is about to be corrupted. This will be "phase 0";
4. For each step (forward in time) perform "parallel universes check" with yellow glider;
5. In this case, check will be successful right away;
6. Remove extra gliders to the right (it should be safe to do); This is "phase 1";
7. Remove yellow glider and advance 24 ticks. This will be envelope with correct bounding box;
8. Advance it until something tries to expand beyond bounding box;
9. In this case, it will happen right away. This will be "phase 2".

Intuitively, I feel that steps 1 and 2 can be made safe for any practical purposes by tweaking amount of expansion and selection algorithm for yellow glider. What do you think?
Second, I think pseudo-period guns won't make much difference. I can try explaining it with some other example if needed.

Code: Select all

x = 353, y = 77, rule = LifeHistory
154.3D107.D78.3D$153.D3.D105.2D77.D3.D$153.D2.2D106.D81.D$153.D.D.D
106.D80.D$153.2D2.D106.D79.D$153.D3.D106.D78.D$154.3D106.3D76.5D11$
11.2A4.2A52.2A4.2A72.2A4.2A52.2A4.2A42.2A4.2A32.2A4.2A32.2A4.2A$11.A.
A2.A.A52.A.A2.A.A72.A.A2.A.A52.A.A2.A.A42.A.A2.A.A32.A.A2.A.A32.A.A2.
A.A$13.A2.A56.4A76.4A56.4A46.4A36.A2BA36.A2BA$12.A4.A53.A2.2A2.A72.A
2.2A2.A52.A2.2A2.A42.A2.2A2.A32.B2A2B2AB32.B2A2B2AB$12.2A2.2A53.A2.2A
2.A72.A2.2A2.A52.A2.2A2.A42.A2.2A2.A32.3A2B3A32.3A2B3A$14.2A57.A2.A
76.A2.A56.A2.A46.A2.A35.BA2BAB34.BA2BAB$6.2A58.2A78.2A58.2A48.2A38.2A
6.2B30.2A6.2B$7.A59.A79.A59.A49.A39.A6.A32.A6.A$7.A.A57.A.A77.A.A4.A
52.A.A4.A42.A.A4.A32.A.AB2.2B32.A.AB2.2B$5.2A.3A.4A49.2A.2A75.2A.2A2.
A.A50.2A.2A2.A.A40.2A.2A2.A.A30.2A.2AB.3A2B28.2A.2AB.3A2B$4.A.A3.3A.
4A.2A43.A.A9.2A66.A.A5.A2.A48.A.A5.A2.A38.A.A5.A2.A28.A.A3.2B2ABA5B
23.A.A3.2B2ABA5B$4.A.A3.2A2.A2.4A43.A.A9.A2.A64.A.A8.A.2A2.E42.A.A8.A
.2A2.E32.A.A8.A.2A2.E22.A.A3.5B3A2BABA21.A.A3.5B3A2BABA$2.2A.A.2A.2A
3.2A4.A40.2A.A.2A7.A2.A62.2A.A.2A5.2A.2A3.2E38.2A.A.2A5.2A.2A3.2E28.
2A.A.2A5.2A.2A3.2E18.2A.A.2A.2B2A3B2A3BA19.2A.A.2A.2B2A3B2A3BA$3.A.A
3.A2.A3.A.3A42.A.A3.A7.A.A63.A.A3.A6.2A3.2E40.A.A3.A6.2A3.2E30.A.A3.A
6.2A3.2E20.A.A.B.A.4BA6BA20.A.A.B.A.4BA6BA$3.A.A.A.A8.3A42.A.A.2A9.A
4.A.A57.A.A.2A54.A.A.2A44.A.A.2A34.A.AB2AB5.BA4BA21.A.AB2AB5.BA4BA$2A
.A56.2A.A.A.2A15.2A54.2A.A.A.2A51.2A.A.A.2A41.2A.A.A.2A31.2A.A.ABAB7.
2B2A20.2A.A.ABAB7.2B2A$A2.A.A21.A32.A2.5A16.A55.A2.5A52.A2.5A42.A2.5A
32.A2.2ABAB32.A2.2ABAB$2.A5.A19.A33.A4.A74.A4.A20.A33.A4.A20.A23.A4.A
34.A4.AB33.A4.AB$3.5A18.3A34.5A75.5A21.A33.5A21.A23.5A35.5A35.5A$167.
3A57.3A$2.A.2A56.A.2A25.A50.A.2A56.A.2A46.A.2A36.A.2A36.A.2A$2.2A.A
56.2A.A23.A.A50.2A.A56.2A.A46.2A.A36.2A.A36.2A.A$90.2A$32.A.A$33.2A
138.A.A57.A.A$33.A140.2A58.2A$96.A77.A59.A$97.2A$96.2A2$181.A59.A$
179.A.A57.A.A$103.A76.2A58.2A$104.A$102.3A5$108.E.E$109.2E$109.E4$
116.A$114.A.A$115.2A4$121.A$122.2A$121.2A4$128.A$129.A$127.3A!