Spaceships in Life-like cellular automata

wwei23 · Post by **wwei23** » October 13th, 2020, 8:21 am

Naszvadi wrote: October 13th, 2020, 3:12 am Congrats! Is this the first spaceship in rule B3/S2? Notice that this rule is totalistic!

I'm kind of surprised that you got this excited about this, since LaundryPizza03 regularly finds spaceships in rules without previously known ones, and no one gets very excited then. Edit: But still, thanks!

I remember searching Fano for spaceships in B3/S2 a few tears ago, and there we're apparently none known.

I'd advise you to trim your quotes, people have gotten mad at me for not trimming mine in the past.

Edit: More tagalongs! These attach to the original tagalong, and there are eight variations on this one.

Code: Select all

x = 189, y = 127, rule = B3/S2
2b3obo3b3o11b3o3bob3o17b3obo3b3o11b3o3bob3o17b3obo3b3o11b3o3bob3o17b3o
bo3b3o11b3o3bob3o$bo2bob2o5b2o7b2o5b2obo2bo15bo2bob2o5b2o7b2o5b2obo2bo
15bo2bob2o5b2o7b2o5b2obo2bo15bo2bob2o5b2o7b2o5b2obo2bo$o2bo4bob2obo9bo
b2obo4bo2bo13bo2bo4bob2obo9bob2obo4bo2bo13bo2bo4bob2obo9bob2obo4bo2bo
13bo2bo4bob2obo9bob2obo4bo2bo$o6b2o3b4o5b4o3b2o6bo13bo6b2o3b4o5b4o3b2o
6bo13bo6b2o3b4o5b4o3b2o6bo13bo6b2o3b4o5b4o3b2o6bo$6bo8b2o3b2o8bo25bo8b
2o3b2o8bo25bo8b2o3b2o8bo25bo8b2o3b2o8bo$5bo10b2ob2o10bo23bo10b2ob2o10b
o23bo10b2ob2o10bo23bo10b2ob2o10bo$4bo2b2o8bobo8b2o2bo21bo2b2o8bobo8b2o
2bo21bo2b2o8bobo8b2o2bo21bo2b2o8bobo8b2o2bo$3b2o4bo17bo4b2o19b2o4bo17b
o4b2o19b2o4bo17bo4b2o19b2o4bo17bo4b2o$7b2o6bobobobo6b2o27b2o6bobobobo
6b2o27b2o6bobobobo6b2o27b2o6bobobobo6b2o$8b2o7bobo7b2o29b2o7bobo7b2o
29b2o7bobo7b2o29b2o7bobo7b2o$8bo2bo3bobobobo3bo2bo29bo2bo3bobobobo3bo
2bo29bo2bo3bobobobo3bo2bo29bo2bo3bobobobo3bo2bo$11bob3o2bo2b3obo35bob
3o2bo2b3obo35bob3o2bo2b3obo35bob3o2bo2b3obo$12bo11bo37bo11bo37bo11bo
37bo11bo$9bo2b3ob5ob3o2bo31bo2b3ob5ob3o2bo31bo2b3ob5ob3o2bo31bo2b3ob5o
b3o2bo$12bo2b2o3b2o2bo37bo2b2o3b2o2bo37bo2b2o3b2o2bo37bo2b2o3b2o2bo$
11bo13bo35bo13bo35bo13bo35bo13bo2$23b3o47b3o47b3o47b3o$19b3o4bo42b3o4b
o42b3o4bo42b3o4bo$22bo2bo46bo2bo46bo2bo46bo2bo$18b3o2bo44b3o2bo44b3o2b
o44b3o2bo$16b2o48b2o48b2o48b2o$13b3obo5b2o38b3obo5b2o38b3obo5b2o38b3ob
o5b2o$12bo2bo3bo42bo2bo3bo42bo2bo3bo42bo2bo3bo$12bobo2bobo2bo39bobo2bo
bo2bo39bobo2bobo2bo39bobo2bobo2bo$17bobo2bobo42bobo2bobo42bobo2bobo42b
obo2bobo$19bo49bo49bo49bo$19bobobo2bo42bobobo2bo42bobobo2bo42bobobo2bo
$21bo2bob2o43bo2bob2o43bo2bob2o43bo2bob2o$27bobo47bobo47bobo47bobo$28b
2o48b2o48b2o48b2o2$28b2o48b2o48b2o48b2o$25b2o2bo45b2o2bo48bo2b2o45bo2b
2o$24bo3bo45bo3bo50bo3bo45bo3bo$23bo5bo43bo5bo48bo5bo43bo5bo$22b2o6bo
41b2o6bo46bo6b2o41bo6b2o2$28b2ob2o45b2ob2o42b2ob2o45b2ob2o$30b2o48b2o
44b2o48b2o$32b2o48b2o40b2o48b2o$32b3o47b3o38b3o47b3o$31bo2bobo44bo2bob
o34bobo2bo44bobo2bo$30bo4b2o43bo4b2o34b2o4bo43b2o4bo$32bo49bo42bo49bo$
33bo49bo40bo49bo$29bob2o46bob2o42b2obo46b2obo$28b2ob2o45b2ob2o42b2ob2o
45b2ob2o$27bo3bobo43bo3bobo40bobo3bo43bobo3bo$26bo49bo54bo49bo2$25b3o
47b3o52b3o47b3o$24b2o48b2o56b2o48b2o$21b2o3bobo42b2o3bobo50bobo3b2o42b
obo3b2o$20bo3bo3b2o40bo3bo3b2o48b2o3bo3bo40b2o3bo3bo$19bo9bobo37bo9bob
o44bobo9bo37bobo9bo$18b2o10b2o38bo9b2o44b2o10b2o36b2o9bo14$2b3obo3b3o
11b3o3bob3o17b3obo3b3o11b3o3bob3o17b3obo3b3o11b3o3bob3o17b3obo3b3o11b
3o3bob3o$bo2bob2o5b2o7b2o5b2obo2bo15bo2bob2o5b2o7b2o5b2obo2bo15bo2bob
2o5b2o7b2o5b2obo2bo15bo2bob2o5b2o7b2o5b2obo2bo$o2bo4bob2obo9bob2obo4bo
2bo13bo2bo4bob2obo9bob2obo4bo2bo13bo2bo4bob2obo9bob2obo4bo2bo13bo2bo4b
ob2obo9bob2obo4bo2bo$o6b2o3b4o5b4o3b2o6bo13bo6b2o3b4o5b4o3b2o6bo13bo6b
2o3b4o5b4o3b2o6bo13bo6b2o3b4o5b4o3b2o6bo$6bo8b2o3b2o8bo25bo8b2o3b2o8bo
25bo8b2o3b2o8bo25bo8b2o3b2o8bo$5bo10b2ob2o10bo23bo10b2ob2o10bo23bo10b
2ob2o10bo23bo10b2ob2o10bo$4bo2b2o8bobo8b2o2bo21bo2b2o8bobo8b2o2bo21bo
2b2o8bobo8b2o2bo21bo2b2o8bobo8b2o2bo$3b2o4bo17bo4b2o19b2o4bo17bo4b2o
19b2o4bo17bo4b2o19b2o4bo17bo4b2o$7b2o6bobobobo6b2o27b2o6bobobobo6b2o
27b2o6bobobobo6b2o27b2o6bobobobo6b2o$8b2o7bobo7b2o29b2o7bobo7b2o29b2o
7bobo7b2o29b2o7bobo7b2o$8bo2bo3bobobobo3bo2bo29bo2bo3bobobobo3bo2bo29b
o2bo3bobobobo3bo2bo29bo2bo3bobobobo3bo2bo$11bob3o2bo2b3obo35bob3o2bo2b
3obo35bob3o2bo2b3obo35bob3o2bo2b3obo$12bo11bo37bo11bo37bo11bo37bo11bo$
9bo2b3ob5ob3o2bo31bo2b3ob5ob3o2bo31bo2b3ob5ob3o2bo31bo2b3ob5ob3o2bo$
12bo2b2o3b2o2bo37bo2b2o3b2o2bo37bo2b2o3b2o2bo37bo2b2o3b2o2bo$11bo13bo
35bo13bo35bo13bo35bo13bo2$23b3o47b3o47b3o47b3o$19b3o4bo42b3o4bo42b3o4b
o42b3o4bo$22bo2bo46bo2bo46bo2bo46bo2bo$18b3o2bo44b3o2bo44b3o2bo44b3o2b
o$16b2o48b2o48b2o48b2o$13b3obo5b2o38b3obo5b2o38b3obo5b2o38b3obo5b2o$
12bo2bo3bo42bo2bo3bo42bo2bo3bo42bo2bo3bo$12bobo2bobo2bo39bobo2bobo2bo
39bobo2bobo2bo39bobo2bobo2bo$17bobo2bobo42bobo2bobo42bobo2bobo42bobo2b
obo$19bo49bo49bo49bo$19bobobo2bo42bobobo2bo42bobobo2bo42bobobo2bo$21bo
2bob2o43bo2bob2o43bo2bob2o43bo2bob2o$27bobo47bobo47bobo47bobo$28b2o48b
2o48b2o48b2o2$28b2o48b2o48b2o48b2o$25b2o2bo45b2o2bo48bo2b2o45bo2b2o$
24bo3bo45bo3bo50bo3bo45bo3bo$23bo5bo43bo5bo48bo5bo43bo5bo$24bo5bo43bo
5bo46bo5bo43bo5bo2$28b2ob2o45b2ob2o42b2ob2o45b2ob2o$30b2o48b2o44b2o48b
2o$32b2o48b2o40b2o48b2o$32b3o47b3o38b3o47b3o$31bo2bobo44bo2bobo34bobo
2bo44bobo2bo$30bo4b2o43bo4b2o34b2o4bo43b2o4bo$32bo49bo42bo49bo$33bo49b
o40bo49bo$29bob2o46bob2o42b2obo46b2obo$28b2ob2o45b2ob2o42b2ob2o45b2ob
2o$27bo3bobo43bo3bobo40bobo3bo43bobo3bo$26bo49bo54bo49bo2$25b3o47b3o
52b3o47b3o$24b2o48b2o56b2o48b2o$21b2o3bobo42b2o3bobo50bobo3b2o42bobo3b
2o$20bo3bo3b2o40bo3bo3b2o48b2o3bo3bo40b2o3bo3bo$19bo9bobo37bo9bobo44bo
bo9bo37bobo9bo$18b2o10b2o38bo9b2o44b2o10b2o36b2o9bo!

They can also attach to the back of each other, here is a spaceship with all eight tagalongs appended to it, showing the various ways to attach tagalongs together.

Code: Select all

x = 41, y = 240, rule = B3/S2
2b3obo3b3o11b3o3bob3o$bo2bob2o5b2o7b2o5b2obo2bo$o2bo4bob2obo9bob2obo4b
o2bo$o6b2o3b4o5b4o3b2o6bo$6bo8b2o3b2o8bo$5bo10b2ob2o10bo$4bo2b2o8bobo
8b2o2bo$3b2o4bo17bo4b2o$7b2o6bobobobo6b2o$8b2o7bobo7b2o$8bo2bo3bobobob
o3bo2bo$11bob3o2bo2b3obo$12bo11bo$9bo2b3ob5ob3o2bo$12bo2b2o3b2o2bo$11b
o13bo2$23b3o$19b3o4bo$22bo2bo$18b3o2bo$16b2o$13b3obo5b2o$12bo2bo3bo$
12bobo2bobo2bo$17bobo2bobo$19bo$19bobobo2bo$21bo2bob2o$27bobo$28b2o2$
28b2o$25b2o2bo$24bo3bo$23bo5bo$24bo5bo2$28b2ob2o$30b2o$32b2o$32b3o$31b
o2bobo$30bo4b2o$32bo$33bo$29bob2o$28b2ob2o$27bo3bobo$26bo2$25b3o$24b2o
$21b2o3bobo$20bo3bo3b2o$19bo9bobo$18b2o10b2o2$18b2o$18bo$14b4o$13bo2bo
2bo$13bobo2b2o$19bo$19bobo$18bo2b2o$23bo$24bo$21b2o2bo$20bo4b2o$21b2o$
22bo$22bo$18b3o2b2o$17bo4bo$18b3o$16b3o2$14b2o$15bo2bo$10b5o2bobo$9bo
2bo7bo$9bobo8b2o2$20b2o$21bo$22b4o$20bo2bo2bo$20b2o2bobo$20bo$18bobo$
17b2o2bo$16bo$15bo$14bo2b2o$13b2o4bo$17b2o$17bo$17bo$15b2o2b3o$17bo4bo
$19b3o$21b3o2$24b2o$21bo2bo$20bobo2b5o$19bo7bo2bo$18b2o8bo2bo$31bo2$
30b2o$32bobo$30b2o2b2o$30bo4b2o2$28b3o$27bo2bo$26bo3bo$25bo$24bo3bo$
23bo3b2o$23bo4bo2$26bobo$26bo3b2o$26bo3bo$28b2ob2o2$32bobo$35bo$35bo$
30b3o2b2obo$29bo2bo5b2o$28bo2bo7b2o$28bo2$28b2o$25bobo$24b2o2b2o$22bob
o4bo$22b2o$29b3o$29bo2bo$29bo3bo$34bo$31bo3bo$31b2o3bo$31bo4bo2$31bobo
$28b2o3bo$29bo3bo$27b2ob2o2$25bobo$24bo$24bo$21bob2o2b3o$20b2o5bo2bo$
18bobo7bo2bo$18b2o11bo2$18b2o$15b2o2bo$14bo3bo$13bo5bo$12b2o6bo2$18b2o
b2o$20b2o$22b2o$22b3o$21bo2bobo$20bo4b2o$22bo$23bo$19bob2o$18b2ob2o$
17bo3bobo$16bo2$15b3o$14b2o$11b2o3bobo$10bo3bo3b2o$9bo9bobo$8b2o10b2o
2$20b2o$20bo2b2o$21bo3bo$20bo5bo$19bo5bo2$17b2ob2o$18b2o$16b2o$15b3o$
13bobo2bo$13b2o4bo$17bo$16bo$17b2obo$17b2ob2o$16bobo3bo$23bo2$22b3o$
24b2o$21bobo3b2o$20b2o3bo3bo$18bobo9bo$18b2o10b2o2$30b2o$31bo$32b4o$
30bo2bo2bo$30b2o2bo2bo$30bo6bo$28bobo$27b2o2bo$26bo$25bo$24bo2b2o$23b
2o4bo$27b2o$27bo$27bo$25b2o2b3o$27bo4bo$29b3o$31b3o2$34b2o$31bo2bo$30b
obo2b5o$29bo7bo2bo$28b2o8bobo!

Edit 2: Another tagalong:

Code: Select all

x = 39, y = 59, rule = B3/S2
2b3obo3b3o11b3o3bob3o$bo2bob2o5b2o7b2o5b2obo2bo$o2bo4bob2obo9bob2obo4b
o2bo$o6b2o3b4o5b4o3b2o6bo$6bo8b2o3b2o8bo$5bo10b2ob2o10bo$4bo2b2o8bobo
8b2o2bo$3b2o4bo17bo4b2o$7b2o6bobobobo6b2o$8b2o7bobo7b2o$8bo2bo3bobobob
o3bo2bo$11bob3o2bo2b3obo$12bo11bo$9bo2b3ob5ob3o2bo$12bo2b2o3b2o2bo$11b
o13bo2$23b3o$19b3o4bo$22bo2bo$18b3o2bo$16b2o$13b3obo5b2o$12bo2bo3bo$
12bobo2bobo2bo$17bobo2bobo$19bo$19bobobo2bo$21bo2bob2o$27bobo$28b2o2$
28b2o$25b2o2bo$24bo3bo$23bo5bo$24bo5bo2$28b2ob2o$30b2o$32b2o$32b3o$31b
o2bobo$30bo4b2o$32bo$33bo$31b2o2$30bo$30bob2obo$31bo3b2o$36bobo$30b2o
5b2o$29b3o$28b4o$26bobo3bob3o$26b2o4bobo2bo$35bo2bo$38bo!

Edit 3: There are now over a hundred different combinations of tagalongs on Catagolue, so I decided to switch to c/4 orthogonal and see what I'd get from that. Longest partial so far:

Code: Select all

x = 35, y = 22, rule = B3/S2
11b3o7b3o$4b2obobobo2bo5bo2bobobob2o$3bobo2bo17bo2bobo$2bo2bobo6bob3ob
o6bobo2bo$3bo12bobo12bo$3bo3bo9bo9bo3bo$3b2obobo17bobob2o$5bo3bo15bo3b
o$4bo5bo13bo5bo$7bo19bo$3b3o3b2o13b2o3b3o$5bo4bobo9bobo4bo$3bo6bobo9bo
bo6bo$2bobo3bo3bo9bo3bo3bobo$7bo2bo13bo2bo$3b3o2bobo13bobo2b3o$5bo6bo
9bo6bo$3bob3o5b2o5b2o5b3obo$2bo29bo$2bob2o2b2o2bob2o3b2obo2b2o2b2obo$
2bo2b2o3bo2bo2bobo2bo2bo3b2o2bo$obo3b2o4bo2bo3bo2bo4b2o3bobo!

LaundryPizza03 · Post by **LaundryPizza03** » November 8th, 2020, 5:10 am

3 c/9o in B3/S5678:

Code: Select all

x = 55, y = 57, rule = B3/S5678
7b2o18b2o18b2o$6b4o17b2o17b4o$5b6o16b2o16b6o$3b10o14b2o14b10o$5b6o15b
4o15b6o$4bob4obo12b8o14b4o$6b4o14b8o13b6o$3bob6obo12b6o14b6o$4b8o13b6o
14b6o$2b12o9b10o12b6o$2b12o9b10o12b6o$4b8o11b10o12b6o$4b8o11b10o13b4o$
3b10o12b6o15b4o$2b12o11b6o13b8o$16o9b6o15b4o$2b12o11b6o15b4o$3b10o12b
6o14b6o$3b10o12b6o14b6o$5b6o14b6o14b6o$6b4o13b10o12b6o$6b4o13b10o13b4o
$25b6o13b8o$23bob6obo11b8o$24b8o12b8o$22b12o10b8o$22b12o11b6o$24b8o13b
6o$24b8o11b10o$24b8o11b10o$23b10o10b10o$22b12o9b10o$22b12o11b6o$21bob
10obo10b6o$23b10o12b6o$22b12o11b6o$23b10o12b6o$24bob4obo13b6o$45b6o$
43b10o$43b10o$45b6o$43bob6obo$44b8o$42b12o$42b12o$44b8o$44b8o$44b8o$
43b10o$42b12o$42b12o$41bob10obo$43b10o$42b12o$43b10o$44bob4obo!

DB entry:

Code: Select all

:LaundryPizza03, 2020:B3/S5678:B378/S5678:9:0:-1:12:22:5b2o$3bob2obo$3bob2obo$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$3b6o$2b8o$12o$2b8o$2b8o$ob8obo$b10o$b10o$b10o$b10o$b10o$ob8obo$bo8bo!

wwei23 · Post by **wwei23** » November 8th, 2020, 11:19 am

LaundryPizza03 wrote: November 8th, 2020, 5:10 am 3 c/9o in B3/S5678:
Code: Select all
RLE of 3 c/9 spaceships
DB entry:
Code: Select all
Database entry of one of the spaceships

What about the entries for the other two spaceships?
Also, what were those spaceships found with?

LaundryPizza03 · Post by **LaundryPizza03** » November 9th, 2020, 9:57 pm

wwei23 wrote: November 8th, 2020, 11:19 am
LaundryPizza03 wrote: November 8th, 2020, 5:10 am 3 c/9o in B3/S5678:
Code: Select all
RLE of 3 c/9 spaceships
DB entry:
Code: Select all
Database entry of one of the spaceships
What about the entries for the other two spaceships?
Also, what were those spaceships found with?

Correction: Only the smallest spaceship is counted, since the other two work in the same rules as this one. They were found using qfind.

wwei23 · Post by **wwei23** » November 10th, 2020, 10:49 am

LaundryPizza03 wrote: November 9th, 2020, 9:57 pm Correction: Only the smallest spaceship is counted, since the other two work in the same rules as this one.

Yeah, but c/9 is kind of a difficult speed to find spaceships at. Every ship should count.

LaundryPizza03 · Post by **LaundryPizza03** » November 10th, 2020, 8:49 pm

The others do work in slightly different INT rulespaces, so I'll leave them for a future NT extension.

wwei23 · Post by **wwei23** » November 10th, 2020, 8:52 pm

Which rules still don't have spaceships?

Layz Boi · Post by **Layz Boi** » November 10th, 2020, 11:11 pm

wwei23 wrote: November 10th, 2020, 8:52 pm Which rules still don't have spaceships?

Rules that lack all of; B01245 S012345. That's for sure!

wwei23 · Post by **wwei23** » November 10th, 2020, 11:54 pm

Layz Boi wrote: November 10th, 2020, 11:11 pm
wwei23 wrote: November 10th, 2020, 8:52 pm Which rules still don't have spaceships?
Rules that lack all of; B01245 S012345. That's for sure!

Wait, how do we know that? There's B3.

Layz Boi · Post by **Layz Boi** » November 11th, 2020, 1:44 am

wwei23 wrote: November 10th, 2020, 11:54 pm Wait, how do we know that? There's B3.

In short, without all those transitions, this subsection (the green cells) along an edge of a bounding diamond of any pattern (red cells) has no predecessors (besides generation 0) that are within the same bounding diamond. So nothing can possibly expand its bounding diamond using b3a past generation 1. (The corners of a bounding diamond can be thought of just specific cases of an edge of a bounding diamond, before anyone asks.)

: random inmage.png (18.06 KiB) Viewed 5074 times

Assume B012 all are not present.

case 0). Any predecessor of the aforementioned green cells would require either B4w or B5a if none of the green cells are on.

case 1). If one or two of the green cells are on in the predecessor, they must have 0 to 5 on neighbors if they are one of the two outer-most green cells, 0-7 if it is the inner-most green cell. Removing S012345 would allow only the inner-most green cell to remain on (S67) to be a predecessor, but that cell would require one or more of the outer-most green cells to be on, but they can't be on in the next generation, so it can't be a predecessor.

On generation 0, the edge of the bounding diamond one greater in size than any object's bounding diamond (grey cells) can only have "case 0" or "case 1" for the equivalent configurations as the green cells mentioned before.

: random inmage2.png (7.65 KiB) Viewed 5074 times

You can get into more detailed enumeration and what-not considering all the non-totalistic transitions and stuff. Using B2ec instead of or in conjunction with B3ai is more complicated, as what stops B2e enables B3a. B0 is whole new can of worms I haven't looked into. And some transitions can be traded for others; (you can add S0 if you also remove B2ki3yr4t) and so forth. It's tedious checking without a script.

wwei23 · Post by **wwei23** » November 11th, 2020, 1:47 am

So, which rules that don't fall into any of these "no spaceship" categories don't have any known spaceships?

Post by **Sokwe** » November 11th, 2020, 2:14 am

wwei23 wrote: November 11th, 2020, 1:47 am So, which rules that don't fall into any of these "no spaceship" categories don't have any known spaceships?

To answer this you need the latest version of the spaceship database and David Eppstein's program for reading the database. Using this program, it is possible to print tables of rules (in the B2 and B3 spaces) showing how many gliders are known in each rule. For example, here is the table for B3 rules that I generated about a month ago using this program (so it may not be quite up-to-date):

Code: Select all

             B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
             3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
                                             4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
                             5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5                
                     6 6 6 6 6 6 6 6                 6 6 6 6 6 6 6 6        
                 7 7 7 7         7 7 7 7         7 7 7 7         7 7 7 7    
               8 8     8 8     8 8     8 8     8 8     8 8     8 8     8 8  
            ----------------------------------------------------------------
S          :                 . . . . . . . . . . . . . . . . . . . . . . . .
S        8 :                 . . . . . . . . . . . . . . . . . . . . . . . .
S       78 :                 . . . . . . . . . . . . . . . . . . . . . . . .
S       7  :                 . . . . . . . . . . . . . . . . . . . . . . . .
S      67  :                 . . . . . . . . . . . . . . . . . . . . . . . .
S      678 :                 . . . . . . . . . . . . . . . . . . . . . . . .
S      6 8 :                 . . . . . . . . . . . . . . . . . . . . . . . .
S      6   :                 . . . . . . . . . . . . . . . . . . . . . . . .
S     56   : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S     56 8 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S     5678 : . . . . . . . . 1 1 4 4 2 2 1 1 . . . . . . . . 2 1 1 1 1 1 1 1
S     567  : . . . . . . . . . . . . . . . . . . . . . . . . 2 1 1 1 . . . .
S     5 7  : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S     5 78 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S     5  8 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S     5    : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S    45    : . . . . 1 1 1 1 3 2 4 3 1 2 1 1 3 3 1 1 1 . 2 3 2 2 3 1 3 3 2 2
S    45  8 : . . . . 1 1 1 1 3 3 4 3 2 2 1 1 2 1 3 1 1 . 2 1 2 2 3 3 4 3 1 1
S    45 78 : 1 1 1 1 1 1 1 1 5 4 6 5 3 4 2 3 3 2 2 1 . . 2 1 3 3 4 3 4 4 2 1
S    45 7  : 1 . . . 1 1 1 1 5 4 6 6 5 4 3 4 1 2 2 3 . . 1 2 4 6 6 5 2 4 4 1
S    4567  : 1 1 1 3 6 7 5 2 3 4 3 3 3 7 5 5 . . . . . . . . 1 2 1 1 2 2 2 2
S    45678 : 1 . . . . . . . 1 1 1 1 1 1 1 1 . . . . . . . . . . . . . . 1 1
S    456 8 : 1 1 1 1 4 4 3 2 4 9 4 5 8 X 6 6 . . 1 1 . . . . 5 3 2 6 5 5 7 8
S    456   : 1 1 . . 2 2 1 2 4 5 4 3 5 5 4 4 . 1 1 2 . . . . 6 4 3 4 7 3 5 5
S    4 6   : . . . . . . . . 2 1 1 1 . . . . 3 3 3 1 1 2 2 1 1 2 1 1 1 1 1 1
S    4 6 8 : . . . . . . . . 2 1 1 2 . . . . 3 3 2 2 4 3 3 1 2 2 2 3 1 1 1 1
S    4 678 : . . . . . . . . 1 1 3 2 1 1 . . 3 2 2 1 1 1 2 2 1 3 1 3 1 1 1 1
S    4 67  : . . . . . . . . 1 1 2 2 1 1 . . 2 3 2 2 3 3 4 3 2 3 3 3 1 1 1 1
S    4  7  : . . . . . . . . . . . . . . . . 2 1 2 2 1 3 1 1 1 1 1 1 1 1 1 2
S    4  78 : . . . . . . . . . . . . . . . . 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2
S    4   8 : . . . . . . . . . . . . . . . . 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
S    4     : . . . . . . . . . . . . . . . . 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34     : 7 7 6 6 7 4 5 6 7 7 6 8 7 7 7 8 3 2 2 4 1 2 1 1 8 5 4 4 5 6 6 9
S   34   8 : 7 7 6 6 6 5 6 6 8 8 8 9 7 6 7 9 2 3 3 2 . 2 1 2 4 6 5 5 7 8 6 7
S   34  78 : X X 7 6 7 5 8 8 X X X X 8 X X 9 1 1 . . . 1 1 . 6 8 6 6 9 9 7 6
S   34  7  : X X 7 6 6 5 6 6 X 8 X X 7 8 X X 1 1 1 1 1 1 . . 3 4 7 7 9 X 8 7
S   34 67  : 4 6 7 6 X X 7 6 8 X X X 9 X X X 1 1 1 1 1 . . 1 7 5 3 6 7 9 6 5
S   34 678 : 4 6 9 7 X X 8 6 9 X 8 9 X X 9 8 1 1 . . 1 . . 1 7 8 4 7 7 8 5 5
S   34 6 8 : 4 5 7 6 X X 7 7 X X 9 X X X X X 1 1 . . . . . . 3 5 5 6 5 5 7 8
S   34 6   : 4 5 5 5 X X 6 7 8 9 8 X X X X X 1 1 . . . . . . 3 3 5 7 4 4 5 6
S   3456   : 2 2 1 1 2 2 2 2 . . . . . . 2 2 . . . . . . . . . . . . . . . .
S   3456 8 : 2 2 1 1 1 1 3 2 . . . . 1 2 3 2 . . . . . . . . 1 1 . . . . . .
S   345678 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S   34567  : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S   345 7  : 8 7 6 5 8 X 7 X 3 5 4 4 8 7 6 4 . . . . . . . . 2 3 3 3 2 2 2 2
S   345 78 : 7 9 X 6 9 X 8 6 5 6 5 5 5 7 6 4 . . . . . . . . 4 5 3 3 2 2 2 2
S   345  8 : X X 7 6 7 8 X 9 6 7 4 3 6 4 6 6 . . . . . . . . 2 3 2 3 2 2 2 2
S   345    : X 9 7 7 X X 9 X 5 4 5 6 7 8 8 8 . . . . . . . . 1 2 1 1 2 2 2 2
S   3 5    : 9 9 5 5 4 4 6 6 8 7 7 8 9 X 7 6 5 6 7 8 2 3 4 5 8 8 8 9 X X X X
S   3 5  8 : 9 9 5 5 3 3 6 6 9 7 8 8 9 X 8 7 4 6 8 9 2 2 2 2 X X X X X X X X
S   3 5 78 : 3 3 3 3 4 4 4 4 8 X X X 8 8 6 6 7 6 4 2 3 3 4 2 X X X X X X X X
S   3 5 7  : 3 3 3 3 5 5 4 4 9 9 8 X 9 X 6 5 5 7 4 4 4 2 3 5 X 8 X X X X X X
S   3 567  : 2 2 X 7 X 9 5 4 9 9 X 9 8 9 8 8 2 1 1 2 . . . . 6 7 6 6 X X 8 X
S   3 5678 : 2 2 8 8 8 7 7 7 9 8 5 6 X X X X 1 2 1 1 . . . . 6 7 4 4 8 7 7 8
S   3 56 8 : 6 6 2 2 5 5 6 5 X 9 X X 8 9 8 7 3 1 3 5 1 1 1 . 9 8 9 9 7 6 7 9
S   3 56   : 6 6 2 2 5 4 5 6 X 8 X X 9 9 7 5 2 1 2 3 . . . . X 9 X 8 X X 8 X
S   3  6   : . . . . . . . . 2 2 2 3 2 2 2 2 5 6 3 3 2 3 3 3 6 5 3 4 3 3 3 4
S   3  6 8 : . . . . . . 1 1 2 2 2 3 2 2 2 2 7 7 5 6 2 2 2 2 7 5 4 4 3 3 3 4
S   3  678 : . . . . 1 2 2 1 4 6 8 7 1 1 1 1 7 7 4 2 6 4 4 7 4 4 5 6 2 2 3 2
S   3  67  : . . . . 1 1 . . 3 3 5 4 1 1 1 1 6 6 3 3 3 5 5 6 4 4 3 4 2 2 2 2
S   3   7  : . . . . . . . . 1 1 1 1 1 1 1 1 2 2 3 2 1 . 1 1 3 3 2 2 4 4 1 2
S   3   78 : . . . . . . . . 1 1 1 1 1 1 1 1 4 2 4 2 1 . 2 1 2 2 2 2 2 2 1 1
S   3    8 : . . . . . . . . 1 1 2 2 1 1 1 1 3 4 2 2 1 1 1 2 4 3 2 2 2 3 1 1
S   3      : . . . . . . . . 1 1 2 2 1 1 1 1 3 4 1 2 1 1 1 1 3 3 3 2 3 4 1 1
S  23      : X X X X X X X X 8 6 9 X X 9 6 8 2 3 3 2 1 2 1 1 3 2 5 4 4 3 3 4
S  23    8 : X X X X X X X X 8 6 X 8 7 6 X 7 1 1 1 1 1 1 2 1 2 2 4 4 3 3 2 2
S  23   78 : X X X X X 9 X X 8 8 X 9 8 X X X 1 1 . 1 . . 1 . 1 1 2 2 1 2 2 1
S  23   7  : X X X X 9 9 X X 8 7 8 8 7 X X 9 2 2 1 1 . . 2 . 1 2 2 1 1 1 2 1
S  23  67  : 8 8 9 X 8 8 9 8 X X 7 9 8 9 9 7 1 1 . . . . . . 1 1 1 1 1 1 1 1
S  23  678 : 9 9 9 X 9 9 9 7 X X 7 8 8 9 8 8 . . . . . . 1 . 1 1 2 2 1 1 2 1
S  23  6 8 : 9 X X X X X 8 9 8 6 7 8 X X X 9 1 1 1 1 1 1 1 1 3 2 2 3 3 3 3 3
S  23  6   : 8 8 X X X X X X 8 7 7 7 X X X X 2 3 2 2 3 3 2 2 5 3 3 4 4 4 5 5
S  23 56   : 9 X 7 7 X X 9 X 4 6 3 3 4 4 6 6 1 1 . . . . 1 1 . . . . . . . .
S  23 56 8 : 8 X 7 6 8 8 X X 5 6 6 4 6 7 8 9 1 1 . . . . 1 1 . . . . . . . .
S  23 5678 : 7 9 X X 7 7 8 8 3 3 2 2 7 7 X 9 . . . . . . . . . . . . . . . .
S  23 567  : 7 9 X 9 8 8 X 7 4 5 3 3 7 9 7 6 . . . . . . . . . . . . . 1 . .
S  23 5 7  : X X 9 X X X X X 6 7 6 7 7 7 7 6 . . . . . . . . 2 2 1 1 2 1 1 1
S  23 5 78 : 9 9 X 9 X X X X 5 7 7 6 6 9 8 8 . . . . . . . . 1 2 1 2 1 1 1 1
S  23 5  8 : 9 9 X X X X X X 4 6 5 7 X X X X . . . . . . . . 1 1 1 1 1 1 1 1
S  23 5    : X X X X X X X X 6 7 9 6 8 8 8 7 . . . . . . . . 1 1 1 1 1 1 1 1
S  2345    : . . . . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . .
S  2345  8 : . . . . . 1 1 1 . . 1 1 . . . . . . . . . . . . . . . . . . . .
S  2345 78 : . . . . 1 1 2 1 . . . . . . . . . . . . . . . . . . . . . . . .
S  2345 7  : . . . . . 1 1 . . . . . . . . . . . . . . . . . . . . . . . . .
S  234567  :                                                                
S  2345678 :                                                                
S  23456 8 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S  23456   : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S  234 6   : 4 5 3 3 3 3 3 3 3 3 3 3 2 3 3 3 . . . . . . . . . . . . . . . .
S  234 6 8 : 4 5 3 3 3 3 3 2 3 3 3 3 2 4 3 3 . . . . . . . . 1 . . . . . . .
S  234 678 : 2 4 4 4 5 5 4 3 2 2 2 2 2 2 1 1 . . . . . . . . 1 1 . . . . . .
S  234 67  : 2 4 4 4 4 4 3 4 2 2 4 2 1 2 1 1 . . . . . . . . . . . . . . . .
S  234  7  : 4 5 3 3 5 5 2 2 3 3 2 2 4 3 1 2 . . . . . . . . . 1 2 1 1 2 . .
S  234  78 : 5 6 4 4 6 6 2 2 2 2 2 4 4 2 2 3 . . . . . . . . . 1 2 1 1 2 . .
S  234   8 : 8 8 4 4 5 5 4 3 5 5 5 5 6 6 6 6 . . . . . . . . . . . . 1 1 . .
S  234     : 7 7 3 3 4 4 4 4 4 4 4 4 4 4 4 4 . . . . . . . . . . . . . . . .
S  2 4     : 6 6 5 5 5 5 6 6 8 7 8 9 X 8 9 X 3 3 2 3 3 3 4 2 7 6 4 8 7 5 7 X
S  2 4   8 : 6 6 5 5 5 5 7 7 X 9 9 X X 9 8 9 4 3 1 2 3 3 5 3 6 7 5 6 8 6 X 9
S  2 4  78 : 4 4 4 4 6 5 7 7 X X X X X X 9 X 4 3 1 1 1 2 2 2 6 6 4 7 9 6 6 6
S  2 4  7  : 4 4 4 4 7 6 6 6 X X X X 9 9 X 9 5 3 3 3 1 1 1 1 6 5 5 8 9 4 7 6
S  2 4 67  : 7 7 8 8 7 7 8 X X X X X X X X X 2 2 3 3 . . . . 8 9 5 5 7 6 8 7
S  2 4 678 : 7 7 8 7 8 8 9 8 X X X X X X X X 3 3 3 4 . . 1 1 7 8 5 7 6 7 7 6
S  2 4 6 8 : 9 9 X X 7 7 X 9 X X X X 9 X X X 1 2 3 3 . 1 1 1 6 6 5 8 7 7 7 8
S  2 4 6   : 8 8 X X 7 7 8 8 X X X X X X X X 3 3 3 2 . 1 . 1 5 7 5 5 8 6 9 X
S  2 456   : X X X X X X X X 5 5 4 5 X X X X 1 1 2 2 . . . . 1 1 1 2 4 1 2 2
S  2 456 8 : 9 9 X X X X X X 5 3 3 5 X X X X 1 1 2 2 . . . . 1 2 . 1 3 2 2 2
S  2 45678 : 9 9 9 9 4 4 4 4 1 1 1 1 3 3 4 4 . . . . . . . . . . . . 1 1 1 1
S  2 4567  : 9 X X X 4 6 6 5 2 3 3 3 8 7 7 6 . . . . . . . . . . . . 1 1 1 1
S  2 45 7  : X 9 7 6 6 9 9 X X X X X X X X X 1 1 1 1 1 1 1 1 2 3 4 4 3 5 5 5
S  2 45 78 : 9 8 6 5 7 8 9 9 X X X X X X X X 1 1 1 1 1 1 1 1 3 2 2 2 4 5 7 5
S  2 45  8 : 9 X X 8 X X X X X X X X X X X X 3 3 3 3 1 1 1 1 8 6 4 4 7 6 7 6
S  2 45    : 9 X 7 7 X X X X X X X X X X X X 3 2 4 5 2 1 1 1 4 4 5 6 6 5 7 8
S  2  5    : 1 1 2 2 4 4 4 5 7 7 7 7 8 6 7 7 7 9 5 4 3 5 5 3 5 5 6 7 7 7 8 8
S  2  5  8 : 2 2 2 2 4 4 4 4 8 7 7 7 8 6 7 7 3 6 4 4 3 4 3 3 5 6 7 X 8 8 7 7
S  2  5 78 : 2 2 2 2 3 3 3 3 7 7 7 6 7 7 7 6 3 3 5 4 2 2 1 1 9 7 6 6 8 9 8 8
S  2  5 7  : 2 2 2 2 3 3 3 3 7 7 6 6 5 5 5 4 6 5 4 4 2 2 3 3 8 9 7 8 9 X 6 8
S  2  567  : 2 2 2 2 4 4 4 3 8 8 6 9 6 7 7 7 1 3 2 2 . . . . 6 4 6 3 7 8 5 4
S  2  5678 : 2 2 3 3 8 9 5 5 X 9 7 X X X X X 2 2 1 2 . . . . 5 6 3 4 X X X 6
S  2  56 8 : 1 1 1 1 4 4 2 2 X 8 X X 6 6 8 8 3 3 3 4 2 2 2 1 7 8 8 6 8 8 5 6
S  2  56   : 1 1 1 1 4 4 2 2 8 9 6 8 6 6 8 8 3 5 3 6 2 1 1 1 X 8 6 7 6 5 7 6
S  2   6   : . . . . 1 1 1 1 5 4 3 3 2 2 3 3 5 4 3 5 6 4 7 9 6 5 5 5 6 5 4 5
S  2   6 8 : . . . . 1 1 1 1 6 5 4 4 2 2 2 2 4 2 1 3 6 4 9 3 4 4 7 6 5 5 4 4
S  2   678 : . . . . 1 1 1 1 9 8 5 5 4 4 3 3 1 2 2 4 4 3 5 5 6 5 6 6 7 8 4 5
S  2   67  : . . . . 1 1 1 1 8 7 6 6 5 5 4 4 1 2 3 8 3 2 3 3 5 4 3 2 6 7 8 X
S  2    7  : . . . . 1 1 1 1 5 6 3 3 2 2 2 2 3 3 2 3 5 4 4 6 3 5 5 5 3 3 3 3
S  2    78 : . . . . 1 1 1 1 3 4 3 2 2 2 2 2 2 2 3 2 8 6 3 3 6 6 5 5 4 5 3 3
S  2     8 : . . . . 1 1 1 1 2 3 3 3 2 2 1 1 3 2 2 3 3 3 4 4 2 2 3 3 4 4 4 4
S  2       : . . . . 1 1 1 1 2 2 3 3 2 2 1 1 2 1 1 2 3 3 5 5 3 3 3 3 4 4 4 4
S 12       : 5 4 4 5 4 4 4 4 4 4 4 4 3 4 4 3 1 1 2 2 1 1 2 2 5 7 4 3 5 4 6 8
S 12     8 : 5 4 4 5 2 2 2 2 6 5 5 5 3 4 4 3 2 2 2 2 1 1 1 2 4 5 3 3 6 6 6 6
S 12    78 : 6 5 4 5 2 2 3 3 8 6 6 6 5 7 4 3 4 4 5 6 1 1 1 1 4 4 5 6 4 4 6 6
S 12    7  : 4 3 3 4 4 4 4 4 6 5 7 6 5 6 6 6 1 1 4 3 3 3 1 1 4 4 4 4 8 7 6 6
S 12   67  : 5 4 4 4 5 5 4 4 9 X X 8 8 8 6 6 2 3 2 2 2 2 2 1 3 3 1 1 3 2 3 3
S 12   678 : 5 4 3 3 4 4 3 3 7 8 9 6 7 8 5 5 2 3 2 2 2 2 4 2 3 3 1 2 3 3 4 4
S 12   6 8 : 3 3 4 4 3 4 3 3 9 8 X X 9 X 8 6 1 1 2 1 2 3 2 1 4 4 2 3 3 3 3 4
S 12   6   : 3 3 4 4 4 4 4 5 7 7 9 8 X X 6 5 3 3 1 1 3 3 2 2 6 6 3 4 2 2 3 3
S 12  56   : 3 3 4 4 6 5 5 4 X 9 9 X 8 X X X 1 1 2 2 1 1 1 1 2 3 4 5 4 4 5 6
S 12  56 8 : 3 4 3 3 5 5 5 5 X 9 8 9 X X 9 8 2 2 3 3 . . . . 2 2 4 3 4 5 4 5
S 12  5678 : 5 5 6 6 7 7 X X X X X 9 X X X X 1 1 1 1 . . . . 2 3 3 1 4 3 5 5
S 12  567  : 5 5 5 5 9 7 6 5 9 9 9 9 X X X X . 1 1 2 . . . . 2 3 2 2 3 3 4 3
S 12  5 7  : 7 6 9 9 6 7 6 7 9 8 7 7 X X X X 3 4 3 3 1 1 3 2 2 2 5 5 3 3 4 4
S 12  5 78 : 5 4 7 9 7 7 9 8 9 X 7 8 X X X X 2 2 1 1 1 1 2 1 4 3 6 6 3 3 2 3
S 12  5  8 : 6 6 7 8 X X 9 9 8 X 9 8 X X 9 8 4 4 5 5 2 2 3 3 8 9 8 6 4 7 5 5
S 12  5    : 8 8 8 8 X X 8 X 8 X 9 8 X X X X 3 3 5 4 1 1 2 2 4 5 6 4 3 3 3 3
S 12 45    : 8 8 5 4 X 9 8 8 4 6 4 4 9 X X 9 2 2 2 2 1 1 . . 1 1 1 1 1 1 1 1
S 12 45  8 : 8 9 5 4 9 9 X 8 5 5 5 5 X X X 9 2 2 2 2 1 1 . . 2 1 1 1 1 1 2 1
S 12 45 78 : X X 5 5 7 8 X X 8 9 X 6 7 9 8 7 . . . . . . . . 1 1 1 2 1 2 2 3
S 12 45 7  : X X 7 6 6 8 9 9 7 6 9 9 5 6 7 7 . . . . . . . . 3 2 2 2 1 3 3 3
S 12 4567  : 7 8 X 9 4 5 4 2 3 3 3 3 4 4 4 4 1 1 1 1 . . . . . . . . . . . .
S 12 45678 : X X 8 8 2 2 2 2 1 1 1 1 1 1 2 2 1 1 1 1 . . . . . . . . . . . .
S 12 456 8 : 5 7 8 8 7 X 8 9 3 3 4 4 6 6 6 4 2 2 2 2 . . . . . . . . . 1 . .
S 12 456   : 5 6 7 7 8 9 7 7 3 4 4 4 4 7 7 7 2 2 2 2 . . . . . . . . . . . .
S 12 4 6   : 9 9 X 9 X X X X X X X X 9 9 X X 2 2 1 1 1 1 2 2 5 5 2 2 2 2 5 5
S 12 4 6 8 : 9 9 X 9 X X X X X X X X X X X X 2 2 1 1 1 1 2 2 4 4 2 2 3 2 6 5
S 12 4 678 : X X X 9 X 8 X X X X 8 9 X X X X 2 3 1 1 1 1 2 2 5 4 2 2 3 3 6 4
S 12 4 67  : X X X 9 X X X 9 9 7 8 X 9 9 X X 2 2 1 1 1 1 2 2 5 5 1 2 2 2 5 3
S 12 4  7  : 8 9 8 8 9 X X 9 X 8 9 8 X X X X 1 1 1 1 1 1 . . 3 3 3 3 3 3 3 3
S 12 4  78 : 9 9 X 9 8 X 9 9 9 9 X 9 X X X X 1 1 1 1 1 1 . . 4 5 3 3 3 3 3 4
S 12 4   8 : X X X 9 X X X X X X 9 8 X X X X 3 4 2 2 1 1 1 1 3 3 3 4 4 4 5 4
S 12 4     : 8 9 8 8 X X X X X 9 X X X X X X 3 3 2 2 . . . . 2 2 2 2 3 3 3 2
S 1234     : . . . . . . . . . . . . . . . .                 . . . . . . . .
S 1234   8 : . . . . . . . . . . . . . . . .                 . . . . . . . .
S 1234  78 : . . . . . . . . . . . . . . . .                 . . . . . . . .
S 1234  7  : . . . . . . . . . . . . . . . .                 . . . . . . . .
S 1234 67  : . . . . . . . . . . . . . . . .                 . . . . . . . .
S 1234 678 : . . . . . . . . . . . . . . . .                 . . . . . . . .
S 1234 6 8 : . . . . . . . . . . . . . . . .                 . . . . . . . .
S 1234 6   : . . . . . . . . . . . . . . . .                 . . . . . . . .
S 123456   :                                                                
S 123456 8 :                                                                
S 12345678 :                                                                
S 1234567  :                                                                
S 12345 7  : . . . . . . . . . . . . . . . .                                
S 12345 78 : . . . . . . . . . . . . . . . .                                
S 12345  8 : . . . . . . . . . . . . . . . .                                
S 12345    : . . . . . . . . . . . . . . . .                                
S 123 5    : 2 1 1 2 1 2 1 1 2 2 1 1 3 1 2 3 . . . . . . . . . . 1 1 . . . .
S 123 5  8 : 1 1 1 2 1 1 1 1 3 3 2 1 2 1 1 2 . . . . . . . . . 1 1 1 1 1 1 .
S 123 5 78 : 1 1 1 1 2 2 1 1 2 2 2 2 1 1 1 1 . . . . . . . . . . . . . . . 1
S 123 5 7  : 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 1 . . . . . . . . . . . . . . 1 .
S 123 567  : . . 1 1 1 1 1 1 . . 1 1 1 1 1 . . . . . . . . . . . . . . . . .
S 123 5678 : . . 2 1 1 1 1 2 . . . . 2 1 1 1 . . . . . . . . . . . . . . . .
S 123 56 8 : . . . . 1 1 1 1 1 1 2 2 1 1 . . . . . . . . . . . . . . . . . .
S 123 56   : . . . . 1 1 . 1 1 1 1 1 1 1 . . . . . . . . . . . . . . . . . .
S 123  6   : 3 1 2 3 4 4 1 1 4 3 2 2 2 3 5 3 . . . . . . . . . . . . . 1 1 .
S 123  6 8 : 3 1 2 2 4 5 2 1 3 3 3 3 3 3 4 2 . . 2 2 . . . . . . . . . . . .
S 123  678 : 2 2 2 1 4 5 2 1 2 3 4 4 3 2 1 1 . . . . . . . . . . . . . . . .
S 123  67  : 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 1 . . . . . . . . . . . . . . . .
S 123   7  : 2 1 2 1 3 3 1 1 4 3 5 6 1 2 2 2 . . . . . . . . . . 1 1 . . 1 1
S 123   78 : 2 1 3 1 3 3 1 2 2 1 4 3 2 4 3 2 . . . . . . . . . . 1 1 . . . .
S 123    8 : 2 1 2 1 4 4 2 1 2 2 2 3 1 1 3 2 1 1 1 1 . . . . 1 1 2 2 1 2 1 1
S 123      : 4 2 1 1 4 4 1 1 1 2 4 4 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3      : 5 5 6 6 5 5 4 5 8 9 7 6 7 7 7 8 5 7 4 3 2 3 1 2 6 7 6 6 8 7 8 9
S 1 3    8 : 5 5 6 6 6 6 4 5 9 9 8 7 6 6 7 7 6 7 6 5 2 2 1 1 6 7 7 6 8 7 X X
S 1 3   78 : 5 5 6 6 5 6 5 4 8 8 9 8 6 7 8 8 3 4 3 4 1 1 1 1 6 6 7 7 8 8 7 9
S 1 3   7  : 5 5 6 6 4 4 4 4 9 8 8 7 7 8 9 9 3 3 3 4 2 1 1 1 7 8 8 8 X X 7 X
S 1 3  67  : 7 7 8 9 7 7 6 6 X X X X 8 X 8 8 3 3 2 3 1 1 1 1 9 8 X X 7 6 5 5
S 1 3  678 : 7 7 8 9 7 8 7 6 X X X X X X 8 8 3 2 3 5 1 1 1 1 7 7 X X 8 7 X 9
S 1 3  6 8 : 6 6 6 6 7 6 7 6 X X X X 9 8 7 7 4 3 2 2 1 1 1 1 7 8 7 7 7 6 8 8
S 1 3  6   : 6 6 6 6 7 6 6 6 X X X 9 X 9 9 X 4 3 2 1 1 1 1 1 7 8 6 6 8 5 6 7
S 1 3 56   : X X 8 8 X X X X X X X X X X X X . . . . . . . . 7 6 5 6 6 6 8 6
S 1 3 56 8 : X X 7 7 X X X X X X X X X X X X . . . . . . . . 4 5 5 4 6 6 9 8
S 1 3 5678 : 9 8 X X X X X X X X 6 9 9 9 X X . . . . . . . . 4 4 3 4 8 8 9 9
S 1 3 567  : X 7 X X X X X X X X X X X X X X . . . . . . . . 5 3 4 3 8 7 8 8
S 1 3 5 7  : X X 8 7 9 9 X X X X X X X X X X 1 1 1 1 . . . . 6 5 5 8 8 6 7 7
S 1 3 5 78 : X X 9 7 9 8 9 X X X X X X X X X 1 1 . . . . . . 7 7 7 7 7 6 7 9
S 1 3 5  8 : X X 9 7 6 9 X X X X X X X X X X 1 1 1 1 . . . . X 8 8 6 4 5 4 4
S 1 3 5    : X X X 8 6 7 X X X X X X X X X X 2 2 1 1 . . . . 9 7 7 7 6 3 4 4
S 1 345    : 4 4 6 6 4 4 7 5 5 4 4 2 3 5 3 3 . . . . 1 1 . . 1 2 1 1 2 3 2 1
S 1 345  8 : 4 4 7 7 6 9 8 6 4 6 5 3 4 3 2 2 . . . . . . . . 1 1 1 1 2 2 2 1
S 1 345 78 : 8 8 7 5 9 9 X 8 3 3 4 3 3 3 4 3 . . . . . . . . 1 1 1 1 2 2 2 1
S 1 345 7  : 9 9 6 6 8 8 8 6 3 4 2 2 4 5 5 3 . . . . . . . . 1 1 1 1 2 2 2 2
S 1 34567  : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S 1 345678 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S 1 3456 8 : 1 1 1 1 1 2 1 1 . . . . . . 1 1 . . . . . . . . . . . . . . . .
S 1 3456   : 1 1 1 1 1 1 1 1 . . . . 1 . 1 1 . . . . . . . . . . . . . . . .
S 1 34 6   : X X X X 8 8 9 X X X 9 9 9 X 9 9 . . . . . . . . 3 3 1 1 3 3 5 5
S 1 34 6 8 : X X X X 8 X X X 9 X 9 9 8 9 9 9 . . . . . . . . 3 3 2 1 2 1 4 3
S 1 34 678 : X X X X X X X X X 9 7 9 X X X X . . . . . . . . 4 3 3 4 2 2 4 4
S 1 34 67  : X X X X 8 X 9 X 8 7 7 8 X X X X . . . . . . . . 2 2 1 2 3 3 3 3
S 1 34  7  : 8 8 8 8 X X X X 8 7 X X X X X 9 . . . . . . . . 3 4 2 2 3 3 2 2
S 1 34  78 : 8 8 8 8 X X 9 X X 7 9 7 X X X X 1 2 . . . . . . 3 3 2 2 3 4 3 2
S 1 34   8 : X X 9 X X X X X X X 8 X X X 8 9 . . . . . . . . 2 2 2 1 2 3 2 3
S 1 34     : X X 9 9 X X X X X X 7 9 X X 9 X . . . . . . . . 2 1 3 1 2 3 2 3
S 1  4     : 3 2 3 4 2 2 2 2 8 7 X X 7 8 7 6 6 7 4 4 4 3 5 6 X X 6 7 9 8 X X
S 1  4   8 : 2 1 2 3 2 2 2 2 9 8 9 9 7 8 7 6 4 7 4 2 2 2 4 4 8 9 5 5 8 8 X X
S 1  4  78 : 1 1 1 1 2 2 2 2 9 7 8 9 7 8 6 6 5 4 6 8 3 3 4 4 X 7 8 9 7 8 X X
S 1  4  7  : 2 2 2 2 2 2 2 2 8 7 9 9 7 8 6 6 4 4 5 7 2 3 5 3 8 8 X 8 7 7 9 X
S 1  4 67  : 1 1 1 1 4 4 2 2 X X X X 7 9 6 5 4 5 5 4 2 2 3 4 9 X 8 9 8 8 X X
S 1  4 678 : 1 1 2 1 5 4 3 4 X X X X 8 X 7 8 7 7 6 8 2 2 3 3 X X 7 X 9 9 X X
S 1  4 6 8 : 2 2 2 2 3 3 3 3 7 9 X 9 7 9 7 6 6 6 5 4 2 3 4 5 X 9 7 X X X X X
S 1  4 6   : 2 2 2 2 3 3 3 3 9 9 X X 9 X 8 7 6 5 5 4 2 2 4 5 7 7 7 9 9 X X X
S 1  456   : 4 4 3 3 6 6 6 6 X X X X X 9 8 6 4 4 4 4 . . 1 1 4 3 3 4 7 8 8 8
S 1  456 8 : 4 4 3 3 6 8 6 7 X 8 7 7 X X X X 2 3 3 2 . . 1 1 3 4 6 7 7 X 8 7
S 1  45678 : 3 3 4 4 2 2 2 2 5 5 5 5 2 2 2 2 1 1 1 1 . . . . . . . . 5 5 5 5
S 1  4567  : 2 4 5 7 8 6 7 8 6 7 6 7 4 4 9 6 1 1 1 1 . . . . 1 1 1 1 5 5 8 6
S 1  45 7  : 2 2 2 2 4 5 3 3 X X X X 9 9 X X 6 6 3 5 2 1 3 2 X 9 8 9 X X X X
S 1  45 78 : 2 2 2 2 4 6 4 3 X X X X X X X X 5 4 2 3 1 1 2 3 7 7 9 7 7 8 X 8
S 1  45  8 : 2 2 2 2 4 4 5 4 X X X X X X 9 8 6 6 3 5 2 3 3 2 9 7 8 X X X X X
S 1  45    : 2 2 2 2 3 3 3 3 X X X X X 9 9 8 6 4 6 5 3 4 3 2 7 6 8 X X X X X
S 1   5    : . . . . 1 1 1 1 3 3 3 3 3 3 4 4 6 6 5 6 4 5 4 3 5 4 5 5 4 3 6 6
S 1   5  8 : . . . . 1 1 1 1 3 3 4 3 3 3 4 4 5 4 3 5 2 2 3 4 5 5 6 6 5 4 6 6
S 1   5 78 : . . . . . . . . 2 2 2 2 2 2 2 2 4 4 7 7 4 3 4 8 6 5 5 6 5 6 4 4
S 1   5 7  : . . . . . . . . 2 2 2 2 2 2 2 2 5 5 X 8 4 2 4 6 5 5 4 5 6 6 4 4
S 1   567  : . . . . 1 1 1 1 6 7 5 6 7 6 3 3 3 3 4 7 . . 4 3 5 7 4 3 6 5 5 6
S 1   5678 : 1 1 1 1 1 1 2 2 9 X 5 9 X X X 7 4 3 3 3 . . 3 2 X X 5 3 X X 7 6
S 1   56 8 : . . . . 1 1 1 1 4 4 5 6 4 5 3 3 5 6 6 5 2 2 2 3 3 5 5 5 5 5 3 3
S 1   56   : . . . . 1 1 1 1 3 4 4 5 3 3 2 2 4 6 7 7 3 2 2 5 3 4 3 5 4 6 3 4
S 1    6   : . . . . . . . . 1 1 2 1 . . . . 2 2 2 2 2 2 3 3 2 3 1 1 3 3 2 2
S 1    6 8 : . . . . . . . . 1 1 2 1 . . . . 2 2 2 2 2 3 5 3 2 3 1 1 3 3 2 2
S 1    678 : . . . . . . . . 2 1 1 1 . . . . 4 5 2 2 2 2 2 2 2 2 5 4 2 2 3 3
S 1    67  : . . . . . . . . 2 1 1 1 . . . . 2 3 3 3 1 1 4 3 2 2 4 4 2 2 2 2
S 1     7  : . . . . . . . . 2 2 3 3 . . . . 1 1 2 1 2 3 1 1 1 1 1 1 1 1 1 1
S 1     78 : . . . . . . . . 2 2 3 3 . . . . 1 1 1 1 1 3 1 1 1 1 2 2 1 1 1 1
S 1      8 : . . . . . . . . 1 1 2 2 . . . . 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1
S 1        : . . . . . . . . 1 1 2 2 . . . . 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
S01        : 1 1 1 1 2 2 2 2 4 4 7 6 4 4 3 4 4 7 4 3 4 2 1 1 5 5 5 5 4 4 4 6
S01      8 : 1 1 1 1 2 2 2 2 4 4 8 6 3 3 2 3 4 7 7 7 5 4 3 3 3 3 4 4 3 3 4 6
S01     78 : 1 1 1 1 2 2 2 2 4 5 7 6 3 3 2 2 3 5 4 3 2 2 3 1 3 4 4 3 2 3 3 4
S01     7  : 1 1 1 1 2 2 2 2 4 5 7 6 3 3 2 2 3 5 4 3 2 2 3 1 3 3 4 4 2 2 3 4
S01    67  : 1 1 1 1 1 1 1 1 4 5 5 5 3 3 3 3 6 6 5 4 2 2 3 2 7 6 5 5 4 4 6 6
S01    678 : 1 1 1 1 1 1 1 1 4 5 5 4 3 3 3 3 6 7 5 4 2 2 3 2 8 8 7 7 4 4 6 6
S01    6 8 : 1 1 1 1 1 1 1 1 6 7 8 9 4 4 3 3 6 9 4 4 1 1 2 2 7 5 6 6 2 4 5 6
S01    6   : 1 1 1 1 1 1 1 1 5 6 7 7 4 4 3 3 7 X 6 6 1 1 2 2 8 6 8 7 4 5 5 6
S01   56   : 3 3 3 3 4 4 3 3 X X 6 6 8 9 7 7 8 6 4 5 1 1 3 3 8 X 5 5 8 8 6 6
S01   56 8 : 2 2 2 2 3 3 2 2 7 7 6 6 9 8 6 8 6 6 5 6 2 2 3 3 6 7 5 7 7 8 8 8
S01   5678 : 2 2 2 2 3 4 5 3 X X 9 9 X X X X 3 2 6 3 . . . . 8 8 9 X 8 X 8 8
S01   567  : 2 2 2 2 3 3 2 2 7 8 9 8 7 8 6 6 4 4 6 8 1 1 1 1 8 9 7 8 7 9 6 5
S01   5 7  : 3 3 3 3 5 5 5 5 7 8 6 6 6 6 6 8 8 9 5 7 1 1 4 3 X X 9 8 X X X X
S01   5 78 : 3 3 3 3 5 5 5 5 6 8 7 6 6 6 5 8 8 7 4 5 1 1 5 4 9 8 7 6 X X X X
S01   5  8 : 3 3 3 3 5 5 5 5 6 6 6 8 7 7 6 8 6 8 6 6 4 4 5 5 X X X 9 X X X X
S01   5    : 5 5 5 5 6 6 6 6 5 6 6 6 8 8 6 9 6 9 5 8 3 3 6 4 X X X X X X X X
S01  45    : 6 4 4 5 6 6 7 5 X X X X X 9 9 9 5 4 3 3 1 1 1 2 8 8 9 X 7 8 X X
S01  45  8 : 4 3 4 5 5 5 6 6 X X X X X X X X 3 4 4 6 . 1 1 1 9 5 9 X 8 6 9 8
S01  45 78 : 5 5 4 5 5 5 6 5 X X X X X X X X 3 3 2 2 1 . 1 1 9 8 X X 8 9 9 9
S01  45 7  : 5 4 5 4 4 5 4 4 X X X X X X X X 3 4 2 2 1 1 2 2 8 8 6 7 5 7 9 7
S01  4567  : 6 6 8 X 7 8 9 6 4 4 5 5 5 8 X 4 1 1 . . . . . . 1 1 . . 2 2 5 3
S01  45678 : 8 8 8 8 5 4 3 3 3 3 3 3 5 5 4 4 1 1 . . . . . . 1 1 . . 2 2 2 2
S01  456 8 : 5 5 5 6 8 7 8 6 X 8 6 6 X X X X 2 3 1 1 . . 1 1 5 5 4 3 7 8 4 4
S01  456   : 6 7 6 6 8 8 7 8 X X 7 9 X X X X 4 3 2 2 . . 1 1 4 3 4 3 5 6 7 5
S01  4 6   : 4 4 4 5 3 3 5 5 X X 9 X X X X X 6 8 5 4 1 1 4 4 X X X 8 X X 9 9
S01  4 6 8 : 4 4 4 5 4 3 5 5 X X X X X X X 8 7 8 4 3 1 1 5 4 X X 9 8 X X X 9
S01  4 678 : 3 4 3 4 8 8 6 6 X X X X X X X 8 6 6 8 6 1 1 2 2 X X X X X X X X
S01  4 67  : 4 4 3 4 5 5 5 5 X X X X X X X 9 6 5 5 6 1 1 2 3 X X 8 X 9 9 X X
S01  4  7  : 4 4 5 5 4 4 3 3 X X X X 8 X X X 6 5 6 4 4 5 4 4 X X X 9 X X X X
S01  4  78 : 4 4 5 4 3 3 4 4 X X X X 9 X X X 6 5 6 5 4 4 4 4 X X 7 9 9 X X X
S01  4   8 : 5 5 5 6 5 4 3 3 X X X X X X X 9 4 4 4 3 2 2 3 2 6 7 X X 8 9 X X
S01  4     : 5 5 5 6 6 5 4 4 X X X X X X X X 5 5 6 5 3 3 3 3 8 9 9 X 9 X X X
S01 34     : X X X X X X X X X X 6 8 X 8 X X . . . . . . . . 2 2 1 1 2 2 2 4
S01 34   8 : X X X X X X X X X X 8 9 X X 9 X . . . . . . . . 1 1 1 1 3 2 1 3
S01 34  78 : X X X X X X X X X X 8 8 X 9 X 9 . . . . . . . . 2 2 2 2 2 3 2 3
S01 34  7  : X X X X X X X X 6 8 9 X 7 6 6 X . . . . . . . . 3 2 2 3 2 2 3 4
S01 34 67  : X X X X 8 X 9 X 7 8 5 5 X X X X . . . . . . . . 2 2 2 1 1 1 2 2
S01 34 678 : X 9 X X 9 X 9 8 9 9 5 7 X 9 X X . . . . . . . . 5 3 2 4 2 3 3 3
S01 34 6 8 : X X X X X X X X 8 9 8 8 9 8 6 6 . . . . . . . . 2 2 2 2 1 2 4 4
S01 34 6   : X X X X X X X X 9 9 8 8 9 9 8 7 . . . . . . . . 2 2 1 2 1 2 5 4
S01 3456   : 1 1 1 1 2 3 1 1 . . . . 1 . 1 1 . . . . . . . . . . . . . . . .
S01 3456 8 : 1 1 1 1 1 1 1 1 . . . . . . 1 1 . . . . . . . . . . . . . . . .
S01 345678 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S01 34567  : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S01 345 7  : 4 3 4 5 7 X 6 6 2 2 2 2 2 4 5 3 . . . . . . . . 1 1 1 1 2 2 2 2
S01 345 78 : 3 3 3 4 6 8 6 4 2 3 2 2 2 2 4 2 . . . . . . . . 1 1 1 1 2 2 2 1
S01 345  8 : 4 4 5 6 5 5 6 3 2 3 3 2 4 3 2 2 . . . . . . . . 1 1 1 1 2 2 2 1
S01 345    : 4 4 6 6 5 7 7 5 3 2 1 2 3 4 4 4 . . . . . . . . 1 2 1 1 2 3 2 1
S01 3 5    : X X X X X X X X X X X X X X X X 1 2 . . . . . . 6 6 4 4 4 4 5 5
S01 3 5  8 : X X X X X X X X X X X X X X X X 1 2 . . . . . . 5 5 6 6 4 4 6 6
S01 3 5 78 : X X X X X X X 9 X X X X X X X X 1 1 . . . . . . 5 6 6 6 6 5 5 5
S01 3 5 7  : X X X X X X 9 9 X X X X X X X X 1 1 . . . . . . 8 6 6 5 3 4 5 5
S01 3 567  : X 9 X X X X X X 7 8 X X X X X X . . . . . . . . 5 4 3 3 3 4 5 4
S01 3 5678 : X X X X X X X X 7 8 7 8 8 7 X X . . . . . . . . 6 6 4 4 4 5 7 6
S01 3 56 8 : X X X X X X X X 9 X X 9 9 9 X X . . . . . . . . 5 5 4 3 3 3 7 6
S01 3 56   : X X X X X X X X 9 X X 9 9 X X X . . . . . . . . 5 5 4 4 3 5 5 6
S01 3  6   : 8 8 8 7 9 9 8 8 9 X 9 9 X X X X 2 2 1 1 1 . . 1 5 6 4 4 6 6 7 6
S01 3  6 8 : 7 7 8 7 9 9 8 8 X X X X X X X X 1 1 1 1 . . . 1 6 5 5 5 6 6 6 6
S01 3  678 : X X 9 9 9 9 8 8 X X X X X X X X 1 1 1 . . . 1 1 5 4 4 4 6 6 8 8
S01 3  67  : X X 9 9 9 9 8 8 X X X X 9 X X 9 1 1 . . . . . 1 4 5 4 5 7 6 7 7
S01 3   7  : 7 6 8 8 X 9 8 8 X X X X 8 X 9 8 1 1 2 1 . . 1 1 7 8 5 6 7 6 9 9
S01 3   78 : 7 6 9 8 9 X 7 7 X X X X 9 9 9 8 1 2 3 1 . . 1 1 6 8 6 5 7 6 8 8
S01 3    8 : 7 7 8 7 8 9 7 8 X X X X 9 9 8 X 1 1 1 1 1 1 2 3 6 5 5 5 6 7 7 7
S01 3      : 7 7 9 8 8 7 7 7 9 9 X 9 8 8 8 X 1 1 1 1 1 1 2 2 6 6 6 7 7 7 6 7
S0123      :                                                                
S0123    8 :                                                                
S0123   78 :                                                                
S0123   7  :                                                                
S0123  67  :                                                                
S0123  678 :                                                                
S0123  6 8 :                                                                
S0123  6   :                                                                
S0123 56   :                                                                
S0123 56 8 :                                                                
S0123 5678 :                                                                
S0123 567  :                                                                
S0123 5 7  :                                                                
S0123 5 78 :                                                                
S0123 5  8 :                                                                
S0123 5    :                                                                
S012345    :                                                                
S012345  8 :                                                                
S012345 78 :                                                                
S012345 7  :                                                                
S01234567  :                                                                
S012345678 :                                                                
S0123456 8 :                                                                
S0123456   :                                                                
S01234 6   :                                                                
S01234 6 8 :                                                                
S01234 678 :                                                                
S01234 67  :                                                                
S01234  7  :                                                                
S01234  78 :                                                                
S01234   8 :                                                                
S01234     :                                                                
S012 4     : 5 5 4 4 7 7 5 6 5 4 5 4 5 6 5 7 . . . . . . . . . . . . . . 1 1
S012 4   8 : 5 5 4 4 7 6 5 5 5 3 4 4 7 8 9 6 . . 1 . . . . . 1 1 1 2 1 1 2 2
S012 4  78 : 4 5 4 4 4 6 4 5 3 4 5 5 5 5 7 7 . . . . . . . . 1 2 1 2 1 1 1 1
S012 4  7  : 4 5 5 5 4 6 4 5 3 5 6 5 5 7 8 7 1 1 1 1 . . . . 1 1 1 1 1 1 1 1
S012 4 67  : 5 6 6 6 4 5 4 4 4 4 6 6 5 6 6 6 1 1 1 1 . . . . 1 1 1 1 1 1 1 1
S012 4 678 : 6 5 5 5 6 5 5 5 8 7 7 7 7 X 8 7 1 1 1 1 . . 1 1 2 2 1 1 2 2 1 1
S012 4 6 8 : 7 7 7 6 5 6 6 7 5 5 6 5 6 7 7 9 1 1 1 1 . . . . 1 1 1 1 1 1 1 1
S012 4 6   : 7 5 6 6 5 6 6 7 5 5 6 5 6 6 7 7 1 1 1 1 . . . . 1 1 1 1 1 1 1 1
S012 456   : 4 5 5 5 5 6 4 3 2 2 2 2 3 6 5 4 1 1 1 1 . . . . . . . . . . . .
S012 456 8 : 4 4 5 5 7 8 8 6 3 3 4 4 4 4 5 3 1 1 1 1 . . . . . . . . . . . .
S012 45678 : 4 4 5 5 2 2 2 2 . . . . . . 1 1 . . . . . . . . . . . . . . . .
S012 4567  : 3 4 6 5 3 4 2 2 1 1 1 1 3 3 2 2 . . . . . . . . . . . . . . . .
S012 45 7  : 7 6 5 6 5 5 4 4 6 6 5 5 5 4 5 4 . . . . . . . . 2 1 1 1 1 1 . 1
S012 45 78 : 7 7 4 6 5 6 4 7 5 4 4 4 6 7 4 4 . . . . . . . . 1 1 1 1 1 1 . .
S012 45  8 : 7 7 7 8 5 6 3 5 3 4 4 4 9 8 7 8 1 1 1 1 . . . . 1 1 2 2 1 1 . .
S012 45    : 8 9 9 X 4 4 4 4 5 4 3 3 8 7 7 7 1 1 1 1 . . . . 1 1 1 1 1 1 . .
S012  5    : 3 4 3 3 6 6 4 4 8 7 4 4 5 5 8 7 1 1 1 2 . . 1 1 3 3 3 3 2 2 2 2
S012  5  8 : 3 3 3 4 4 3 4 5 5 6 6 5 4 4 5 5 1 1 1 1 . . 1 1 3 2 3 3 2 3 1 1
S012  5 78 : 3 3 2 2 4 5 3 3 8 8 6 4 4 5 4 4 . . . . . . 1 1 2 1 3 3 2 1 1 1
S012  5 7  : 2 3 2 2 4 6 4 3 7 7 6 4 3 5 5 5 . . . . . . 1 1 2 2 2 3 1 1 1 1
S012  567  : 4 4 2 2 3 3 3 3 6 8 5 5 7 7 9 7 . . . . . . . . . . . . . . . .
S012  5678 : 4 4 5 4 4 4 4 6 8 8 6 5 8 9 X 9 . . . . . . . . . . . . . . . .
S012  56 8 : 4 3 2 2 4 3 3 4 7 8 5 6 4 4 6 4 . . . . . . . . 1 2 2 1 1 1 . .
S012  56   : 4 3 2 3 3 5 5 5 6 5 4 5 5 5 6 4 . . . . . . . . . 2 1 1 1 1 . 1
S012   6   : 1 1 1 1 1 1 1 1 4 4 5 5 4 4 4 5 . . . . . . . . . . . . . . . .
S012   6 8 : 1 1 1 1 2 1 1 1 4 4 5 4 4 2 3 3 . . . . . . . . . . . . . . . .
S012   678 : 1 1 1 1 1 1 1 1 4 4 4 5 2 4 2 2 . . . . . . . . . . . . . . . .
S012   67  : 1 1 2 1 1 1 1 2 3 3 5 5 3 4 3 3 . . . . . . . . . . . . . . . .
S012    7  : 1 1 1 1 1 1 1 1 2 4 3 2 2 1 1 1 1 1 . . . . . . . . . . . . . .
S012    78 : 1 1 1 1 1 1 1 1 2 3 2 3 2 1 1 2 1 1 . . . . . . . . . . . . 1 .
S012     8 : 1 1 1 1 1 1 1 1 1 1 4 3 2 3 1 1 1 1 1 1 . . . . . . . . . . . .
S012       : 1 1 1 1 1 1 1 1 1 1 3 2 1 1 1 1 1 1 1 1 . . . . . . . . . . . .
S0 2       : 1 1 1 1 3 4 2 1 3 3 5 4 3 3 3 3 5 4 5 4 3 2 2 4 3 5 3 4 4 4 4 4
S0 2     8 : 1 1 1 1 2 4 2 1 3 4 5 5 3 3 3 3 7 6 3 5 2 1 2 4 2 3 5 5 3 4 4 2
S0 2    78 : 1 1 2 2 3 4 1 1 5 6 9 8 6 6 5 5 6 6 3 4 2 1 1 1 8 7 6 7 4 4 4 7
S0 2    7  : 1 1 2 2 3 3 1 1 4 6 8 7 4 5 5 4 4 4 4 5 1 1 1 2 6 4 5 4 5 5 5 7
S0 2   67  : 1 1 2 2 4 4 3 3 7 7 7 7 9 8 8 8 2 4 2 2 2 1 1 1 7 8 7 7 6 6 6 5
S0 2   678 : 1 1 3 3 4 4 2 3 7 7 7 7 8 7 7 7 3 3 1 1 1 . 3 2 9 9 X 9 6 6 6 6
S0 2   6 8 : 1 1 2 2 3 3 2 2 7 7 7 8 6 6 6 6 3 3 2 2 1 1 1 2 4 3 5 4 5 5 5 5
S0 2   6   : 1 1 2 2 4 4 2 2 7 8 6 7 7 7 8 8 4 3 3 3 2 3 1 2 2 2 6 3 6 6 6 4
S0 2  56   : 3 3 4 4 7 6 5 5 X X X X X X X 9 2 3 3 3 2 1 2 1 9 9 6 7 7 5 9 8
S0 2  56 8 : 3 3 4 4 5 6 4 3 X X X X X X 9 X 2 2 4 4 2 1 2 1 X X 9 7 6 5 6 6
S0 2  5678 : 2 2 3 3 8 9 8 7 X X X X X X X X 2 2 1 1 . . . . 6 5 6 7 9 9 7 7
S0 2  567  : 2 2 3 3 5 4 3 3 X X X X X X X 9 2 4 5 4 1 . . 1 4 3 5 6 8 7 9 9
S0 2  5 7  : 3 3 3 3 3 3 3 3 9 X X 8 X X X 9 3 4 4 5 2 2 2 3 7 8 X 9 X 9 9 9
S0 2  5 78 : 3 3 3 3 3 3 3 3 8 X X X X 8 X 9 2 4 3 3 2 1 2 2 8 8 X X X 7 8 9
S0 2  5  8 : 3 3 3 3 4 5 5 4 X 9 X X 8 8 X X 6 8 6 5 3 3 2 3 6 8 6 4 9 7 6 6
S0 2  5    : 4 3 3 3 4 5 4 3 7 7 X 9 9 X X X 6 5 5 4 4 2 6 4 6 7 4 5 8 7 6 7
S0 2 45    : 9 X 8 9 X X X X X X X 8 X X X X 3 3 3 3 . . . . 4 4 5 4 5 6 6 6
S0 2 45  8 : 9 8 9 8 X X X X X X X X X X X X 3 3 3 3 . . . . 6 4 4 3 5 5 5 6
S0 2 45 78 : X X 8 9 X 8 9 X X X X X X X 9 X 2 2 1 1 . . . . 2 3 3 3 3 4 4 5
S0 2 45 7  : 9 X 9 7 X X 8 8 X X 9 9 9 9 9 9 3 3 1 1 . . . . 2 3 3 3 3 2 4 6
S0 2 4567  : X X X X 7 X 9 7 3 4 4 4 8 8 9 8 . . . . . . . . . . . . 1 1 2 2
S0 2 45678 : X X X X 5 5 6 6 2 2 3 3 4 4 4 4 . . . . . . . . . . . . 1 1 2 2
S0 2 456 8 : 9 X X X X X X X 7 6 6 7 X X X X 1 1 2 2 . . . . 1 1 1 2 3 1 2 2
S0 2 456   : 8 9 X X X X X X 7 7 6 7 X X X X 1 1 2 2 . . . . 1 1 1 1 3 1 3 3
S0 2 4 6   : 9 9 8 X X 9 X X X X X X X X X X 2 2 2 2 1 1 1 1 4 5 5 4 7 5 6 8
S0 2 4 6 8 : 9 9 9 9 X X X X X X X X X X X X 2 2 2 2 . . 1 3 6 8 4 5 7 7 7 9
S0 2 4 678 : 9 8 9 8 X X X X X X X X X X X X 3 2 3 4 . . 1 1 6 6 5 6 6 7 8 X
S0 2 4 67  : 8 7 9 8 X 9 X X X X X X X X X X 1 1 2 2 1 1 1 1 5 5 4 4 7 6 X 8
S0 2 4  7  : 7 7 7 7 X X X X X X X X X X X X 4 2 1 1 2 2 3 3 8 6 7 9 7 8 X X
S0 2 4  78 : 7 7 7 7 X X 9 9 X X X X X X X X 2 1 1 1 1 1 1 1 6 6 7 8 8 7 X X
S0 2 4   8 : 8 8 9 8 X X X X X X X X 9 8 X 9 2 2 2 1 1 1 2 2 6 8 8 7 9 8 8 9
S0 2 4     : 8 8 8 7 9 X X X X X X X 8 8 X X 3 2 2 2 2 2 3 3 5 7 6 7 9 6 8 X
S0 234     : 4 4 3 3 4 4 4 2 1 1 2 2 2 2 2 2 . . . . . . . . . . . . . . . .
S0 234   8 : 5 5 4 4 4 4 4 2 2 2 3 3 3 3 4 4 . . . . . . . . . 1 2 1 . . . .
S0 234  78 : 3 4 4 4 4 6 3 2 1 2 2 2 3 3 3 3 . . . . . . . . 1 1 1 1 1 1 1 .
S0 234  7  : 3 4 3 3 4 6 3 3 2 3 1 2 4 3 3 3 . . . . . . . . 1 1 1 1 1 1 1 .
S0 234 67  : 2 4 3 3 4 3 3 3 2 2 2 2 2 2 2 2 . . . . . . . . . . . . . . . .
S0 234 678 : 2 4 3 3 4 4 5 4 2 2 2 2 3 2 2 1 . . . . . . . . 1 1 . . . . . .
S0 234 6 8 : 3 4 4 4 3 4 2 3 3 3 3 3 3 3 3 3 . . . . . . . . 1 . . . . . . .
S0 234 6   : 3 4 3 3 3 3 3 4 3 3 4 4 3 3 3 3 . . . . . . . . . . . . . . . .
S0 23456   : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S0 23456 8 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S0 2345678 :                                                                
S0 234567  :                                                                
S0 2345 7  : . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . .
S0 2345 78 : . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . .
S0 2345  8 : . . . . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . .
S0 2345    : . . . . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . .
S0 23 5    : 9 X 8 9 X X X X 7 7 6 4 7 8 X 9 . . . . . . . . 1 1 1 . 1 1 2 1
S0 23 5  8 : 9 9 8 9 X X X X 5 5 5 6 8 7 X 9 . . . . . . . . 1 1 1 1 1 1 2 1
S0 23 5 78 : 9 9 8 8 X X X X 5 6 6 6 8 9 X 8 . . . . . . . . 1 2 1 1 1 1 1 1
S0 23 5 7  : 9 9 8 8 X X X X 5 6 6 6 7 9 X X . . . . . . . . 2 2 2 1 1 2 1 1
S0 23 567  : 8 9 X 8 7 8 8 8 3 5 3 3 6 7 9 7 . . . . . . . . . . 1 . . 1 . .
S0 23 5678 : 7 9 X X 4 4 8 7 3 3 2 2 5 6 X 9 . . . . . . . . . . . . . . . .
S0 23 56 8 : 9 9 7 8 9 7 X X 3 3 3 3 5 5 X X . . . . . . . . . . . . . . . .
S0 23 56   : X 9 8 8 8 8 X X 3 3 2 3 3 3 7 7 . . . . . . . . . . . . . . . .
S0 23  6   : 9 X X 8 X X X X 8 7 6 7 8 X 8 7 1 2 . . . . . . 2 1 1 2 1 1 1 1
S0 23  6 8 : 8 9 9 7 X X 8 9 8 6 6 8 7 8 9 9 1 1 1 . . . . . 2 1 1 2 1 1 1 1
S0 23  678 : 8 X 8 9 9 7 8 8 X 9 6 7 6 7 7 7 1 1 . . . . . . 1 1 2 1 1 1 1 1
S0 23  67  : 8 9 X X 9 8 9 9 X X 7 8 7 8 9 8 1 1 . . . . . . 1 1 1 1 1 1 1 1
S0 23   7  : 9 9 8 8 7 7 9 8 7 7 7 7 X 9 7 8 . . . . . . . 1 1 1 3 1 1 1 1 1
S0 23   78 : 9 9 9 9 7 7 8 7 9 9 6 7 X 9 9 X . . . . . . . 1 1 1 2 2 1 1 2 1
S0 23    8 : X X X X 8 6 8 X 7 6 7 8 X X 8 8 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1
S0 23      : X X X X 8 7 8 X 6 5 7 6 9 8 7 6 1 1 2 2 1 1 1 1 1 1 3 3 1 1 1 2
S0  3      : 1 1 1 1 1 1 1 1 5 4 5 6 4 5 5 4 5 5 5 4 6 4 5 5 5 5 3 2 8 8 4 6
S0  3    8 : 1 1 1 1 1 1 1 1 6 6 5 5 4 5 5 4 5 5 4 5 4 3 4 5 5 5 6 5 9 9 6 7
S0  3   78 : 1 1 1 1 1 1 1 1 7 7 5 7 5 5 6 4 4 4 3 5 5 3 2 5 5 7 5 3 8 8 5 7
S0  3   7  : 1 1 1 1 1 1 1 1 5 6 5 8 5 5 5 4 5 5 3 4 5 1 2 3 5 8 6 3 9 8 5 5
S0  3  67  : 1 1 1 1 2 2 2 2 6 7 8 8 6 5 7 7 7 3 4 4 3 2 1 1 X 9 8 X X 8 6 7
S0  3  678 : 1 1 1 1 2 3 4 3 5 5 X 9 5 6 6 6 6 3 3 4 2 2 1 1 9 8 9 8 X 8 4 4
S0  3  6 8 : 1 1 1 1 3 3 2 2 6 6 6 8 5 5 6 6 4 3 3 3 1 1 2 2 9 7 9 8 X X 6 6
S0  3  6   : 1 1 1 1 3 3 2 2 7 7 7 8 6 6 7 7 5 5 3 5 2 1 1 3 9 8 9 9 X 9 5 7
S0  3 56   : 7 7 3 3 8 8 7 8 X X X X X X X 8 4 4 3 3 1 1 1 1 6 8 6 7 8 8 6 7
S0  3 56 8 : 7 7 3 3 8 X 9 8 X X X X 9 X 9 8 3 4 3 3 . . . 1 9 8 7 8 6 6 6 6
S0  3 5678 : 4 6 X X X X X 9 X 7 6 7 X X X X 1 1 1 . . . . . 5 3 5 4 9 6 X X
S0  3 567  : 3 3 8 6 X X 6 6 X X X X X X X X 2 1 1 1 . . . . 6 7 6 5 6 6 8 7
S0  3 5 7  : 6 6 5 5 8 9 5 6 X X X X 8 X 8 9 2 3 2 3 2 1 2 1 X 7 9 9 X X X X
S0  3 5 78 : 6 6 5 6 X X 6 6 X X X X 8 X 8 9 4 3 2 2 2 1 2 2 8 7 X 7 9 9 7 8
S0  3 5  8 : X X 5 5 5 4 7 8 X 9 X X 9 X 8 X 4 4 3 3 2 2 2 2 X 9 X X 9 9 8 X
S0  3 5    : X X 5 5 4 3 7 7 8 8 9 8 9 X 9 X 3 4 3 3 2 4 1 2 8 5 7 8 8 8 7 8
S0  345    : 9 9 5 6 8 X 8 7 5 5 5 6 8 X 7 6 . . . . . . . . 1 2 2 2 2 2 2 2
S0  345  8 : 9 9 5 4 8 X X 8 8 5 4 5 8 8 7 7 . . . . . . . . 2 3 3 3 2 2 2 2
S0  345 78 : 7 9 8 6 8 X 8 7 5 7 3 5 6 7 9 6 . . . . . . . . 2 2 2 2 2 2 2 2
S0  345 7  : 8 8 7 6 8 X 8 9 3 5 4 4 7 7 7 3 . . . . . . . . 1 1 2 2 2 2 2 2
S0  34567  : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S0  345678 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S0  3456 8 : 2 2 1 2 2 2 3 2 . . . . 2 4 2 2 . . . . . . . . 2 2 1 1 . . . .
S0  3456   : 2 2 2 1 3 4 2 2 . . . . 1 1 2 2 . . . . . . . . . . . . . . . .
S0  34 6   : 7 7 8 8 X X 9 9 8 9 9 X X X X X 1 1 . . . . . . 4 3 5 5 4 4 6 5
S0  34 6 8 : 6 6 9 9 X X 9 9 8 8 9 X X X X X 1 1 . . . . . . 4 4 6 6 6 5 6 7
S0  34 678 : 7 8 9 X X X X X 9 9 9 8 X X X X 1 2 . . . . . . 7 7 5 5 4 5 6 6
S0  34 67  : 9 X 9 9 X X X X 8 X X X X X X 9 1 1 . . . . . . 5 4 3 5 4 5 5 6
S0  34  7  : X X 8 9 8 6 9 X X X X X X X X X 1 1 . . . . . . 6 7 5 4 8 7 8 7
S0  34  78 : X X 9 X 8 6 X X X X X X X 9 X X 1 2 . . . . . . 5 4 5 3 9 9 8 7
S0  34   8 : 6 6 9 X 7 9 7 6 7 9 X 7 6 7 X 8 2 2 1 2 1 1 1 1 6 6 6 5 8 8 9 9
S0  34     : 6 6 9 9 8 7 7 6 5 9 4 6 7 X X 8 2 1 1 1 1 1 1 1 5 5 7 5 X 9 X X
S0   4     : . . . . . . . . 1 1 2 1 2 1 1 1 6 6 5 7 5 5 5 6 4 5 5 4 3 3 2 4
S0   4   8 : . . . . . . . . 1 1 2 1 2 1 1 1 5 5 5 5 5 4 4 4 4 5 7 8 3 3 3 5
S0   4  78 : . . . . . . . . 2 1 2 1 1 1 2 1 X 9 7 5 6 4 6 5 6 6 5 4 6 4 3 5
S0   4  7  : . . . . . . . . 2 1 2 2 1 1 2 1 7 9 6 5 8 5 7 7 5 6 6 6 4 4 2 5
S0   4 67  : . . . . . . . . 4 3 2 3 1 1 1 1 5 5 8 X 6 6 5 5 7 6 6 6 6 5 3 4
S0   4 678 : . . . . . . . . 3 2 2 5 3 5 2 1 6 9 9 7 3 4 4 5 7 7 9 8 8 5 4 4
S0   4 6 8 : . . . . . . . . 2 3 3 3 2 1 1 1 5 6 7 X 6 7 6 6 5 7 6 6 5 6 6 6
S0   4 6   : . . . . . . . . 2 1 2 3 2 1 1 1 6 8 8 8 6 3 5 4 4 7 6 6 5 6 6 6
S0   456   : 1 1 1 1 4 3 2 4 6 4 5 6 6 4 6 5 1 2 3 3 3 1 1 2 3 5 6 5 6 4 8 7
S0   456 8 : 1 1 2 1 6 6 3 4 6 8 8 6 X 7 7 7 1 1 2 2 . . . . 7 4 5 5 5 4 8 6
S0   45678 : 2 2 2 2 . . . . 1 1 1 1 1 1 1 1 1 1 2 2 . . . . 2 2 1 1 2 2 2 2
S0   4567  : 1 1 1 1 4 7 5 2 3 5 6 4 4 5 5 6 1 1 2 2 . . . . 2 2 1 1 3 3 3 3
S0   45 7  : 1 . 1 1 2 2 1 1 7 6 6 8 3 3 3 4 6 4 4 5 4 3 2 2 7 7 8 9 7 7 7 6
S0   45 78 : 1 1 2 2 2 2 1 1 5 7 4 5 4 3 4 5 7 4 6 5 1 2 2 2 8 8 7 X 8 9 9 8
S0   45  8 : . . . . 1 1 1 1 3 5 5 4 4 3 3 2 4 5 4 5 . 2 3 3 7 8 8 X 5 6 8 7
S0   45    : . . . . 1 1 1 1 3 4 3 4 3 4 2 2 6 8 4 9 1 4 3 4 6 6 6 7 6 6 8 8
S0    5    : . . . . . . . . . . . . . . . . 7 6 5 6 . 1 . . 5 5 3 4 2 2 1 1
S0    5  8 : . . . . . . . . . . . . . . . . 7 6 5 6 . 1 . 1 3 3 3 4 2 2 1 1
S0    5 78 : . . . . . . . . . . . . . . . . 8 6 5 7 1 1 1 1 2 2 2 3 3 3 1 1
S0    5 7  : . . . . . . . . . . . . . . . . 8 7 6 7 1 1 1 1 4 3 2 3 2 2 1 1
S0    567  : . . . . . . . . . . 1 1 1 1 . . 7 6 5 4 1 1 2 1 2 2 4 3 1 1 2 2
S0    5678 : . . . . . . . . 1 1 1 1 2 2 1 1 7 7 4 4 . . . . 4 3 3 3 4 4 5 2
S0    56 8 : . . . . . . . . . . . . . . . . 7 7 6 4 1 1 3 2 2 3 4 2 1 1 1 1
S0    56   : . . . . . . . . . . . . . . . . 6 9 4 3 2 3 3 3 2 2 2 2 1 1 1 1
S0     6   : . . . . . . . . . . . . . . . . 3 3 4 4 . . . . 1 1 1 1 . . . .
S0     6 8 : . . . . . . . . . . . . . . . . 3 3 4 4 . . . . 1 1 1 1 . . . .
S0     678 : . . . . . . . . . . . . . . . . 3 3 5 5 . . . . 1 1 1 1 . . . .
S0     67  : . . . . . . . . . . . . . . . . 3 3 5 5 . . . . 1 1 1 1 . . . .
S0      7  : . . . . . . . . . . . . . . . . 3 4 5 4 . . . . 1 1 1 1 . . . .
S0      78 : . . . . . . . . . . . . . . . . 3 4 5 4 . . . . 1 1 1 1 . . . .
S0       8 : . . . . . . . . . . . . . . . . 3 4 5 4 . . . . 1 1 1 1 . . . .
S0         : . . . . . . . . . . . . . . . . 3 4 5 4 . . . . 1 1 1 1 . . . .

Here, a dot means no ships are known, and 'X' means 10 or more ships (or maybe speeds?) are known.

wwei23 · Post by **wwei23** » November 13th, 2020, 4:17 pm

I found a 2c/3 wickstretcher. Here's hopes that a matching 2c/3 wickeater can be found.

Code: Select all

x = 26, y = 39, rule = B246/S013456
11bo2bo$11b4o$9b8o$10b2o2b2o$6b14o$5b2ob2o6b2ob2o$2bob3o2b8o2b3obo$2b
22o$ob3o2b12o2b3obo$b8o8b8o$b2ob2o5b4o5b2ob2o$b2ob3obobob2obobob3ob2o
$b3ob2obob6obob2ob3o$b2ob2ob4o4b4ob2ob2o$bobo2b2o2b6o2b2o2bobo$b4o4b2o
b2ob2o4b4o$bobob4ob6ob4obobo$b5ob4o4b4ob5o$bobob3o2b6o2b3obobo$b5ob4o
b2ob4ob5o$bobob3o2b6o2b3obobo$b5ob4o4b4ob5o$bobob4ob6ob4obobo$b4o4b2o
b2ob2o4b4o$bobo2b2o2b6o2b2o2bobo$b2ob2ob4o4b4ob2ob2o$b3ob2obob6obob2o
b3o$b2ob3obobob2obobob3ob2o$b2ob2o5b4o5b2ob2o$b8o8b8o$ob3o2b12o2b3obo
$2b22o$2bob3o2b8o2b3obo$5b2ob2o6b2ob2o$6b14o$10b2o2b2o$9b8o$11b4o$11b
o2bo!

LaundryPizza03 · Post by **LaundryPizza03** » November 19th, 2020, 10:56 pm

This one, from the same rule as one of Eppsteiin's replicators, came out unexpectedly broad.

Code: Select all

#C completed spaceship: xq5_xenjrd9zef1363p3kss08z1c4pajf0sstr9zy2m7eqoot1kgzy11102w4245fe2
#C Catagolue URL: https://catagolue.hatsya.com/object/xq5_xenjrd9zef1363p3kss08z1c4pajf0sstr9zy2m7eqoot1kgzy11102w4245fe2/b357s3458
#C breadth = 21
#CLL state-numbering golly
x = 18, y = 26, rule = B357/S3458
7bo$5b3o$4b2o2bo$3b2o2bo$3bo2b3o$4bob2o$b3ob2obo$b2o2bobo$b2ob3o3b
o$b7ob4o$b5o4b3o$3o2b3o3b3o$b4obo2bobo$b6o3bo$4b3ob4o$2bo2bo2b2obo
bo$4bo2bo4bo$5b2obob2obo$7b2o4bo$8bo5bo$5b8obo$6b4ob6o$8bobob3obo$
13bob2o$11bo3b3o$15bo!

DB entry:

Code: Select all

:LaundryPizza03, 2020:B357/S3458:B357/S3458:5:-1:2:18:24:4b5o$3b4o$3b2o2bo$3bo2b3o$4b3o$b3ob3o$2ob3obo$2o2bo3b3o$2o4bo2b2obo$6bob3o$o2bob2o3b3o$4b3o4bo$b2o3bob3o$bob2obob5o$3bobo2b4o$7bo4b2o$6b4o$6b3o3bobo$8b5o$6bo2b4ob2o$5b2o7b2o$8bo3bo2b3o$11bob4o$15b2o!

wwei23 · Post by **wwei23** » November 19th, 2020, 11:10 pm

LaundryPizza03 wrote: November 19th, 2020, 10:56 pm This one, from the same rule as one of Eppsteiin's replicators, came out unexpectedly broad.

Wow! Nice work! Any tagalongs yet?

LaundryPizza03 · Post by **LaundryPizza03** » November 19th, 2020, 11:15 pm

wwei23 wrote: November 19th, 2020, 11:10 pm
LaundryPizza03 wrote: November 19th, 2020, 10:56 pm This one, from the same rule as one of Eppsteiin's replicators, came out unexpectedly broad.
Wow! Nice work! Any tagalongs yet?

No, I stopped there to turn my attention to another rule. But it should be possible to retrace my steps or continue from this spaceship.

wwei23 · Post by **wwei23** » November 19th, 2020, 11:23 pm

LaundryPizza03 wrote: November 19th, 2020, 11:15 pm No, I stopped there to turn my attention to another rule. But it should be possible to retrace my steps or continue from this spaceship.

Please send the latest backup file. I might continue the search for you.

LaundryPizza03 · Post by **LaundryPizza03** » November 19th, 2020, 11:27 pm

wwei23 wrote: November 19th, 2020, 11:23 pm
LaundryPizza03 wrote: November 19th, 2020, 11:15 pm No, I stopped there to turn my attention to another rule. But it should be possible to retrace my steps or continue from this spaceship.
Please send the latest backup file. I might continue the search for you.

I can't. .bin is not supported in attachments.

bubblegum · Post by **bubblegum** » November 19th, 2020, 11:27 pm

LaundryPizza03 wrote: November 19th, 2020, 11:27 pm
wwei23 wrote: November 19th, 2020, 11:23 pm
LaundryPizza03 wrote: November 19th, 2020, 11:15 pm No, I stopped there to turn my attention to another rule. But it should be possible to retrace my steps or continue from this spaceship.
Please send the latest backup file. I might continue the search for you. :P
I can't. .bin is not supported in attachments.

Just append .txt to the end.

wwei23 · Post by **wwei23** » November 19th, 2020, 11:28 pm

Or zip it. Though google drive will probably be needed for this.

LaundryPizza03 · Post by **LaundryPizza03** » November 19th, 2020, 11:31 pm

wwei23 wrote: November 19th, 2020, 11:28 pm Or zip it. Though google drive will probably be needed for this.

Okay.

wwei23 · Post by **wwei23** » November 19th, 2020, 11:36 pm

LaundryPizza03 wrote: November 19th, 2020, 11:31 pm
wwei23 wrote: November 19th, 2020, 11:28 pm Or zip it. Though google drive will probably be needed for this.
Okay.

Thank you! I will continue the search when I get a chance to do so.

LaundryPizza03 · Post by **LaundryPizza03** » November 24th, 2020, 2:24 am

I'm using an automated LLS script to catalog distinct oscillators (per the criteria for gliders.db) in OT rules without B0. I am proceeding in order of increasing XYP — the area of the oscillator's bounding box (XY) multiplied by its period (P). At time of writing, all oscillators with XYP ≤ 40 cell-generations have been found. I don't expect to have found any new oscillators at this level, but most are not yet included in oscillators.db.txt.

LaundryPizza03 · Post by **LaundryPizza03** » November 28th, 2020, 1:01 am

This is the smallest p5 oscillator, the only one that fits in a 3*3 box. It was most likely discovered by Apple Bottom in December 2015, in the rule B457/S0123578.

Code: Select all

x = 3, y = 3, rule = B45/S01235
3o2$bo!

DB entry:

Code: Select all

:Apple Bottom, 2015:B45/S01235:B4578/S0123578:5:0:0:3:3:3o2$bo!

wwei23 · Post by **wwei23** » November 28th, 2020, 1:09 am

LaundryPizza03 wrote: November 28th, 2020, 1:01 am This is the smallest p5 oscillator, the only one that fits in a 3*3 box.

You mean in that rule or in any rule at all?

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