For general discussion about Conway's Game of Life.
dvgrn
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### Re: Thread for basic questions

Layz Boi wrote:
February 19th, 2020, 5:18 pm
Whats the logic or explanation behind the names given to object symmetries?

Also.. What's the general standard for the equivalent of "glide symmetry" in oscillators? For example, the "cis-queen-bee-shuttle." At any single step in its oscillation, it's asymmetric. However, it is composed of two, identical, mirrored halves that are just displaced in time when considering the whole oscillation. Is there simply no distinction, unless its a ship or what?
"Temporal glide symmetry" has been used a few times for this kind of thing, e.g., by Moosey at the end of the next linked thread.

Extrementhusiast started a thread about naming different temporal symmetries half a decade ago, but nothing seems to have been settled enough to add to the Symmetry page of the LifeWiki. That list might help answer your "logic or explanation" question also.

There was some discussion in LifeLine Volume 3 particularly of p2 symmetries, in an illustration labeled "The variety of flip-flop symmetry".

GUYTU6J
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### Re: Thread for basic questions

These two sentences seemed somewhat contradicting to me:
Lifewiki wrote:The colour of a glider is a property of the glider which remains constant while the glider is moving along a straight path ... A reflected version has to be advanced by two ticks to bring it back to one of these "canonical" phases, which has the effect of moving the key cells to the opposite color.
Then I realized that the color-defining cell of a glider on a single lane is alternating between two adjacent diagonals (1hd away):
color.png (7.61 KiB) Viewed 2260 times
So in fact the concepts of quarter/half/full diagonal, lane (of a glider) and color are closely related. Can we explain all of them visually with a superimposed checkerboard agar in Lifewiki like this? (These images are created in golly with two layers)
hdfd.png (3.93 KiB) Viewed 2260 times
Skimmed to: Soup search results Pg59
To be done: butter synthesis
Why do others have so much time posting around?
-GUYTU6J

Hunting
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### Re: Thread for basic questions

How was the bumpers and bouncers found? Is it possible to have similar things in LeapLife? We need to find a glider-reflecting that needs sparking at one moment first, right? (Is there a tool for that, I mean, that works with OCA?)
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JP21
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### Re: Thread for basic questions

Hunting wrote:
February 21st, 2020, 2:21 am
How was the bumpers and bouncers found? Is it possible to have similar things in LeapLife? We need to find a glider-reflecting that needs sparking at one moment first, right? (Is there a tool for that, I mean, that works with OCA?)
They found it with some tools/programs.
I've been trying forever to create one in your rule.
A 13 year old guy that have useless discoveries about life and other rules.

Code: Select all

``````x = 13, y = 20, rule = B3/S23
11b2o\$11b2o4\$8b2o\$8b2o2\$2o\$2o3\$3b2o\$3b2o2\$11b2o\$10b2o\$12bo\$3b2o\$3b2o!
``````

dvgrn
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### Re: Thread for basic questions

JP21 wrote:
February 21st, 2020, 3:56 am
Hunting wrote:
February 21st, 2020, 2:21 am
How was the bumpers and bouncers found? Is it possible to have similar things in LeapLife? We need to find a glider-reflecting that needs sparking at one moment first, right? (Is there a tool for that, I mean, that works with OCA?)
They found it with some tools/programs.
I've been trying forever to create one in your rule.
There's no tool specifically for finding glider reflectors. The general method was to collect sparky oscillators, catalysts, useful-looking reactions, and general expertise about the rule for a decade or two, and keep trying to put the pieces together until something works as a glider reflector.

Some of the relevant tools might be configurable to work with different Life-like rules, if you were lucky. But at least when bouncers were discovered, isotropic non-totalistic rules hadn't really been considered much by the people who were writing search programs and simulators/editors for Life problems. MCell had a syntax that supported non-totalistic rules, but Alan Hensel's notation and support for that in his applet and in Life32 didn't come along until 2000 or so, if I remember right.

Hunting
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### Re: Thread for basic questions

dvgrn wrote:
February 21st, 2020, 9:18 am
JP21 wrote:
February 21st, 2020, 3:56 am
Hunting wrote:
February 21st, 2020, 2:21 am
How was the bumpers and bouncers found? Is it possible to have similar things in LeapLife? We need to find a glider-reflecting that needs sparking at one moment first, right? (Is there a tool for that, I mean, that works with OCA?)
They found it with some tools/programs.
I've been trying forever to create one in your rule.
There's no tool specifically for finding glider reflectors. The general method was to collect sparky oscillators, catalysts, useful-looking reactions, and general expertise about the rule for a decade or two, and keep trying to put the pieces together until something works as a glider reflector.

Some of the relevant tools might be configurable to work with different Life-like rules, if you were lucky. But at least when bouncers were discovered, isotropic non-totalistic rules hadn't really been considered much by the people who were writing search programs and simulators/editors for Life problems. MCell had a syntax that supported non-totalistic rules, but Alan Hensel's notation and support for that in his applet and in Life32 didn't come along until 2000 or so, if I remember right.
Wow! I guess I'd start collecting sparky oscillators, catalysts, useful-looking reactions, and general expertise about the rule. Thanks.

(How do you find useful-looking reactions? By skill?)
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JP21
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### Re: Thread for basic questions

Hunting wrote:
February 21st, 2020, 9:33 am
dvgrn wrote:
February 21st, 2020, 9:18 am
JP21 wrote:
February 21st, 2020, 3:56 am

They found it with some tools/programs.
I've been trying forever to create one in your rule.
There's no tool specifically for finding glider reflectors. The general method was to collect sparky oscillators, catalysts, useful-looking reactions, and general expertise about the rule for a decade or two, and keep trying to put the pieces together until something works as a glider reflector.

Some of the relevant tools might be configurable to work with different Life-like rules, if you were lucky. But at least when bouncers were discovered, isotropic non-totalistic rules hadn't really been considered much by the people who were writing search programs and simulators/editors for Life problems. MCell had a syntax that supported non-totalistic rules, but Alan Hensel's notation and support for that in his applet and in Life32 didn't come along until 2000 or so, if I remember right.
Wow! I guess I'd start collecting sparky oscillators, catalysts, useful-looking reactions, and general expertise about the rule. Thanks.

(How do you find useful-looking reactions? By skill?)
By luck or searches.
A 13 year old guy that have useless discoveries about life and other rules.

Code: Select all

``````x = 13, y = 20, rule = B3/S23
11b2o\$11b2o4\$8b2o\$8b2o2\$2o\$2o3\$3b2o\$3b2o2\$11b2o\$10b2o\$12bo\$3b2o\$3b2o!
``````

Hunting
Posts: 2164
Joined: September 11th, 2017, 2:54 am

### Re: Thread for basic questions

JP21 wrote:
February 21st, 2020, 10:01 am
Hunting wrote:
February 21st, 2020, 9:33 am
dvgrn wrote:
February 21st, 2020, 9:18 am

There's no tool specifically for finding glider reflectors. The general method was to collect sparky oscillators, catalysts, useful-looking reactions, and general expertise about the rule for a decade or two, and keep trying to put the pieces together until something works as a glider reflector.

Some of the relevant tools might be configurable to work with different Life-like rules, if you were lucky. But at least when bouncers were discovered, isotropic non-totalistic rules hadn't really been considered much by the people who were writing search programs and simulators/editors for Life problems. MCell had a syntax that supported non-totalistic rules, but Alan Hensel's notation and support for that in his applet and in Life32 didn't come along until 2000 or so, if I remember right.
Wow! I guess I'd start collecting sparky oscillators, catalysts, useful-looking reactions, and general expertise about the rule. Thanks.

(How do you find useful-looking reactions? By skill?)
By luck or searches.
Well I was referring to a discussion in the ATPP thread

- (Replying to AbhpzTa) How did you find catalysts in ATPP? By luck?
- Probably by skill

Wait this isn't the sandbox
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muzik
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### Re: Thread for basic questions

Does there exist a pattern like the tremi snark that emits gliders on two out of three inputs?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

dvgrn
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### Re: Thread for basic questions

muzik wrote:
February 21st, 2020, 1:32 pm
Does there exist a pattern like the tremi snark that emits gliders on two out of three inputs?
Sure, there are lots of them as long as you don't mind them being a little bigger.

Code: Select all

``````x = 132, y = 56, rule = LifeHistory
37.2A\$36.B2AB11.2A.A.2A\$37.3B4.A.2A.A2.A.2A2.A\$36.B.B5.2A.A.2A.A4.A.A
13.A\$36.5B8.B2.5A.A12.3A\$36.6B6.2ABA4.A13.A\$36.8B4.2A.A.A3.A12.2A27.A
\$37.13B2.A.A3.A9.4B25.3A\$35.13B5.A3.2A8.3B26.A\$34.15B18.4B25.2A\$34.
15B4.B12.5B8.2A12.5B\$33.17B.B.2B11.6B8.A11.4B\$33.29B2.8B8.A.AB2.B4.6B
\$32.9B2A2B2A11BD14B8.2AB.3B3.7B\$31.9BABA2B2A9B3D13B11.16B\$30.2AB3.6BA
13BDBD4B.7B12.17B\$29.A2.A4.19BD15B12.9B2D6B\$28.A.2A5.6B3.B2.2B2.19B
11.10B2D6B\$28.A7.6B14.17B8.18B14.2A\$27.2A6.9B14.15B.2B2.8B2D10B12.2A
2.A\$34.4B4.2A15.22BD4B2D9B11.3A.2A11.A\$33.4B5.A16.8B.13BDBD8B2D4B9.A
4.B10.3A\$32.4B7.3A11.8B3.2B2A9B3D4B2.2B2D3B11.3AB2AB7.A\$32.3B10.A11.
2A3.B5.2B2A11BD4B2.7B13.A.2AB.4B2.2A\$32.2B24.A10.18B3.7B17.10B\$32.B
22.3A12.B.3B2.3B10.7B17.8B\$55.A21.2B12.6B17.11B\$77.B13.7B10.4B2.12B\$
91.6B11.18B\$90.6B11.19B\$90.6B11.17B\$89.8B10.17B\$90.6B8.B2.18B\$20.B2A
67.7B5.23B3.B\$20.ABA65.38B.B2A\$20.2BA63.B.2B2A11BDB2A21B2A\$20.3B62.2A
3B2A9B3DB2A22B\$85.2A14BDBD21B.3B\$86.15BD23B\$84.5B2.B2.2B2.26B\$84.2A4.
3B7.4B2.7B3.8B\$85.A4.B2AB12.6B8.5B\$82.3A6.2A15.3B11.4B\$82.A26.B13.4B\$
124.4B\$125.4B\$126.4B\$127.4B\$128.4B\$129.3B4\$.2A\$A.A\$2.A!``````
Or of course you could take the output of a regular period tripler (like the glider output at the right here, or just a tremi-Snark), and XOR it with an earlier signal split off from the input of the tripler. Or do I mean NAND? Either one, I guess.

JP21
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Location: PH

### Re: Thread for basic questions

Can anybody give or at least tell me all of the periodic Eater 2?

Code: Select all

``````x = 77, y = 20, rule = B3/S23
73bo\$47b2ob2o19b3o\$47b2obobo17bo3b2o\$bo17bo16bo13bobo6bo10b2o2bo\$2bo
17bo16bo9b2obob2o6bo11b2o2bo\$3o15b3o14b3o7b3o10b3o7b5obobo\$44bo4b2ob4o
11bo8bo\$8b2o16b2o15bob6o4bo10bob3o2bo\$4b2obobo12b2obobo11b2obobo4b2o2b
2o7b2obobo4bo\$4b2obo2b2obo8b2obo2b2obo7b2obo2bo16b2obo2bo2bo\$8bobob2o
12bobob2o11bobo2b3obo13bobo\$4b2ob2o5b2o6b2ob2o12b2ob2o2bo3bobo2bo6b2ob
2o2bo\$4bo4b5o2bo5bo4b5o7bo3bo6bob4o6bo3bo\$5b3obobo2b2o7b3obobo2bo7b3ob
obo4bo11b3obobo\$7bo3bobo11bo3bobo11bo2bo6bo12bo2bo\$11bobo15bob2o9bo4bo
4b2o11bo4bo\$7bo4bo12bo4bo2bo9b4o19b4o\$7b2o16b2o5b2o\$45b2o21b2o\$45b2o
21b2o!
``````
A 13 year old guy that have useless discoveries about life and other rules.

Code: Select all

``````x = 13, y = 20, rule = B3/S23
11b2o\$11b2o4\$8b2o\$8b2o2\$2o\$2o3\$3b2o\$3b2o2\$11b2o\$10b2o\$12bo\$3b2o\$3b2o!
``````

blah
Posts: 248
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### Re: Thread for basic questions

How do you generate a set of bitwise operations to compute a given lifelike rule, with the pattern encoded as a bitmap? My understanding is that lifelib can be compiled for separate rules, generating iterator functions using vector operations automatically, although looking through the source I see that B3/S23 has special coding, which would imply the automated process can still be beat by hand-optimisation.

My question isn't necessarily about lifelib in particular though, I want to understand this on a more basic algorithmic level. Is there any documentation or recommended reading on the subject?
succ

calcyman
Posts: 2143
Joined: June 1st, 2009, 4:32 pm

### Re: Thread for basic questions

It's a huge area of research called 'logic synthesis'. You'll probably want to read about Berkeley's ABC package together with Donald Knuth's fascicle on Boolean optimisation.
What do you do with ill crystallographers? Take them to the mono-clinic!

77topaz
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### Re: Thread for basic questions

JP21 wrote:
February 24th, 2020, 5:36 am
Can anybody give or at least tell me all of the periodic Eater 2?

Code: Select all

``````(snip)
``````
I think there are infinitely many possible oscillators with the one specific stator segment that allows the Eater 2 functionality.

Bullet51
Posts: 556
Joined: July 21st, 2014, 4:35 am

### Re: Thread for basic questions

GUYTU6J wrote:
February 5th, 2020, 1:37 am
What's the growth rate?

Code: Select all

``````x = 7, y = 9, rule = B2n3aikq4iq/S2-i3-a4i
2b3o\$2bobo\$2bo2b2o\$3bo2bo\$4b3o\$3bo\$2bo\$obo\$3o!
#C [[ GRAPH ]]
``````
The fractal curve appearing in the population plot is precisely the Takagi function in the limit of #generations→∞.

To see the fact, plot a time-history graph of the evolution of the CA, in the sense of Wolfram:

Code: Select all

``````x = 441, y = 881, rule = B/S012345678
2o\$2o\$2o\$3o\$3o\$4o\$4o\$2ob2o\$2ob2o\$2ob3o\$6o\$7o\$7o\$3ob4o\$2o3b3o\$2o4b3o\$2o
5b2o\$3o5b2o\$3o5b2o\$4o4b3o\$4o4b3o\$2ob2o3b4o\$2ob2o3b4o\$2ob3o2b5o\$6o2b5o\$
7ob6o\$7ob6o\$3ob11o\$2o3b10o\$2o4b10o\$2o5bob7o\$3o7b7o\$3o8b6o\$4o8b6o\$4o9b
5o\$2ob2o9b5o\$2ob2o10b4o\$2ob3o10b4o\$6o11b3o\$7o11b3o\$7o12b2o\$3ob4o12b2o\$
2o3b3o12b2o\$2o4b3o11b3o\$2o5b2o11b3o\$3o5b2o10b4o\$3o5b2o10b4o\$4o4b3o9b5o
\$4o4b3o9b5o\$2ob2o3b4o8b6o\$2ob2o3b4o8b6o\$2ob3o2b5o7b7o\$6o2b5o7b7o\$7ob6o
6b8o\$7ob6o6b8o\$3ob11o5b9o\$2o3b10o5b9o\$2o4b10o4b10o\$2o5bob7o4b10o\$3o7b
7o3b11o\$3o8b6o3b11o\$4o8b6o2b12o\$4o9b5o2b12o\$2ob2o9b5ob13o\$2ob2o10b4ob
13o\$2ob3o10b18o\$6o11b17o\$7o11b17o\$7o12bob14o\$3ob4o14b14o\$2o3b3o15b13o\$
2o4b3o15b13o\$2o5b2o16b12o\$3o5b2o16b12o\$3o5b2o17b11o\$4o4b3o17b11o\$4o4b
3o18b10o\$2ob2o3b4o18b10o\$2ob2o3b4o19b9o\$2ob3o2b5o19b9o\$6o2b5o20b8o\$7ob
6o20b8o\$7ob6o21b7o\$3ob11o21b7o\$2o3b10o22b6o\$2o4b10o22b6o\$2o5bob7o23b5o
\$3o7b7o23b5o\$3o8b6o24b4o\$4o8b6o24b4o\$4o9b5o25b3o\$2ob2o9b5o25b3o\$2ob2o
10b4o26b2o\$2ob3o10b4o26b2o\$6o11b3o26b2o\$7o11b3o25b3o\$7o12b2o25b3o\$3ob
4o12b2o24b4o\$2o3b3o12b2o24b4o\$2o4b3o11b3o23b5o\$2o5b2o11b3o23b5o\$3o5b2o
10b4o22b6o\$3o5b2o10b4o22b6o\$4o4b3o9b5o21b7o\$4o4b3o9b5o21b7o\$2ob2o3b4o
8b6o20b8o\$2ob2o3b4o8b6o20b8o\$2ob3o2b5o7b7o19b9o\$6o2b5o7b7o19b9o\$7ob6o
6b8o18b10o\$7ob6o6b8o18b10o\$3ob11o5b9o17b11o\$2o3b10o5b9o17b11o\$2o4b10o
4b10o16b12o\$2o5bob7o4b10o16b12o\$3o7b7o3b11o15b13o\$3o8b6o3b11o15b13o\$4o
8b6o2b12o14b14o\$4o9b5o2b12o14b14o\$2ob2o9b5ob13o13b15o\$2ob2o10b4ob13o
13b15o\$2ob3o10b18o12b16o\$6o11b17o12b16o\$7o11b17o11b17o\$7o12bob14o11b
17o\$3ob4o14b14o10b18o\$2o3b3o15b13o10b18o\$2o4b3o15b13o9b19o\$2o5b2o16b
12o9b19o\$3o5b2o16b12o8b20o\$3o5b2o17b11o8b20o\$4o4b3o17b11o7b21o\$4o4b3o
18b10o7b21o\$2ob2o3b4o18b10o6b22o\$2ob2o3b4o19b9o6b22o\$2ob3o2b5o19b9o5b
23o\$6o2b5o20b8o5b23o\$7ob6o20b8o4b24o\$7ob6o21b7o4b24o\$3ob11o21b7o3b25o\$
2o3b10o22b6o3b25o\$2o4b10o22b6o2b26o\$2o5bob7o23b5o2b26o\$3o7b7o23b5ob27o
\$3o8b6o24b4ob27o\$4o8b6o24b32o\$4o9b5o25b31o\$2ob2o9b5o25b31o\$2ob2o10b4o
26bob28o\$2ob3o10b4o28b28o\$6o11b3o29b27o\$7o11b3o29b27o\$7o12b2o30b26o\$3o
b4o12b2o30b26o\$2o3b3o12b2o31b25o\$2o4b3o11b3o31b25o\$2o5b2o11b3o32b24o\$
3o5b2o10b4o32b24o\$3o5b2o10b4o33b23o\$4o4b3o9b5o33b23o\$4o4b3o9b5o34b22o\$
2ob2o3b4o8b6o34b22o\$2ob2o3b4o8b6o35b21o\$2ob3o2b5o7b7o35b21o\$6o2b5o7b7o
36b20o\$7ob6o6b8o36b20o\$7ob6o6b8o37b19o\$3ob11o5b9o37b19o\$2o3b10o5b9o38b
18o\$2o4b10o4b10o38b18o\$2o5bob7o4b10o39b17o\$3o7b7o3b11o39b17o\$3o8b6o3b
11o40b16o\$4o8b6o2b12o40b16o\$4o9b5o2b12o41b15o\$2ob2o9b5ob13o41b15o\$2ob
2o10b4ob13o42b14o\$2ob3o10b18o42b14o\$6o11b17o43b13o\$7o11b17o43b13o\$7o
12bob14o44b12o\$3ob4o14b14o44b12o\$2o3b3o15b13o45b11o\$2o4b3o15b13o45b11o
\$2o5b2o16b12o46b10o\$3o5b2o16b12o46b10o\$3o5b2o17b11o47b9o\$4o4b3o17b11o
47b9o\$4o4b3o18b10o48b8o\$2ob2o3b4o18b10o48b8o\$2ob2o3b4o19b9o49b7o\$2ob3o
2b5o19b9o49b7o\$6o2b5o20b8o50b6o\$7ob6o20b8o50b6o\$7ob6o21b7o51b5o\$3ob11o
21b7o51b5o\$2o3b10o22b6o52b4o\$2o4b10o22b6o52b4o\$2o5bob7o23b5o53b3o\$3o7b
7o23b5o53b3o\$3o8b6o24b4o54b2o\$4o8b6o24b4o54b2o\$4o9b5o25b3o54b2o\$2ob2o
9b5o25b3o53b3o\$2ob2o10b4o26b2o53b3o\$2ob3o10b4o26b2o52b4o\$6o11b3o26b2o
52b4o\$7o11b3o25b3o51b5o\$7o12b2o25b3o51b5o\$3ob4o12b2o24b4o50b6o\$2o3b3o
12b2o24b4o50b6o\$2o4b3o11b3o23b5o49b7o\$2o5b2o11b3o23b5o49b7o\$3o5b2o10b
4o22b6o48b8o\$3o5b2o10b4o22b6o48b8o\$4o4b3o9b5o21b7o47b9o\$4o4b3o9b5o21b
7o47b9o\$2ob2o3b4o8b6o20b8o46b10o\$2ob2o3b4o8b6o20b8o46b10o\$2ob3o2b5o7b
7o19b9o45b11o\$6o2b5o7b7o19b9o45b11o\$7ob6o6b8o18b10o44b12o\$7ob6o6b8o18b
10o44b12o\$3ob11o5b9o17b11o43b13o\$2o3b10o5b9o17b11o43b13o\$2o4b10o4b10o
16b12o42b14o\$2o5bob7o4b10o16b12o42b14o\$3o7b7o3b11o15b13o41b15o\$3o8b6o
3b11o15b13o41b15o\$4o8b6o2b12o14b14o40b16o\$4o9b5o2b12o14b14o40b16o\$2ob
2o9b5ob13o13b15o39b17o\$2ob2o10b4ob13o13b15o39b17o\$2ob3o10b18o12b16o38b
18o\$6o11b17o12b16o38b18o\$7o11b17o11b17o37b19o\$7o12bob14o11b17o37b19o\$
3ob4o14b14o10b18o36b20o\$2o3b3o15b13o10b18o36b20o\$2o4b3o15b13o9b19o35b
21o\$2o5b2o16b12o9b19o35b21o\$3o5b2o16b12o8b20o34b22o\$3o5b2o17b11o8b20o
34b22o\$4o4b3o17b11o7b21o33b23o\$4o4b3o18b10o7b21o33b23o\$2ob2o3b4o18b10o
6b22o32b24o\$2ob2o3b4o19b9o6b22o32b24o\$2ob3o2b5o19b9o5b23o31b25o\$6o2b5o
20b8o5b23o31b25o\$7ob6o20b8o4b24o30b26o\$7ob6o21b7o4b24o30b26o\$3ob11o21b
7o3b25o29b27o\$2o3b10o22b6o3b25o29b27o\$2o4b10o22b6o2b26o28b28o\$2o5bob7o
23b5o2b26o28b28o\$3o7b7o23b5ob27o27b29o\$3o8b6o24b4ob27o27b29o\$4o8b6o24b
32o26b30o\$4o9b5o25b31o26b30o\$2ob2o9b5o25b31o25b31o\$2ob2o10b4o26bob28o
25b31o\$2ob3o10b4o28b28o24b32o\$6o11b3o29b27o24b32o\$7o11b3o29b27o23b33o\$
7o12b2o30b26o23b33o\$3ob4o12b2o30b26o22b34o\$2o3b3o12b2o31b25o22b34o\$2o
4b3o11b3o31b25o21b35o\$2o5b2o11b3o32b24o21b35o\$3o5b2o10b4o32b24o20b36o\$
3o5b2o10b4o33b23o20b36o\$4o4b3o9b5o33b23o19b37o\$4o4b3o9b5o34b22o19b37o\$
2ob2o3b4o8b6o34b22o18b38o\$2ob2o3b4o8b6o35b21o18b38o\$2ob3o2b5o7b7o35b
21o17b39o\$6o2b5o7b7o36b20o17b39o\$7ob6o6b8o36b20o16b40o\$7ob6o6b8o37b19o
16b40o\$3ob11o5b9o37b19o15b41o\$2o3b10o5b9o38b18o15b41o\$2o4b10o4b10o38b
18o14b42o\$2o5bob7o4b10o39b17o14b42o\$3o7b7o3b11o39b17o13b43o\$3o8b6o3b
11o40b16o13b43o\$4o8b6o2b12o40b16o12b44o\$4o9b5o2b12o41b15o12b44o\$2ob2o
9b5ob13o41b15o11b45o\$2ob2o10b4ob13o42b14o11b45o\$2ob3o10b18o42b14o10b
46o\$6o11b17o43b13o10b46o\$7o11b17o43b13o9b47o\$7o12bob14o44b12o9b47o\$3ob
4o14b14o44b12o8b48o\$2o3b3o15b13o45b11o8b48o\$2o4b3o15b13o45b11o7b49o\$2o
5b2o16b12o46b10o7b49o\$3o5b2o16b12o46b10o6b50o\$3o5b2o17b11o47b9o6b50o\$
4o4b3o17b11o47b9o5b51o\$4o4b3o18b10o48b8o5b51o\$2ob2o3b4o18b10o48b8o4b
52o\$2ob2o3b4o19b9o49b7o4b52o\$2ob3o2b5o19b9o49b7o3b53o\$6o2b5o20b8o50b6o
3b53o\$7ob6o20b8o50b6o2b54o\$7ob6o21b7o51b5o2b54o\$3ob11o21b7o51b5ob55o\$
2o3b10o22b6o52b4ob55o\$2o4b10o22b6o52b60o\$2o5bob7o23b5o53b59o\$3o7b7o23b
5o53b59o\$3o8b6o24b4o54bob56o\$4o8b6o24b4o56b56o\$4o9b5o25b3o57b55o\$2ob2o
9b5o25b3o57b55o\$2ob2o10b4o26b2o58b54o\$2ob3o10b4o26b2o58b54o\$6o11b3o26b
2o59b53o\$7o11b3o25b3o59b53o\$7o12b2o25b3o60b52o\$3ob4o12b2o24b4o60b52o\$
2o3b3o12b2o24b4o61b51o\$2o4b3o11b3o23b5o61b51o\$2o5b2o11b3o23b5o62b50o\$
3o5b2o10b4o22b6o62b50o\$3o5b2o10b4o22b6o63b49o\$4o4b3o9b5o21b7o63b49o\$4o
4b3o9b5o21b7o64b48o\$2ob2o3b4o8b6o20b8o64b48o\$2ob2o3b4o8b6o20b8o65b47o\$
2ob3o2b5o7b7o19b9o65b47o\$6o2b5o7b7o19b9o66b46o\$7ob6o6b8o18b10o66b46o\$
7ob6o6b8o18b10o67b45o\$3ob11o5b9o17b11o67b45o\$2o3b10o5b9o17b11o68b44o\$
2o4b10o4b10o16b12o68b44o\$2o5bob7o4b10o16b12o69b43o\$3o7b7o3b11o15b13o
69b43o\$3o8b6o3b11o15b13o70b42o\$4o8b6o2b12o14b14o70b42o\$4o9b5o2b12o14b
14o71b41o\$2ob2o9b5ob13o13b15o71b41o\$2ob2o10b4ob13o13b15o72b40o\$2ob3o
10b18o12b16o72b40o\$6o11b17o12b16o73b39o\$7o11b17o11b17o73b39o\$7o12bob
14o11b17o74b38o\$3ob4o14b14o10b18o74b38o\$2o3b3o15b13o10b18o75b37o\$2o4b
3o15b13o9b19o75b37o\$2o5b2o16b12o9b19o76b36o\$3o5b2o16b12o8b20o76b36o\$3o
5b2o17b11o8b20o77b35o\$4o4b3o17b11o7b21o77b35o\$4o4b3o18b10o7b21o78b34o\$
2ob2o3b4o18b10o6b22o78b34o\$2ob2o3b4o19b9o6b22o79b33o\$2ob3o2b5o19b9o5b
23o79b33o\$6o2b5o20b8o5b23o80b32o\$7ob6o20b8o4b24o80b32o\$7ob6o21b7o4b24o
81b31o\$3ob11o21b7o3b25o81b31o\$2o3b10o22b6o3b25o82b30o\$2o4b10o22b6o2b
26o82b30o\$2o5bob7o23b5o2b26o83b29o\$3o7b7o23b5ob27o83b29o\$3o8b6o24b4ob
27o84b28o\$4o8b6o24b32o84b28o\$4o9b5o25b31o85b27o\$2ob2o9b5o25b31o85b27o\$
2ob2o10b4o26bob28o86b26o\$2ob3o10b4o28b28o86b26o\$6o11b3o29b27o87b25o\$7o
11b3o29b27o87b25o\$7o12b2o30b26o88b24o\$3ob4o12b2o30b26o88b24o\$2o3b3o12b
2o31b25o89b23o\$2o4b3o11b3o31b25o89b23o\$2o5b2o11b3o32b24o90b22o\$3o5b2o
10b4o32b24o90b22o\$3o5b2o10b4o33b23o91b21o\$4o4b3o9b5o33b23o91b21o\$4o4b
3o9b5o34b22o92b20o\$2ob2o3b4o8b6o34b22o92b20o\$2ob2o3b4o8b6o35b21o93b19o
\$2ob3o2b5o7b7o35b21o93b19o\$6o2b5o7b7o36b20o94b18o\$7ob6o6b8o36b20o94b
18o\$7ob6o6b8o37b19o95b17o\$3ob11o5b9o37b19o95b17o\$2o3b10o5b9o38b18o96b
16o\$2o4b10o4b10o38b18o96b16o\$2o5bob7o4b10o39b17o97b15o\$3o7b7o3b11o39b
17o97b15o\$3o8b6o3b11o40b16o98b14o\$4o8b6o2b12o40b16o98b14o\$4o9b5o2b12o
41b15o99b13o\$2ob2o9b5ob13o41b15o99b13o\$2ob2o10b4ob13o42b14o100b12o\$2ob
3o10b18o42b14o100b12o\$6o11b17o43b13o101b11o\$7o11b17o43b13o101b11o\$7o
12bob14o44b12o102b10o\$3ob4o14b14o44b12o102b10o\$2o3b3o15b13o45b11o103b
9o\$2o4b3o15b13o45b11o103b9o\$2o5b2o16b12o46b10o104b8o\$3o5b2o16b12o46b
10o104b8o\$3o5b2o17b11o47b9o105b7o\$4o4b3o17b11o47b9o105b7o\$4o4b3o18b10o
48b8o106b6o\$2ob2o3b4o18b10o48b8o106b6o\$2ob2o3b4o19b9o49b7o107b5o\$2ob3o
2b5o19b9o49b7o107b5o\$6o2b5o20b8o50b6o108b4o\$7ob6o20b8o50b6o108b4o\$7ob
6o21b7o51b5o109b3o\$3ob11o21b7o51b5o109b3o\$2o3b10o22b6o52b4o110b2o\$2o4b
10o22b6o52b4o110b2o\$2o5bob7o23b5o53b3o110b2o\$3o7b7o23b5o53b3o109b3o\$3o
8b6o24b4o54b2o109b3o\$4o8b6o24b4o54b2o108b4o\$4o9b5o25b3o54b2o108b4o\$2ob
2o9b5o25b3o53b3o107b5o\$2ob2o10b4o26b2o53b3o107b5o\$2ob3o10b4o26b2o52b4o
106b6o\$6o11b3o26b2o52b4o106b6o\$7o11b3o25b3o51b5o105b7o\$7o12b2o25b3o51b
5o105b7o\$3ob4o12b2o24b4o50b6o104b8o\$2o3b3o12b2o24b4o50b6o104b8o\$2o4b3o
11b3o23b5o49b7o103b9o\$2o5b2o11b3o23b5o49b7o103b9o\$3o5b2o10b4o22b6o48b
8o102b10o\$3o5b2o10b4o22b6o48b8o102b10o\$4o4b3o9b5o21b7o47b9o101b11o\$4o
4b3o9b5o21b7o47b9o101b11o\$2ob2o3b4o8b6o20b8o46b10o100b12o\$2ob2o3b4o8b
6o20b8o46b10o100b12o\$2ob3o2b5o7b7o19b9o45b11o99b13o\$6o2b5o7b7o19b9o45b
11o99b13o\$7ob6o6b8o18b10o44b12o98b14o\$7ob6o6b8o18b10o44b12o98b14o\$3ob
11o5b9o17b11o43b13o97b15o\$2o3b10o5b9o17b11o43b13o97b15o\$2o4b10o4b10o
16b12o42b14o96b16o\$2o5bob7o4b10o16b12o42b14o96b16o\$3o7b7o3b11o15b13o
41b15o95b17o\$3o8b6o3b11o15b13o41b15o95b17o\$4o8b6o2b12o14b14o40b16o94b
18o\$4o9b5o2b12o14b14o40b16o94b18o\$2ob2o9b5ob13o13b15o39b17o93b19o\$2ob
2o10b4ob13o13b15o39b17o93b19o\$2ob3o10b18o12b16o38b18o92b20o\$6o11b17o
12b16o38b18o92b20o\$7o11b17o11b17o37b19o91b21o\$7o12bob14o11b17o37b19o
91b21o\$3ob4o14b14o10b18o36b20o90b22o\$2o3b3o15b13o10b18o36b20o90b22o\$2o
4b3o15b13o9b19o35b21o89b23o\$2o5b2o16b12o9b19o35b21o89b23o\$3o5b2o16b12o
8b20o34b22o88b24o\$3o5b2o17b11o8b20o34b22o88b24o\$4o4b3o17b11o7b21o33b
23o87b25o\$4o4b3o18b10o7b21o33b23o87b25o\$2ob2o3b4o18b10o6b22o32b24o86b
26o\$2ob2o3b4o19b9o6b22o32b24o86b26o\$2ob3o2b5o19b9o5b23o31b25o85b27o\$6o
2b5o20b8o5b23o31b25o85b27o\$7ob6o20b8o4b24o30b26o84b28o\$7ob6o21b7o4b24o
30b26o84b28o\$3ob11o21b7o3b25o29b27o83b29o\$2o3b10o22b6o3b25o29b27o83b
29o\$2o4b10o22b6o2b26o28b28o82b30o\$2o5bob7o23b5o2b26o28b28o82b30o\$3o7b
7o23b5ob27o27b29o81b31o\$3o8b6o24b4ob27o27b29o81b31o\$4o8b6o24b32o26b30o
80b32o\$4o9b5o25b31o26b30o80b32o\$2ob2o9b5o25b31o25b31o79b33o\$2ob2o10b4o
26bob28o25b31o79b33o\$2ob3o10b4o28b28o24b32o78b34o\$6o11b3o29b27o24b32o
78b34o\$7o11b3o29b27o23b33o77b35o\$7o12b2o30b26o23b33o77b35o\$3ob4o12b2o
30b26o22b34o76b36o\$2o3b3o12b2o31b25o22b34o76b36o\$2o4b3o11b3o31b25o21b
35o75b37o\$2o5b2o11b3o32b24o21b35o75b37o\$3o5b2o10b4o32b24o20b36o74b38o\$
3o5b2o10b4o33b23o20b36o74b38o\$4o4b3o9b5o33b23o19b37o73b39o\$4o4b3o9b5o
34b22o19b37o73b39o\$2ob2o3b4o8b6o34b22o18b38o72b40o\$2ob2o3b4o8b6o35b21o
18b38o72b40o\$2ob3o2b5o7b7o35b21o17b39o71b41o\$6o2b5o7b7o36b20o17b39o71b
41o\$7ob6o6b8o36b20o16b40o70b42o\$7ob6o6b8o37b19o16b40o70b42o\$3ob11o5b9o
37b19o15b41o69b43o\$2o3b10o5b9o38b18o15b41o69b43o\$2o4b10o4b10o38b18o14b
42o68b44o\$2o5bob7o4b10o39b17o14b42o68b44o\$3o7b7o3b11o39b17o13b43o67b
45o\$3o8b6o3b11o40b16o13b43o67b45o\$4o8b6o2b12o40b16o12b44o66b46o\$4o9b5o
2b12o41b15o12b44o66b46o\$2ob2o9b5ob13o41b15o11b45o65b47o\$2ob2o10b4ob13o
42b14o11b45o65b47o\$2ob3o10b18o42b14o10b46o64b48o\$6o11b17o43b13o10b46o
64b48o\$7o11b17o43b13o9b47o63b49o\$7o12bob14o44b12o9b47o63b49o\$3ob4o14b
14o44b12o8b48o62b50o\$2o3b3o15b13o45b11o8b48o62b50o\$2o4b3o15b13o45b11o
7b49o61b51o\$2o5b2o16b12o46b10o7b49o61b51o\$3o5b2o16b12o46b10o6b50o60b
52o\$3o5b2o17b11o47b9o6b50o60b52o\$4o4b3o17b11o47b9o5b51o59b53o\$4o4b3o
18b10o48b8o5b51o59b53o\$2ob2o3b4o18b10o48b8o4b52o58b54o\$2ob2o3b4o19b9o
49b7o4b52o58b54o\$2ob3o2b5o19b9o49b7o3b53o57b55o\$6o2b5o20b8o50b6o3b53o
57b55o\$7ob6o20b8o50b6o2b54o56b56o\$7ob6o21b7o51b5o2b54o56b56o\$3ob11o21b
7o51b5ob55o55b57o\$2o3b10o22b6o52b4ob55o55b57o\$2o4b10o22b6o52b60o54b58o
\$2o5bob7o23b5o53b59o54b58o\$3o7b7o23b5o53b59o53b59o\$3o8b6o24b4o54bob56o
53b59o\$4o8b6o24b4o56b56o52b60o\$4o9b5o25b3o57b55o52b60o\$2ob2o9b5o25b3o
57b55o51b61o\$2ob2o10b4o26b2o58b54o51b61o\$2ob3o10b4o26b2o58b54o50b62o\$
6o11b3o26b2o59b53o50b62o\$7o11b3o25b3o59b53o49b63o\$7o12b2o25b3o60b52o
49b63o\$3ob4o12b2o24b4o60b52o48b64o\$2o3b3o12b2o24b4o61b51o48b64o\$2o4b3o
11b3o23b5o61b51o47b65o\$2o5b2o11b3o23b5o62b50o47b65o\$3o5b2o10b4o22b6o
62b50o46b66o\$3o5b2o10b4o22b6o63b49o46b66o\$4o4b3o9b5o21b7o63b49o45b67o\$
4o4b3o9b5o21b7o64b48o45b67o\$2ob2o3b4o8b6o20b8o64b48o44b68o\$2ob2o3b4o8b
6o20b8o65b47o44b68o\$2ob3o2b5o7b7o19b9o65b47o43b69o\$6o2b5o7b7o19b9o66b
46o43b69o\$7ob6o6b8o18b10o66b46o42b70o\$7ob6o6b8o18b10o67b45o42b70o\$3ob
11o5b9o17b11o67b45o41b71o\$2o3b10o5b9o17b11o68b44o41b71o\$2o4b10o4b10o
16b12o68b44o40b72o\$2o5bob7o4b10o16b12o69b43o40b72o\$3o7b7o3b11o15b13o
69b43o39b73o\$3o8b6o3b11o15b13o70b42o39b73o\$4o8b6o2b12o14b14o70b42o38b
74o\$4o9b5o2b12o14b14o71b41o38b74o\$2ob2o9b5ob13o13b15o71b41o37b75o\$2ob
2o10b4ob13o13b15o72b40o37b75o\$2ob3o10b18o12b16o72b40o36b76o\$6o11b17o
12b16o73b39o36b76o\$7o11b17o11b17o73b39o35b77o\$7o12bob14o11b17o74b38o
35b77o\$3ob4o14b14o10b18o74b38o34b78o\$2o3b3o15b13o10b18o75b37o34b78o\$2o
4b3o15b13o9b19o75b37o33b79o\$2o5b2o16b12o9b19o76b36o33b79o\$3o5b2o16b12o
8b20o76b36o32b80o\$3o5b2o17b11o8b20o77b35o32b80o\$4o4b3o17b11o7b21o77b
35o31b81o\$4o4b3o18b10o7b21o78b34o31b81o\$2ob2o3b4o18b10o6b22o78b34o30b
82o\$2ob2o3b4o19b9o6b22o79b33o30b82o\$2ob3o2b5o19b9o5b23o79b33o29b83o\$6o
2b5o20b8o5b23o80b32o29b83o\$7ob6o20b8o4b24o80b32o28b84o\$7ob6o21b7o4b24o
81b31o28b84o\$3ob11o21b7o3b25o81b31o27b85o\$2o3b10o22b6o3b25o82b30o27b
85o\$2o4b10o22b6o2b26o82b30o26b86o\$2o5bob7o23b5o2b26o83b29o26b86o\$3o7b
7o23b5ob27o83b29o25b87o\$3o8b6o24b4ob27o84b28o25b87o\$4o8b6o24b32o84b28o
24b88o\$4o9b5o25b31o85b27o24b88o\$2ob2o9b5o25b31o85b27o23b89o\$2ob2o10b4o
26bob28o86b26o23b89o\$2ob3o10b4o28b28o86b26o22b90o\$6o11b3o29b27o87b25o
22b90o\$7o11b3o29b27o87b25o21b91o\$7o12b2o30b26o88b24o21b91o\$3ob4o12b2o
30b26o88b24o20b92o\$2o3b3o12b2o31b25o89b23o20b92o\$2o4b3o11b3o31b25o89b
23o19b93o\$2o5b2o11b3o32b24o90b22o19b93o\$3o5b2o10b4o32b24o90b22o18b94o\$
3o5b2o10b4o33b23o91b21o18b94o\$4o4b3o9b5o33b23o91b21o17b95o\$4o4b3o9b5o
34b22o92b20o17b95o\$2ob2o3b4o8b6o34b22o92b20o16b96o\$2ob2o3b4o8b6o35b21o
93b19o16b96o\$2ob3o2b5o7b7o35b21o93b19o15b97o\$6o2b5o7b7o36b20o94b18o15b
97o\$7ob6o6b8o36b20o94b18o14b98o\$7ob6o6b8o37b19o95b17o14b98o\$3ob11o5b9o
37b19o95b17o13b99o\$2o3b10o5b9o38b18o96b16o13b99o\$2o4b10o4b10o38b18o96b
16o12b100o\$2o5bob7o4b10o39b17o97b15o12b100o\$3o7b7o3b11o39b17o97b15o11b
101o\$3o8b6o3b11o40b16o98b14o11b101o\$4o8b6o2b12o40b16o98b14o10b102o\$4o
9b5o2b12o41b15o99b13o10b102o\$2ob2o9b5ob13o41b15o99b13o9b103o\$2ob2o10b
4ob13o42b14o100b12o9b103o\$2ob3o10b18o42b14o100b12o8b104o\$6o11b17o43b
13o101b11o8b104o\$7o11b17o43b13o101b11o7b105o\$7o12bob14o44b12o102b10o7b
105o\$3ob4o14b14o44b12o102b10o6b106o\$2o3b3o15b13o45b11o103b9o6b106o\$2o
4b3o15b13o45b11o103b9o5b107o\$2o5b2o16b12o46b10o104b8o5b107o\$3o5b2o16b
12o46b10o104b8o4b108o\$3o5b2o17b11o47b9o105b7o4b108o\$4o4b3o17b11o47b9o
105b7o3b109o\$4o4b3o18b10o48b8o106b6o3b109o\$2ob2o3b4o18b10o48b8o106b6o
2b110o\$2ob2o3b4o19b9o49b7o107b5o2b110o\$2ob3o2b5o19b9o49b7o107b5ob111o\$
6o2b5o20b8o50b6o108b4ob111o\$7ob6o20b8o50b6o108b116o\$7ob6o21b7o51b5o
109b115o\$3ob11o21b7o51b5o109b115o\$2o3b10o22b6o52b4o110bob112o\$2o4b10o
22b6o52b4o112b112o\$2o5bob7o23b5o53b3o113b111o\$3o7b7o23b5o53b3o113b111o
\$3o8b6o24b4o54b2o114b110o\$4o8b6o24b4o54b2o114b110o\$4o9b5o25b3o54b2o
115b109o\$2ob2o9b5o25b3o53b3o115b109o\$2ob2o10b4o26b2o53b3o116b108o\$2ob
3o10b4o26b2o52b4o116b108o\$6o11b3o26b2o52b4o117b107o\$7o11b3o25b3o51b5o
117b107o\$7o12b2o25b3o51b5o118b106o\$3ob4o12b2o24b4o50b6o118b106o\$2o3b3o
12b2o24b4o50b6o119b105o\$2o4b3o11b3o23b5o49b7o119b105o\$2o5b2o11b3o23b5o
49b7o120b104o\$3o5b2o10b4o22b6o48b8o120b104o\$3o5b2o10b4o22b6o48b8o121b
103o\$4o4b3o9b5o21b7o47b9o121b103o\$4o4b3o9b5o21b7o47b9o122b102o\$2ob2o3b
4o8b6o20b8o46b10o122b102o\$2ob2o3b4o8b6o20b8o46b10o123b101o\$2ob3o2b5o7b
7o19b9o45b11o123b101o\$6o2b5o7b7o19b9o45b11o124b100o\$7ob6o6b8o18b10o44b
12o124b100o\$7ob6o6b8o18b10o44b12o125b99o\$3ob11o5b9o17b11o43b13o125b99o
\$2o3b10o5b9o17b11o43b13o126b98o\$2o4b10o4b10o16b12o42b14o126b98o\$2o5bob
7o4b10o16b12o42b14o127b97o\$3o7b7o3b11o15b13o41b15o127b97o\$3o8b6o3b11o
15b13o41b15o128b96o\$4o8b6o2b12o14b14o40b16o128b96o\$4o9b5o2b12o14b14o
40b16o129b95o\$2ob2o9b5ob13o13b15o39b17o129b95o\$2ob2o10b4ob13o13b15o39b
17o130b94o\$2ob3o10b18o12b16o38b18o130b94o\$6o11b17o12b16o38b18o131b93o\$
7o11b17o11b17o37b19o131b93o\$7o12bob14o11b17o37b19o132b92o\$3ob4o14b14o
10b18o36b20o132b92o\$2o3b3o15b13o10b18o36b20o133b91o\$2o4b3o15b13o9b19o
35b21o133b91o\$2o5b2o16b12o9b19o35b21o134b90o\$3o5b2o16b12o8b20o34b22o
134b90o\$3o5b2o17b11o8b20o34b22o135b89o\$4o4b3o17b11o7b21o33b23o135b89o\$
4o4b3o18b10o7b21o33b23o136b88o\$2ob2o3b4o18b10o6b22o32b24o136b88o\$2ob2o
3b4o19b9o6b22o32b24o137b87o\$2ob3o2b5o19b9o5b23o31b25o137b87o\$6o2b5o20b
8o5b23o31b25o138b86o\$7ob6o20b8o4b24o30b26o138b86o\$7ob6o21b7o4b24o30b
26o139b85o\$3ob11o21b7o3b25o29b27o139b85o\$2o3b10o22b6o3b25o29b27o140b
84o\$2o4b10o22b6o2b26o28b28o140b84o\$2o5bob7o23b5o2b26o28b28o141b83o\$3o
7b7o23b5ob27o27b29o141b83o\$3o8b6o24b4ob27o27b29o142b82o\$4o8b6o24b32o
26b30o142b82o\$4o9b5o25b31o26b30o143b81o\$2ob2o9b5o25b31o25b31o143b81o\$
2ob2o10b4o26bob28o25b31o144b80o\$2ob3o10b4o28b28o24b32o144b80o\$6o11b3o
29b27o24b32o145b79o\$7o11b3o29b27o23b33o145b79o\$7o12b2o30b26o23b33o146b
78o\$3ob4o12b2o30b26o22b34o146b78o\$2o3b3o12b2o31b25o22b34o147b77o\$2o4b
3o11b3o31b25o21b35o147b77o\$2o5b2o11b3o32b24o21b35o148b76o\$3o5b2o10b4o
32b24o20b36o148b76o\$3o5b2o10b4o33b23o20b36o149b75o\$4o4b3o9b5o33b23o19b
37o149b75o\$4o4b3o9b5o34b22o19b37o150b74o\$2ob2o3b4o8b6o34b22o18b38o150b
74o\$2ob2o3b4o8b6o35b21o18b38o151b73o\$2ob3o2b5o7b7o35b21o17b39o151b73o\$
6o2b5o7b7o36b20o17b39o152b72o\$7ob6o6b8o36b20o16b40o152b72o\$7ob6o6b8o
37b19o16b40o153b71o\$3ob11o5b9o37b19o15b41o153b71o\$2o3b10o5b9o38b18o15b
41o154b70o\$2o4b10o4b10o38b18o14b42o154b70o\$2o5bob7o4b10o39b17o14b42o
155b69o\$3o7b7o3b11o39b17o13b43o155b69o\$3o8b6o3b11o40b16o13b43o156b68o\$
4o8b6o2b12o40b16o12b44o156b68o\$4o9b5o2b12o41b15o12b44o157b67o\$2ob2o9b
5ob13o41b15o11b45o157b67o\$2ob2o10b4ob13o42b14o11b45o158b66o\$2ob3o10b
18o42b14o10b46o158b66o\$6o11b17o43b13o10b46o159b65o\$7o11b17o43b13o9b47o
159b65o\$7o12bob14o44b12o9b47o160b64o\$3ob4o14b14o44b12o8b48o160b64o\$2o
3b3o15b13o45b11o8b48o161b63o\$2o4b3o15b13o45b11o7b49o161b63o\$2o5b2o16b
12o46b10o7b49o162b62o\$3o5b2o16b12o46b10o6b50o162b62o\$3o5b2o17b11o47b9o
6b50o163b61o\$4o4b3o17b11o47b9o5b51o163b61o\$4o4b3o18b10o48b8o5b51o164b
60o\$2ob2o3b4o18b10o48b8o4b52o164b60o\$2ob2o3b4o19b9o49b7o4b52o165b59o\$
2ob3o2b5o19b9o49b7o3b53o165b59o\$6o2b5o20b8o50b6o3b53o166b58o\$7ob6o20b
8o50b6o2b54o166b58o\$7ob6o21b7o51b5o2b54o167b57o\$3ob11o21b7o51b5ob55o
167b57o\$2o3b10o22b6o52b4ob55o168b56o\$2o4b10o22b6o52b60o168b56o\$2o5bob
7o23b5o53b59o169b55o\$3o7b7o23b5o53b59o169b55o\$3o8b6o24b4o54bob56o170b
54o\$4o8b6o24b4o56b56o170b54o\$4o9b5o25b3o57b55o171b53o\$2ob2o9b5o25b3o
57b55o171b53o\$2ob2o10b4o26b2o58b54o172b52o\$2ob3o10b4o26b2o58b54o172b
52o\$6o11b3o26b2o59b53o173b51o\$7o11b3o25b3o59b53o173b51o\$7o12b2o25b3o
60b52o174b50o\$3ob4o12b2o24b4o60b52o174b50o\$2o3b3o12b2o24b4o61b51o175b
49o\$2o4b3o11b3o23b5o61b51o175b49o\$2o5b2o11b3o23b5o62b50o176b48o\$3o5b2o
10b4o22b6o62b50o176b48o\$3o5b2o10b4o22b6o63b49o177b47o\$4o4b3o9b5o21b7o
63b49o177b47o\$4o4b3o9b5o21b7o64b48o178b46o\$2ob2o3b4o8b6o20b8o64b48o
178b46o\$2ob2o3b4o8b6o20b8o65b47o179b45o\$2ob3o2b5o7b7o19b9o65b47o179b
45o\$6o2b5o7b7o19b9o66b46o180b44o\$7ob6o6b8o18b10o66b46o180b44o\$7ob6o6b
8o18b10o67b45o181b43o\$3ob11o5b9o17b11o67b45o181b43o\$2o3b10o5b9o17b11o
68b44o182b42o\$2o4b10o4b10o16b12o68b44o182b42o\$2o5bob7o4b10o16b12o69b
43o183b41o\$3o7b7o3b11o15b13o69b43o183b41o\$3o8b6o3b11o15b13o70b42o184b
40o\$4o8b6o2b12o14b14o70b42o184b40o\$4o9b5o2b12o14b14o71b41o185b39o\$2ob
2o9b5ob13o13b15o71b41o185b39o\$2ob2o10b4ob13o13b15o72b40o186b38o\$2ob3o
10b18o12b16o72b40o186b38o\$6o11b17o12b16o73b39o187b37o\$7o11b17o11b17o
73b39o187b37o\$7o12bob14o11b17o74b38o188b36o\$3ob4o14b14o10b18o74b38o
188b36o\$2o3b3o15b13o10b18o75b37o189b35o\$2o4b3o15b13o9b19o75b37o189b35o
\$2o5b2o16b12o9b19o76b36o190b34o\$3o5b2o16b12o8b20o76b36o190b34o\$3o5b2o
17b11o8b20o77b35o191b33o\$4o4b3o17b11o7b21o77b35o191b33o\$4o4b3o18b10o7b
21o78b34o192b32o\$2ob2o3b4o18b10o6b22o78b34o192b32o\$2ob2o3b4o19b9o6b22o
79b33o193b31o\$2ob3o2b5o19b9o5b23o79b33o193b31o\$6o2b5o20b8o5b23o80b32o
194b30o\$7ob6o20b8o4b24o80b32o194b30o\$7ob6o21b7o4b24o81b31o195b29o\$3ob
11o21b7o3b25o81b31o195b29o\$2o3b10o22b6o3b25o82b30o196b28o\$2o4b10o22b6o
2b26o82b30o196b28o\$2o5bob7o23b5o2b26o83b29o197b27o\$3o7b7o23b5ob27o83b
29o197b27o\$3o8b6o24b4ob27o84b28o198b26o\$4o8b6o24b32o84b28o198b26o\$4o9b
5o25b31o85b27o199b25o\$2ob2o9b5o25b31o85b27o199b25o\$2ob2o10b4o26bob28o
86b26o200b24o\$2ob3o10b4o28b28o86b26o200b24o\$6o11b3o29b27o87b25o201b23o
\$7o11b3o29b27o87b25o201b23o\$7o12b2o30b26o88b24o202b22o\$3ob4o12b2o30b
26o88b24o202b22o\$2o3b3o12b2o31b25o89b23o203b21o\$2o4b3o11b3o31b25o89b
23o203b21o\$2o5b2o11b3o32b24o90b22o204b20o\$3o5b2o10b4o32b24o90b22o204b
20o\$3o5b2o10b4o33b23o91b21o205b19o\$4o4b3o9b5o33b23o91b21o205b19o\$4o4b
3o9b5o34b22o92b20o206b18o\$2ob2o3b4o8b6o34b22o92b20o206b18o\$2ob2o3b4o8b
6o35b21o93b19o207b17o\$2ob3o2b5o7b7o35b21o93b19o207b17o\$6o2b5o7b7o36b
20o94b18o208b16o\$7ob6o6b8o36b20o94b18o208b16o\$7ob6o6b8o37b19o95b17o
209b15o\$3ob11o5b9o37b19o95b17o209b15o\$2o3b10o5b9o38b18o96b16o210b14o\$
2o4b10o4b10o38b18o96b16o210b14o\$2o5bob7o4b10o39b17o97b15o211b13o\$3o7b
7o3b11o39b17o97b15o211b13o\$3o8b6o3b11o40b16o98b14o212b12o\$4o8b6o2b12o
40b16o98b14o212b12o\$4o9b5o2b12o41b15o99b13o213b11o\$2ob2o9b5ob13o41b15o
99b13o213b11o\$2ob2o10b4ob13o42b14o100b12o214b10o\$2ob3o10b18o42b14o100b
12o214b10o\$6o11b17o43b13o101b11o215b9o\$7o11b17o43b13o101b11o215b9o\$7o
12bob14o44b12o102b10o216b8o\$3ob4o14b14o44b12o102b10o216b8o\$2o3b3o15b
13o45b11o103b9o217b7o\$2o4b3o15b13o45b11o103b9o217b7o\$2o5b2o16b12o46b
10o104b8o218b6o\$3o5b2o16b12o46b10o104b8o218b6o\$3o5b2o17b11o47b9o105b7o
219b5o\$4o4b3o17b11o47b9o105b7o219b5o\$4o4b3o18b10o48b8o106b6o220b4o\$2ob
2o3b4o18b10o48b8o106b6o220b4o\$2ob2o3b4o19b9o49b7o107b5o221b3o\$2ob3o2b
5o19b9o49b7o107b5o221b3o\$6o2b5o20b8o50b6o108b4o222b2o\$7ob6o20b8o50b6o
108b4o222b2o\$7ob6o21b7o51b5o109b3o222b2o\$3ob11o21b7o51b5o109b3o221b3o\$
2o3b10o22b6o52b4o110b2o221b3o\$2o4b10o22b6o52b4o110b2o220b4o\$2o5bob7o
23b5o53b3o110b2o220b4o\$3o7b7o23b5o53b3o109b3o219b5o\$3o8b6o24b4o54b2o
109b3o219b5o\$4o8b6o24b4o54b2o108b4o218b6o\$4o9b5o25b3o54b2o108b4o218b6o
\$2ob2o9b5o25b3o53b3o107b5o217b7o\$2ob2o10b4o26b2o53b3o107b5o217b7o\$2ob
3o10b4o26b2o52b4o106b6o216b8o\$6o11b3o26b2o52b4o106b6o216b8o\$7o11b3o25b
3o51b5o105b7o215b9o\$7o12b2o25b3o51b5o105b7o215b9o!
``````
and find out the shape of the bump satisfies the function equation of the Takagi function: f(x)=f(2x mod 1)/2+min(x,1-x).
Still drifting.

GUYTU6J
Posts: 971
Joined: August 5th, 2016, 10:27 am
Location: 中国

### Re: Thread for basic questions

Bullet51 wrote:
February 27th, 2020, 10:20 am
GUYTU6J wrote:
February 5th, 2020, 1:37 am
What's the growth rate?

Code: Select all

``````x = 7, y = 9, rule = B2n3aikq4iq/S2-i3-a4i
2b3o\$2bobo\$2bo2b2o\$3bo2bo\$4b3o\$3bo\$2bo\$obo\$3o!
#C [[ GRAPH ]]
``````
The fractal curve appearing in the population plot is precisely the Takagi function in the limit of #generations→∞.
...
Thanks! Can we implement this in CGoL? (Of course just a barrel is enough)
Is the property that the fuse burns twice as fast as the wickstretcher engine necessary?
Skimmed to: Soup search results Pg59
To be done: butter synthesis
Why do others have so much time posting around?
-GUYTU6J

Hunting
Posts: 2164
Joined: September 11th, 2017, 2:54 am

### Re: Thread for basic questions

GUYTU6J wrote:
February 27th, 2020, 12:36 pm
Bullet51 wrote:
February 27th, 2020, 10:20 am
GUYTU6J wrote:
February 5th, 2020, 1:37 am
What's the growth rate?

Code: Select all

``````x = 7, y = 9, rule = B2n3aikq4iq/S2-i3-a4i
2b3o\$2bobo\$2bo2b2o\$3bo2bo\$4b3o\$3bo\$2bo\$obo\$3o!
#C [[ GRAPH ]]
``````
The fractal curve appearing in the population plot is precisely the Takagi function in the limit of #generations→∞.
...
Thanks! Can we implement this in CGoL? (Of course just a barrel is enough)
Is the property that the fuse burns twice as fast as the wickstretcher engine necessary?
Of course we can - just use 0E0P. XD
Proud member of the p22ers!

Working on:

LeapLife Demonoid

metametapixel
Posts: 5
Joined: February 29th, 2020, 6:30 pm

### Re: Thread for basic questions

The lowest-period LWSS gun I can make is period 30, using Gosper Glider Guns. Is there a smaller-period one? I know period 14 would be the lowest possible...

JP21
Posts: 814
Joined: October 26th, 2019, 5:39 am
Location: PH

### Re: Thread for basic questions

metametapixel wrote:
February 29th, 2020, 6:57 pm
The lowest-period LWSS gun I can make is period 30, using Gosper Glider Guns. Is there a smaller-period one? I know period 14 would be the lowest possible...
I'm definitely not an expert but I know for a fact that pseudo-period LWSS guns at period 14(?) had already been created but for a full period, I think it is 20.
Period 24:

Code: Select all

``````x = 97, y = 97, rule = B3/S23
34bo2bo\$32b6o\$28b2obo8bo\$24b2obobobob8o2bo\$22b3ob2o3bobo7b3o\$21bo4b3o
2bo3bo3b2o\$22b3o3b2ob4obo3bob2o\$23bobo3bo5bo4bo2bo4b2obo\$21bo8bob2o2b
2o2b2o5bob2obo\$21b5ob4obo4b3o7bo4bo\$26b2o4bo4bob3o2b2obob2ob2o\$23b5ob
3o4b2ob2o3bobobobobo\$22bo5b2o4b2obob2o5bo5bo\$23b5o6b2obo3bo3bobob2ob2o
\$11b2ob2o9b2o2bo5bobo4bo2b3obobo\$12bobobobob2o3b3obo6bo2bobo4b3o2bo\$
11bo2bo7bo6b2o3b3o8bobob2o\$11b3o2bo4b2o11bo10bo\$16b4obo23b2o\$13b2obo6b
o13bo7b2o\$12bo4bo3bo15b2o6b2o\$12b3obo4bo15bo7bo\$22bo2bo4bo14bobob2o\$
12b3obo4bo6b2ob2o13b3o2bo\$12bo4bo3bo8bo5bo8b3obobo\$13b2obo6bo13bo7bobo
b2ob2o\$16b4obo13b3o8bo5bo\$11b3o2bo4b2o21bobobobobo\$11bo2bo7bo9b2o10b2o
bob2ob2o\$12bobobobob2o10bo14bo4bo\$11b2ob2o17b3o6bo4bob2obo\$35bo7bo4b2o
bo\$41b3o4\$48bo\$49bo\$47b3o4\$54bo\$55bo\$53b3o\$49b2o\$50b2o\$49bo2\$52b2o\$51b
2o\$43b2o8bo\$44b2o\$43bo2\$58b2o\$57b2o\$37b2o20bo\$38b2o\$37bo2\$64b2o\$63b2o\$
31b2o23bob2o5bo6bo\$32b2o21bob2obo11b3o17b2ob2o\$24bo6bo5b2obo14bo4bo14b
o10b2o3bobobo\$2ob2o17b3o11bob2obo12b2ob2obob2o10b2o9bob5obo2bo\$bobobo
3b2o10bo14bo4bo13bobobobobo6b2o14bob2ob2ob3o\$o2bob5obo9b2o10b2obob2ob
2o12bo3bobo7b2o15bobo4bo\$3ob2ob2obo14b2o6bobobobobo12b2obo4bo8bo5bo6b
3o4bob2o\$3bo4bobo15b2o7bobo3bo14bobo2b2o13b3o5b3o4b2o2bo\$2b2obo4b3o6bo
5bo8bo4bob2o13bo2bobo13b2ob2o3b2o6b5o\$bo2b2o4b3o5b3o13b2o2bobo16b2o4bo
12b3o4b3o\$b5o6b2o3b2ob2o13bobo2bo20bo8bo6bo5b2o6b5o\$11b3o4b3o12bo4b2o
21bo6b2ob2o11b3o4b2o2bo\$b5o6b2o5bo6bo8bo26bo2bo4bo13b3o4bob2o\$bo2b2o4b
3o11b2ob2o6bo25bo24bobo4bo\$2b2obo4b3o13bo4bo2bo26bo11bo3b2obo5bob2ob2o
b3o\$3bo4bobo24bo21b2o4bo8bobo6bo3bob5obo2bo\$3ob2ob2obo5bob2o3bo11bo20b
o2bobo4b2o2b2o5bo8b2o3bobobo\$o2bob5obo3bo6bobo8bo4b2o16bobo2b2o3b3o9b
2ob2o9b2ob2o\$bobobo3b2o8bo5b2o2b2o4bobo2bo13b2obo4bo3b3obob2o8b3o\$2ob
2o9b2ob2o9b3o3b2o2bobo14bo3bobo7b2obo5b2o5bo\$12b3o8b2obob3o3bo4bob2o
12bobobobobo6bo5b3o3b3o\$11bo5b2o5bob2o7bobo3bo12b2ob2obob2o2b3o6bo4b2o
\$12b3o3b3o5bo6bobobobobo13bo4bo5bo2b2o4bob4o2b4o\$15b2o4bo6b3o2b2obob2o
b2o12bob2obo4b2o4bo2b2obo4bo3bo\$10b4o2b4obo4b2o2bo5bo4bo14bob2o4bobo5b
o5bo5bo\$10bo3bo4bob2o2bo4b2o4bob2obo22b2obo5b4obo3b4o\$12bo5bo5bo5bobo
4b2obo26b3ob2o3bo2bo6bo\$11b4o3bob4o5bob2o31b3o7bobo3b2ob3o\$10bo6bo2bo
3b2ob3o34bo2b8obobobob2o\$11b3ob2o3bobo7b3o34bo8bob2o\$13b2obobobob8o2bo
37b6o\$17b2obo8bo40bo2bo\$21b6o\$23bo2bo!
``````
Edit: This P24 also exists:

Code: Select all

``````x = 71, y = 67, rule = B3/S23
10b2ob2o15b2ob2o\$10b2obo4b2o5b2o4bob2o\$13bo2bo3b2ob2o3bo2bo\$13b2obo11b
ob2o\$16bo11bo8bo\$8bobo6bo3bobo3bo8b3o\$6b3ob3o5b3o3b3o8bo3b2o\$5bo7bo5bo
5bo8b2o2b3o\$6bob6o3b3o5b3o5bobo\$6b2o4bo4b3o5b3o4b3ob4o2b2o\$8bo3b2o4b2o
5b2o4bo3bo4bob2o\$7bobo2bobo5bo3bo5b2o3bob2obobobo\$8bo2bo6bo2bobo2bo4bo
bobob2obo3b2o\$11bo3bobo3bobo3bo4b2obo4bo3bo\$11bo3bo2bo2bobo2bo5b2o2b4o
b3o\$11bo6b3o3b3o13bobo\$11bo2bo20b3o2b2o\$12bo7bo14b2o3bo\$10bobobo5bo16b
3o\$9bobob2o23bo\$9bobo6bo3bo7bo\$10b2o4b3obob3o6bo\$15bo3b2o4bo3b3o\$15bob
2o2b2obobo\$16bo2b2o2b2obo\$17b2o2b2obob2o\$11b3o5bo2bobobo2bo6bo\$10b6o3b
4ob2o2b2o7bo4bo2bo\$10bob3obo6bo11b3o8bo\$9bo3bob2o4bobo7b2o9bo3bo\$9b4ob
4o3b2o9b2o9b4o\$7b2o4bob3o13bo\$5b2obob2obo2b2o\$4b2o2bob2obob2o17b2o\$4b
3obo4b2o18b2o\$4b4ob4o12b2o8bo\$2o3b2obo3bo13b2o28b2o\$2o3bob3obo13bo30bo
bo\$6b6o46bo\$4o4b3o29b2o12b4ob2o2b2o\$o2bo35b2o13bo4bobo2bo\$19b2o5b2o13b
o10b2o2b2obob2o\$20b2o5bo23bo2b2o3bobo\$10bo8bo5bo24bob2o2b2obobo\$10b2o
11b4o23bo4bo4bo\$2b3o6b2o9bo4bo2b2o14b2o3b3obob3o4b2o\$3bobo4b2o9bob2ob
2o2bo9b2o3b2o6b2ob2o6bobo\$4b2o15bo2bo3b2o2bo6bo2bo4bo13b2obobo\$20b2obo
2b2o2b5o3bobobo18bobobo\$4b2o12bo4bobobobo5bobo2bob2o19bo\$3bobo4b2o6bob
2o2bo2bobob2ob2ob2obo3bo17b2o\$2b3o6b2o5bo3bobob2obob2obo5b2ob3o15b3o\$
10b2o8b2obobo3bo5bobobo3b3o15b3o\$10bo10bobobo3bob3obo2b2o3b3o4bo5bo4b
3o\$21bo2bo5b2o2b2o7b3o3b3o3b3o3b3o3bo\$22b2o9bobo2bob2o2bo3bo2b2ob2o2bo
3b2o2bobo\$o2bo14b2o8b3ob2ob4obob2o4b3o5b3o7bo2bo\$4o3b2o10bo8bo2bo3bo3b
2obo20bo\$6bo3b9o10bobob2ob2o3bo2bo18b6obo\$2o4bobob7o2b3o6b2ob2obobob2o
bob2o17bo7bo\$2o3b2ob2o2b4o2bo2bo18bobo20b3ob3o\$8bo2bo7b2o19bobo8b2ob2o
9bobo\$5b2obobobo28bo7b2obobob2o\$6bo4bo32b2o3bo7bo3b2o\$6bob3o33bo4b3o3b
3o4bo\$7b2o32b2obo17bob2o\$41b2ob2o15b2ob2o!
``````
Edit : Why are the new users (maybe only 2) posting in this day?!
A 13 year old guy that have useless discoveries about life and other rules.

Code: Select all

``````x = 13, y = 20, rule = B3/S23
11b2o\$11b2o4\$8b2o\$8b2o2\$2o\$2o3\$3b2o\$3b2o2\$11b2o\$10b2o\$12bo\$3b2o\$3b2o!
``````

metametapixel
Posts: 5
Joined: February 29th, 2020, 6:30 pm

### Re: Thread for basic questions

Thanks!

metametapixel
Posts: 5
Joined: February 29th, 2020, 6:30 pm

### Re: Thread for basic questions

I know that for most patterns (all patterns except for so-called “Gardens of Eden”), there is some pattern which will evolve into it on the next generation. Is there any easy way to try to find such a pattern or do you have to do a brute-force search until you either come up something that evolves into it or until you determine that it is a Garden of Eden? Is there a program that will try to find the previous generation for you or do you have to do that by hand?

dvgrn
Moderator
Posts: 6488
Joined: May 17th, 2009, 11:00 pm
Contact:

### Re: Thread for basic questions

metametapixel wrote:
March 2nd, 2020, 5:35 pm
I know that for most patterns (all patterns except for so-called “Gardens of Eden”), there is some pattern which will evolve into it on the next generation. Is there any easy way to try to find such a pattern or do you have to do a brute-force search until you either come up something that evolves into it or until you determine that it is a Garden of Eden? Is there a program that will try to find the previous generation for you or do you have to do that by hand?
There are several programs capable of this. The easiest to use and most cross-platform one might be JLS (JavaLifeSearch).

-- And yes, what you describe is pretty close to right. JLS does an exhaustive search, and eventually if there are no solutions it will stop searching and tell you so. It's not exactly a brute-force search, because JLS isn't just listing all possible patterns, running them one tick, and checking to see if it happens to be the pattern you're looking for. JLS skips a bajillion options that it has logically determined can't possibly lead to the search pattern.

It's still fairly brute-force-ish in a lot of ways, though: "if the state of {next unknown cell} can't be logically deduced, try it in state 0, and then if that doesn't work, try it in state 1".

Here's a very quick checklist about how to set up a predecessor search in JLS. It really out to be written up a little more thoroughly, probably as a LifeWiki tutorial. If you take notes while you're figuring out how to do it, please post here everything that you temporarily found to be confusing or mystifying, so that future new predecessor-hunters won't have to go through the same pain.

Excruciating detail is probably better than not enough detail. It's worth getting a good tutorial out there on the LifeWiki for this particular subject.

Hunting
Posts: 2164
Joined: September 11th, 2017, 2:54 am

### Re: Thread for basic questions

Is there a non-totalistic modification of dr (Or doeabit supports non-totalistic rule originallu)? Iwant to run iy in LeapLIFE.
Proud member of the p22ers!

Working on:

LeapLife Demonoid

JP21
Posts: 814
Joined: October 26th, 2019, 5:39 am
Location: PH

### Re: Thread for basic questions

Hunting wrote:
March 8th, 2020, 4:37 am
Is there a non-totalistic modification of dr (Or doeabit supports non-totalistic rule originallu)? Iwant to run iy in LeapLIFE.
Can't understand what you mean.
A 13 year old guy that have useless discoveries about life and other rules.

Code: Select all

``````x = 13, y = 20, rule = B3/S23
11b2o\$11b2o4\$8b2o\$8b2o2\$2o\$2o3\$3b2o\$3b2o2\$11b2o\$10b2o\$12bo\$3b2o\$3b2o!
``````

Hunting
Posts: 2164
Joined: September 11th, 2017, 2:54 am

### Re: Thread for basic questions

JP21 wrote:
March 8th, 2020, 5:13 am
Hunting wrote:
March 8th, 2020, 4:37 am
Is there a non-totalistic modification of dr (Or doeabit supports non-totalistic rule originallu)? Iwant to run iy in LeapLIFE.
Can't understand what you mean.
Delwted.
Last edited by Hunting on March 8th, 2020, 5:16 am, edited 1 time in total.
Proud member of the p22ers!

Working on:

LeapLife Demonoid