User:DroneBetter/qfind results
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Revision as of 14:36, 6 July 2024 by DroneBetter (talk | contribs) (considerably many results found with gfind and qfind! in B36/S245, 2c/4, 2c/6, 2c/8, 4c/8 glide-symmetric completed; in B36/S12, c/6 w19o; in B3578/S24678, 2c/6 and 4c/8 glide-symmetric; also many strengthened lower bounds and 7 additional citations (some things I had found (after the citee), others I had not))
I had long assumed that openmp was simply not yet supported on macOS until I learned that the gcc command in fact uses Clang albeit named misleadingly
as such, having used Homebrew, I am now able to compile qfind, and finally create tables of bounds upon spaceship widths (which I will do here :-)
all links included are to the minimal spaceship found (first outputted, only minimal by bounding box, not population), however (where a table cell is split) the second subrow excludes members of a subset of the symmetry and those comprised of two smaller noninteracting spaceships, choosing the first nontrivial output instead to maximise information content
note that qfind is restricted to orthogonal searches, however it is very fast at them
however, its gfind ancestor of yore is usually used for diagonal and glide-symmetric searches; inputs to find glide-symmetric spaceships are in logical (halved) period rather than actual, this table uses actual for consistency with others
you may add your own results (disproofs for lower bounds and spaceship examples for upper), however (to avoid confusion) I would like others to include citations of forum posts in which they explicitly state their results, so that authorship can be determined without having to go through the page's history; I also sometimes look for old coinciding discoveries that occurred before this table's beginning to cite
no gutter column is included for rules that are not gutter-preserving, even if sometimes spaceships within them happen to be
thank you very dearly to ascendantDreamweaver for using a 48-core computer with 512GB of RAM to which they had access, for increasing logical widths for 2c/5 and 3c/7 to 12 in the first four rules (except for B36/S12, in which 2c/5's are small enough that I managed on my own)
all results labelled as JLS are due to wwei23
non-orthogonal spaceships are of course found with other programs, widths are measured with the scheme of a line of cells parallel to the diirection of movement replacing a column (ie. half-diagonals (1√2-units) for diagonal spaceships, 1√5-units for knightships)[1]
B36/S245 (sqrt replicator rule)
(I like the name a lot for some reason)
ascendantDreamweaver did the searches that led to finding the asymmetrical 2c/5 and 2c/7, as well as obtaining the present best lower bounds for 3c/7, 3c/8 (except for the 3c/8 even, which they found!), 2c/9 asymmetric, 4c/9, 5c/10 asymmetric and 5c/11
| Velocity | Asymmetric | Symmetric | Glide-symmetric | ||
|---|---|---|---|---|---|
| odd | even | odd | even | ||
| (1,0)c/2 | 6 | 13 | 14 | ||
| (1,0)c/3 | 6 | 11[n 1][n 2] | 6 | ||
| 6 | |||||
| (1,1)c/3 | 13[n 3] | 13[n 4] | |||
| (1,0)c/4 | 4 | 9 | 10 | ||
| 12 | |||||
| (2,0)c/4 | 7[n 5] | 13 | 14 | 13 (gfind)[n 6] | 14[n 7] (gfind) |
| (1,1)c/4 | 10[n 8] | 17[n 9] | 12[n 10] | ||
| (1,0)c/5 | 8 | 11[n 11] | 12 | ||
| (2,0)c/5 | 12 | 19 | 20 | ||
| (1,1)c/5 | 12[n 12] | 15[n 13] | |||
| (2,1)c/5 | w ≤ 67 | ||||
| (1,0)c/6 | 9 | 13 | 14 | ||
| (2,0)c/6 | 7[n 14] | 11[n 15] | 10 | 11 (gfind) | 12 (gfind) |
| (3,0)c/6 | 7 | 13 | 14 | ||
| (1,1)c/6 | 9 (gfind) | 15 (gfind) | 16[n 16] | ||
| (2,2)c/6 | 10 (gfind) | 11 (gfind) | 20 (gfind) | ||
| (2,1)c/6 | w ≤ 58[8] | ||||
| (1,0)c/7 | 9[n 17] | 13 | 14 | ||
| (2,0)c/7 | 11[n 18] | 17[n 19] | 16 | ||
| (3,0)c/7 | 12 | 23 | 24 | ||
| (1,1)c/7 | 7 | 7 | |||
| 6 | |||||
| (2,2)c/7 | 8 (gfind) | 15 (gfind) | |||
| (1,0)c/8 | 7[n 20] | 13[n 21] | 14[n 22] | ||
| (2,0)c/8 | 7 | 9[n 23] | 9[n 24] (gfind) |
10[n 25] (gfind) | |
| (3,0)c/8 | 10[n 26] | 19[n 27] | 20 | ||
| (4,0)c/8 | 7 | 13 | 14 | 13 (gfind) | 14 (gfind) |
| (1,1)c/8 | 7 (gfind) | 11 (gfind) | 12[n 16] | ||
| (2,2)c/8 | 6 (gfind) | 11 (gfind) | 10 (gfind) | ||
| (1,0)c/9 | 7[n 28] | 11[n 29] | 12[n 30] | ||
| (2,0)c/9 | 8[n 31] | 15[n 32] | 16[n 33] | ||
| (3,0)c/9 | 7 | 11 | 12 | ||
| (4,0)c/9 | 12 | 23[n 34] | 24[n 35] | ||
| (1,1)c/9 | 4 (gfind) | 7 (gfind) | |||
| (2,2)c/9 | 5 (gfind) | 9 (gfind) | |||
| (3,3)c/9 | 6 (gfind) | 11 (gfind) | |||
| (1,0)c/10 | 6 | 11[n 36] | 12[n 37] | ||
| (2,0)c/10 | 7[n 38] | 11 | 12 | 9 (gfind) | 10 (gfind) |
| (3,0)c/10 | 8 | 13 | 14 | ||
| (4,0)c/10 | 8 | 15 | 16 | 11 (gfind) | 12 (gfind) |
| (5,0)c/10 | 8 | 13 | 14 | ||
| (1,1)c/10 | 5 (gfind) | 7 (gfind) | 8 (gfind) | ||
| (3,3)c/10 | 6 (gfind) | 11 (gfind) | 10 (gfind) | ||
| (1,0)c/11 | 5 | 9 | 10 | ||
| (2,0)c/11 | 6 | 11 | 12[n 39] | ||
| (3,0)c/11 | 7 | 13[n 40] | 12 | ||
| (4,0)c/11 | 9 | 15 | 16[n 41] | ||
| (5,0)c/11 | 10 | 19[n 42] | 20[n 43] | ||
| (1,0)c/12 | 5 | 9 | 10 | ||
| (2,0)c/12 | 5 | 9 | 10 | 7 (gfind) | 6 (gfind) |
| (3,0)c/12 | 5 | 9 | 10 | ||
| (4,0)c/12 | 6 | 9 | 10 | 7 (gfind) | 8 (gfind) |
| (5,0)c/12 | 8 | 15 | 16 | ||
| (6,0)c/12 | 7 | 13 | 14 | 11 (gfind) | 12 (gfind) |
| (2,0)c/14 | 4 | 7 | 8 | 5 (gfind) | 6 (gfind) |
| (4,0)c/14 | 5 | 9 | 12 | 7 (gfind) | 6 (gfind) |
| (6,0)c/14 | 7 | 13 | 14 | 9 (gfind) | 8 (gfind) |
| (7,0)c/14 | 6 < w ≤ 10 | 11 | 12 | ||
| (3,0)c/15 | 4 | 7 | 8 | ||
| (5,0)c/15 | 5 | 9 | 10 | ||
| (4,0)c/16 | 4 | 7 | 8 | 5 (gfind) | 6 (gfind) |
| (6,0)c/16 | 6 | 9 | 10 | 7 (gfind) | 6 |
| (8,0)c/16 | 6 | 11 | 12 | 7 (gfind) | 8 (gfind) |
| (10,0)c/20 | 5 < w ≤ 10 | 9 | 10 | 7 (gfind) | 6 (gfind) |
| (4,0)c/23 | 3 | 5 | 6 < w ≤ 10 | ||
| (26,0)c/52 | w ≤ 17 | ||||
I found the 4c/14 with ikpx2 as a new speed before performing qfind searches up to width 10 that proved its minimality, then found the true-period 2c/7's
| (click above to open LifeViewer) |
the flocks
thank you to Lapintra/TrollDu13EtDu14/Lapin Acharné for finding a surprisingly small 2c/8 in apgsearch,[11] which works in all three rules and has been proven to be minimal-width by ascendantDreamweaver
the dreamweaver also increased c/5 to logical width 11 (except in B36/S12, where my laptop's 10 was sufficient in odd and even, and they have not done asymmetrical yet), 4c/9 to 11 and 2c/8 even (in which none were known previously) to 18, 16 (found), and 18, respectively
B3/S12 (Flock)
all partials for c/2 seem to be single-row irrespective of period, I conjecture there are no c/2's in this rule
| Velocity | Asymmetric | Symmetric | Gutter-preserving | Glide-symmetric | ||
|---|---|---|---|---|---|---|
| odd | even | odd | even | |||
| (1,0)c/3 | 11 20 (JLS)[12] 24 (ikpx2)[13] |
21 39 (JLS)[12] 47 (ikpx2)[13] |
22 40 (JLS)[12] 48 (ikpx2)[13] |
23 < w ≤ 71[14] 41 (JLS)[12] 49 (ikpx2)[13] | ||
| 38 (LLSSS)[15] | ||||||
| (1,0)c/4 | 11 | 17 | 22 | 17 | ||
| 13 (JLS)[13] | ||||||
| (1,1)c/4 | 13 (gfind) | 25 (gfind) | 27 (gfind) | 24 (gfind) < w ≤ 36 | ||
| (1,0)c/5 | 11 < w ≤ 18 | 21 | 24[n 44] | 23 | ||
| (2,0)c/5 | 12 | 25[n 44] | 24 < w ≤ 34 | 25 | ||
| (1,1)c/5 | 11 (gfind) | 21 (gfind) 17 (JLS)[13] |
23 (gfind) | |||
| (1,0)c/6 | 10 | 17 < w ≤ 21 | 18 | 19 | ||
| (2,0)c/6 | 10 | 19 | 20 | 21 | 17 (gfind) | 18 (gfind) |
| (1,1)c/6 | 9 (gfind) | 17 (gfind) | 19 (gfind) | 16 (gfind) < w ≤ 24 | ||
| (1,0)c/7 | 9 | 17[n 45][n 46] | 18[n 47] | 19[n 48] | ||
| (2,0)c/7 | 10 | 19 | 20 | 21 | ||
| (3,0)c/7 | 12 | 23 | 24 | 25 | ||
| (1,1)c/7 | 8 (gfind) | 13 (gfind) | 15 (gfind) | |||
| (1,0)c/8 | 7 | 13 | 14 | 15 | ||
| (2,0)c/8 | 10[n 44] | 17[n 44] | 18 | 17 | 13 (gfind) < w ≤ 17 | 12 (gfind) |
| (1,1)c/8 | 7 (gfind) | 13 (gfind) | 13 (gfind) | 12 (gfind) | ||
| (2,2)c/8 | 8 (gfind) | 15 (gfind) | 15 (gfind) < w ≤ 21 | 14 (gfind) | ||
| (3,0)c/8 | 10 | 19 | 20 | 21 | ||
| (1,0)c/9 | 7 | 11 | 12 | 13 | ||
| (2,0)c/9 | 8 | 13 | 14 | 15 | ||
| (3,0)c/9 | 9 | 17 | 18 | 19 | ||
| (4,0)c/9 | 11 | 21 | 22 | 23 | ||
B36/S12 (HighFlock)
- see also User:AforAmpere/2x2 for B36/S125
| Velocity | Asymmetric | Symmetric | Glide-symmetric | ||
|---|---|---|---|---|---|
| odd | even | odd | even | ||
| (1,0)c/3 | 11 | 21 | 22 | ||
| 14 (JLS)[16] | 29 (JLS) | 30 (JLS) | |||
| (1,0)c/4 | 10 | 15 | 16 | ||
| (1,1)c/4 | 13 (gfind) | 25 (gfind) | 26[n 16] | ||
| (1,0)c/5 | 10[n 49] < w ≤ 14 11 (gfind)[17] |
19 | 20 | ||
| (2,0)c/5 | 11[n 44] | 17[n 50] | 20 | ||
| (1,1)c/5 | 11 (gfind) | 21 (gfind) | |||
| (1,0)c/6 | 10[n 51] | 19 | 18 | ||
| (2,0)c/6 | 10 < w ≤ 15 | 19 | 20 | 17 (gfind) | 18 (gfind) |
| (1,1)c/6 | 9 (gfind) | 15 (gfind) | 16 (gfind) < w ≤ 24 | ||
| (1,0)c/7 | 9 | 17[n 52] | 18[n 53] | ||
| (2,0)c/7 | 10 | 19 | 20[n 54] | ||
| (3,0)c/7 | 12 | 23 | 24 | ||
| (1,0)c/8 | 7 | 11 | 12 | ||
| (2,0)c/8 | 10[n 44] | 17 | 16[n 55] | 13 (gfind) | 12 (gfind) |
| (3,0)c/8 | 10 | 19 | 20 | ||
| (1,1)c/8 | 6 (gfind) | 11 (gfind) | 12 (gfind) | ||
| (2,2)c/8 | 8 (gfind) | 13 (gfind) < w ≤ 21 | 14 (gfind) | ||
| (1,0)c/9 | 6 | 11 | 12 | ||
| (2,0)c/9 | 8 | 13 | 14 | ||
| (3,0)c/9 | 9 | 15 | 16 | ||
| (4,0)c/9 | 11 | 21 | 22 | ||
| (1,0)c/10 | 6 | 11 | 12 | ||
| (2,0)c/10 | 6 | 11 | 12 | 9 (gfind) | 8 (gfind) |
| (3,0)c/10 | 7 | 13 | 14 | ||
| (4,0)c/10 | 8[n 25] | 17[n 25] | 18[n 25] | 13 (gfind) | 8[n 25] |
| 8 < w ≤ 19 | 17 | 18 | |||
| (3,0)c/15 | 4 | 9 | 8 | ||
| (12,0)c/30 | 5 < w ≤ 24 | 7 | 6 | 4 | 5 |
B38/S12 (Pedestrian Flock)
| Velocity | Asymmetric | Symmetric | Gutter-preserving | Glide-symmetric | ||
|---|---|---|---|---|---|---|
| odd | even | odd | even | |||
| (1,0)c/3 | 11 < w ≤ 38[15] 20 (JLS) |
21 27 (JLS) |
22 28 (JLS) |
23 < w ≤ 71[14] 27 (JLS) | ||
| (1,0)c/4 | 11 | 17 | 22 | 17 | ||
| 13 (gfind)[19] | ||||||
| (1,1)c/4 | 13 (gfind) | 25 (gfind) < w ≤ 33 | 27 (gfind) | 24 (gfind) < w ≤ 36 | ||
| (1,0)c/5 | 11 13 (gfind)[20] |
21 | 24[n 44] | 23 | ||
| (2,0)c/5 | 12 | 25[n 44] | 24 < w ≤ 34 | 25 | ||
| (1,1)c/5 | 11 (gfind) | 21 (gfind) | 23 (gfind) | |||
| (1,0)c/6 | 10 | 17 < w ≤ 21 | 18 | 19 | ||
| (2,0)c/6 | 10 | 19 | 20 | 21 | 17 (gfind) | 18 (gfind) |
| (1,1)c/6 | 9 (gfind) | 17 (gfind) | 19 (gfind) | 16 (gfind) < w ≤ 24 | ||
| (1,0)c/7 | 9 | 15[n 46] | 16 | 17 | ||
| (2,0)c/7 | 10 | 19 | 20 | 21 | ||
| (3,0)c/7 | 12 | 23 | 24 | 25 | ||
| (1,1)c/7 | 8 (gfind) | 13 (gfind) | 15 (gfind) | |||
| (1,0)c/8 | 7 | 13 | 14 | 15 | ||
| (2,0)c/8 | 10[n 44] | 17[n 44] | 18 | 17 | 13 < w ≤ 17 | 12 |
| (3,0)c/8 | 10 | 19 | 20 | 21 | ||
| (2,2)c/8 | 7 (gfind) | 13 (gfind) | 15 < w ≤ 21 | 12 (gfind) | ||
| (4,0)c/9 | 11 | 21 | 22 | 23 | ||
B3ai4/S23
thank you to the dreamweaver once more for improving the 2c/5 and 3c/7 bounds (and thereby finding the surprisingly small 2c/5 asymmetrical)
| Velocity | Asymmetric | Odd-symmetric | Even-symmetric |
|---|---|---|---|
| (1,0)c/2 | 12 | 23 | 24 |
| (1,0)c/3 | 10 | 21 | 22 |
| (1,0)c/4 | 10 | 19 | 20 |
| (2,0)c/4 | 11 | 21 | 22 |
| (1,0)c/5 | 10[n 56] | 17 | 18 |
| (2,0)c/5 | 11 | 21 | 22 |
| (1,0)c/6 | 9 | 15 | 16 |
| (2,0)c/6 | 10 < w ≤ 15 | 21 | 20 |
| (1,0)c/7 | 7 | 13 | 14 |
| (2,0)c/7 | 9 | 15 | 16 |
| (3,0)c/7 | 11 | 21 | 22 |
B34kz5e7c8/S23-a4ityz5k (yujh rule :-)
| Velocity | Asymmetric | Odd-symmetric | Even-symmetric | Gutter-preserving |
|---|---|---|---|---|
| (1,0)c/2 | 11 | 11 | 24 | 11 |
| 15 | 24 | |||
| (1,0)c/3 | 11 | 11 | 20 | 11 |
| 11 | 17 | |||
| (1,0)c/4 | 9 | 9 | 16 | 13 |
| (2,0)c/4 | 5 | 11 | 12 | 11 |
| 14 | 13 | |||
| (1,0)c/5 | 8 | 17 | 18 | 17 |
| 20 | 19 | |||
| (2,0)c/5 | 11 | 19 | 20 < w ≤ 26 | 21 |
| (1,0)c/6 | 10 | 17 | 18 | 19 |
| (2,0)c/6 | 10 | 17 | 20 | 19 |
| (3,0)c/6 | 10 | 15 | 20 | 19 |
| (1,0)c/7 | 9 | 15 | 16 | 17 |
| (2,0)c/7 | 9 | 17 | 18 | 19 |
| (3,0)c/7 | 10 | 19 | 20 | 21 |
| (1,0)c/8 | 7 | 13 | 14 | 15 |
| (2,0)c/8 | 8 | 15 | 16 | 17 |
| (3,0)c/8 | 10 | 19 | 20 | 21 |
| (4,0)c/8 | 7 | 11 | 14 | 13 |
| (3,0)c/9 | 8 < w ≤ 17 | 13 | 16 | 15 |
| (5,0)c/10 | 8 | 15 < w ≤ 21 | 16 | 15 |
| (6,0)c/12 | 7 | 11 | 14 | 13 |
| (7,0)c/14 | 6 | 11 < w ≤ 19 | 12 | 13 |
| (11,0)c/22 | 5 | 7 < w ≤ 17 | 8 | 9 |
| (12,0)c/24 | 4 | 7 < w ≤ 21 | 8 < w ≤ 24 | 9 |
| (10,0)c/26 | 4 < w ≤ 7 | 7 | 8 | 9 |
| (click above to open LifeViewer) |
self-complementaries
B35678/S4678 (Holstein)
c/2 reports no partial results are found in any symmetry
c/4 w24e searched by dreamweaver
| Velocity | Asymmetric | Symmetric | Glide-symmetric | ||
|---|---|---|---|---|---|
| odd | even | odd | even | ||
| (1,0)c/2 | 14 28 (gfind) |
27 55 (gfind) |
28 56 (gfind) | ||
| (1,0)c/3 | 13 | 19[n 57] | 20 | ||
| 15 (JLS)[21] | |||||
| (1,1)c/3 | 20 (gfind) | 37 (gfind) | |||
| (1,0)c/4 | 11 | 21[n 58] | 24[n 59] | ||
| (1,1)c/4 | 15 (gfind) | 29 (gfind) | 28 (gfind) | ||
| (1,0)c/5 | 10 | 15 | 14 | ||
| (2,0)c/5 | 12 | 23 | 24 | ||
| (1,1)c/5 | 11 (gfind) | 21 (gfind) | |||
| (1,0)c/6 | 10 | 19 | 20[n 60] | ||
| (2,0)c/6 | 10 | 19 | 20 | 17 (gfind) | 18 (gfind) |
| (1,1)c/6 | 8 (gfind) | 15 (gfind) | 16 (gfind) | ||
| (1,0)c/7 | 9 | 15 | 16 | ||
| (2,0)c/7 | 10 | 19 | 20 | ||
| (3,0)c/7 | 12 | 21 | 22 | ||
| (1,0)c/8 | 8 | 13 | 14 | ||
| (2,0)c/8 | 8 | 15 | 16 | 11 (gfind) | 12 (gfind) |
| (3,0)c/8 | 11 | 19 | 20 | ||
| (1,0)c/9 | 7 | 13 | 14 | ||
| (2,0)c/9 | 9 | 15 | 16 | ||
| (3,0)c/9 | 10 | 17 | 18 | ||
| (4,0)c/9 | 11 | 21 | 22 | ||
B3578/S24678 (Geology)
| Velocity | Asymmetric | Symmetric | Gutter-preserving | Glide-symmetric | ||
|---|---|---|---|---|---|---|
| odd | even | odd | even | |||
| (1,0)c/2 | 7 | 11 | 10 | 11 | ||
| (1,0)c/3 | 7 | 11 | 10 | 13 | ||
| (1,1)c/3 | 9 (gfind) | 17 (gfind) | 19 (gfind) | |||
| (1,0)c/4 | 7 | 11 | 12 | 13 | ||
| (2,0)c/4 | 7[n 61] | 11 | 10 | 11 | 9 (gfind) | 10 (gfind) |
| (1,1)c/4 | 10 (gfind) | 13 (gfind)[n 62] | 17 (gfind) | 12 (gfind) | ||
| (1,0)c/5 | 8 | 11 | 12 | 13[n 25] | ||
| (2,0)c/5 | 10 | 13 | 16 | 19 | ||
| (1,1)c/5 | 8 (gfind) | 13 (gfind) | 17 (gfind) | |||
| (2,1)c/5 | w ≤ 38[23] | |||||
| (1,0)c/6 | 7 | 11 | 10 | 15 | ||
| 15 | ||||||
| (2,0)c/6 | 7 | 11 | 10 | 13 | 9 (gfind) | 10 (gfind) |
| (3,0)c/6 | 7 | 11 | 10 | 13 | ||
| (1,1)c/6 | 7 (gfind) | 11 (gfind) | 13 (gfind) | 12 (gfind) | ||
| (1,0)c/7 | 7 | 11[24] | 12 | 15[25] | ||
| (2,0)c/7 | 8 | 13 | 14[26] | 17 | ||
| (3,0)c/7 | 9 | 17[27] | 18 | 19 | ||
| (1,1)c/7 | 6 (gfind) | 13 (gfind) | 13 (gfind) | |||
| (1,0)c/8 | 6 | 9 | 10 | 11 | ||
| (2,0)c/8 | 6 | 9 | 10 | 13 | 9 (gfind) | 10 (gfind) |
| (3,0)c/8 | 9 | 15 | 16 | 19 | ||
| (4,0)c/8 | 7 | 11 | 10 | 11 | 11 (gfind) | 10 (gfind) |
| (1,0)c/9 | 6 | 9 | 10 | 11 | ||
| (2,0)c/9 | 6 | 11 | 12 | 13 | ||
| (3,0)c/9 | 6 | 9 | 10 | 13 | ||
| (4,0)c/9 | 9 | 17 | 18 | 19 | ||
| (2,0)c/10 | 5 | 9 | 10 | 11 | 9 (gfind) | 8 (gfind) |
| (5,0)c/10 | 7 | 11 | 10 | 13 | ||
| (4,0)c/11 | 7 | 13 | 12 | 13 | ||
| (6,0)c/12 | 6 | 11 | 10 | 13 | 7 (gfind) | 10 (gfind) |
notes
collapsed due to considerable length
- ↑ 84 cells; shortest at width 13 is 127 and at 15 is 56
- ↑ non-monotonic!
- ↑ [2] found a 71-cell version, gfind found a 68-cell
at width 14, the shortest is 72 cells, and at width 15, gfind seems to return the width-13 result - ↑ first found in [2], 106 cells, shortest at width 15 is 84 cells, at 17 is 78, at 19 and 21 is 60, at 23, 25 and 27 is 82
- ↑ 62 cells, smallest at width 8 is 26 cells
- ↑ 100 cells; shortest at width 15 is 66 (or if you'd prefer one which isn't an odd-symmetric with phase-shifted p4 backends, 83)
- ↑ though this is shortest, it is 71 cells, and this spaceship is 58
- ↑ first found in [2], also the first spaceship to be found in a width-10 or 11 gfind search
- ↑ first found in [2], 107 cells, shortest at width 19 and 21 is this 46-cell one
- ↑ 60 cells, shortest at width 14 and 16 is this 62-cell one, at 18 and 20 is this 54-cell one
- ↑ 113 cells, shortest at width 13 is the same, at 15 is 69 cells
- ↑ 373 cells, found and verified minimal-width in [3]
note that the smallest known is 146 cells at width 17[4] - ↑ 184 cells, found in [5] then [6], gfind agrees
gfind reports the same spaceship for width 17
Note the smallest known symmetrical one is a 152-cell width-19 found by May13[7] - ↑ 71 cells, width 8 reduces to 61 cells
- ↑ 171 cells, width 13 reduces to 142 cells, 15 to 107
- ↑ 16.0 16.1 16.2 found by ikpx2, disproof of lower widths by gfind
- ↑ 9*654 partial
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2o$2b4o$5bo$2b2o2bo$2bobo$3b2o$4b2o$3b2obo$3bo3bo$2bobo2bo$2b3obo$4bobo$3bob2o$4bo2$6bobo$5b3o$8bo$2b3ob3o$3b3o$2bo3bo$2b2obo$5bobo$2o2bo2$2b6o$4bob2o$bo$bo$2b3o$5b2o$3b4o$3b2obo$4b3o
$6bo$4b3o$5bo$2bo$b2o$2b2o$o2b2o2$2obo$2bo2bo$bob3obo$4bobo$5b2o$5bo$6bo$4bo$4bo$2b2o$2b2obo$bo2b2o$b3o$5b3o$2ob2obobo$3o2bobo$2b6o$2b2o2b3o$2bo2bobo$o2b3o2bo$o2b3obo$b5o2bo$obo3bo$4b
o2bo$3b3o$4b3o$2b3o$bob2o$2bob2o$2bob2o$2bobobo$b2obo$b2o2b2o$b3o$2bo$2bobo$bo3bo$3bo$3b3o$6bo$5b3o$4b2obo$o2bob2o$b2o$2bobo2$bo$2bo$2b3o$2bobo$3b3o$4b2o$5bo$4bo$5b2o$3b4o$2bob4o$3bo2
b2o$3bobo$3bo$3bob2o$5bo$3b2o$3bobo$5b2o2$6bo2$4bob2o$3bo$4b2o$3bo2bo$2bo2b2o$3b3o$4b2o2$4bo2bo$5b2o$3bo3bo$2b2o$2bo$3bobo$2b4o$2bo2bo$b3obo$bo2bo$3bo2b2o$3bo2bo$4b4o$4bo$5bo$bo2bo$2b
3o$bo2b2o$bo2bobo$2b4o$b3o$6bo$6bo$5bo$5b2o$5bobo$6b3o$7bo$3b4o$b2o$b2o$2bob2o$2bo$o$2o2$2b2o$2bo$3b5o$6bo$6bo$2bo3bo$b2obo$bobobo$2b2obo2$b2obo$4bo$3bo$bo2b2o$3b2o2bo$3b2obo$3bo2$2b2
o$3bo$3bo$b2o$b2o$2bobo2$5b3o$7bo$4b2o$4bo$4bobo2$2b2o3b2o$2bob4o$4bo$4b2o$bo$3o$o2b2o$3bo$bo2$2b3o$3b2o$2bo$2bobo$4bo2$3b2o$3b3o$3bob2o$3bo$4b2o$3b3o$3b3o$2bob2o$5b2o$b3o$b4o$7bo$5bo
b2o$b2o3b3o$obo$obo2bo2bo$7bo$7bo2$5b2o2$6bo$4bo$2b3o$2bobo$2bo4bo$3bo2b2o$3bo$3bo$6bo$5bo$2b3o$2bobob2o$bob2obo$2obob2o$2o3bo$5bo$2b4o$2bob3o$2bo$4bo$2bo$4bobo$bobobo$4b3o$4bo2bo$3b5
o$4bobo$4b2o$5b2o$4b2o$4bo$6bo$3b2o2bo$4b2obo$5o$3bo2bo$4obo$2b4o$bo$3bobo$4b2o$3b3o$3bo3bo$6b2o$6bo$4bo$2b3o$b3o$3bobo$5bo$7bo$5b2o$3b3obo$5b2o$2bobo$2b2o2bo$4bo2$3bobo$5b2o$4b2o$4b3
o$4b2o$4bo2$2bobo$3b2o$b2o$2o2bob2o$o2b2o2bo$bo3bo$6bo$7b2o2$5b3o2$3b2o$2bo$2b3o$3b2obo$3bobo3$3b2o$3b2o2bo$3bo2b3o$2bob3obo$4bo$3b2o$b3o$2b3o3$2b3o$2b3o$2bo3bo$2bobobo$3b2o$bob2o$obo
$4bobo$2bo$3b4o$3b2obo2$4b2o$3bo2bo$4bob2o$4bobo$3b2ob2o$4bob2o$4b2obo$4bo$4bobo$3b3obo$4b3o$3bo$5b2o$4b3o$4bo$bo2b2o$2o4bo$b4o$obo2bo$b2o$2bo3b2o$2b5o$2b2o3bo$5b2o$5bo$7bo$5b2o$5bo$5
bobo$4bob2o$3b3obo$2b3obo$2bob2obo$bob2ob2o$2b4obo$6bo$3bo$4bo$4b2obo$5bobo2$4bobo$5b2o2$4b2o$4bo$3b2o$4bo2$4b2o$3b3obo$3bo2b2o$3bobo$3bobobo$4bo2bo$4bo2bo$5b2o$3b2o2b2o$4b2o2bo$4bob2
o$5b3o$5b3o$5b2o$6bobo$3b2ob2o2$6b2o$5b4o$6b2o$5b3o$3b2obo$b3obo$b4o$2b2o2bo$2bo$bo4bo$4b3o3$3b3o2$3bo$2b2o$b2obo$bo2bobo$2b3obo2$2bob3o$4b2o$5b2o3$2bo$2ob2o$bobo$o3bo$bobo$3bo$2bobo$
2b4o$3b5o$3bo3b2o$5bobo$6bobo$6bo$3b2o$3bobo$2b3obo$4b2obo$b4ob2o2$4bo$2bob3o$2b6o$2b2obobo$3b3ob2o$3b2o2bo$2bo4bo$2b2o$bo2b2o$2b2obo$bo2$2bo$2b4o$bo3bo$4b2o$4b3o$5b2o$5b2o$6bo$2bob2o
$3b2obo$3bob2o$3b2o$3b2o$2b2o$3bo$2bobo$bo$2b2o$3bo$bo$2bo$2b4o$2bo2bo$b2ob2o$bo2bo$3o2b2o$bobo$bo2b3o$b4o$ob3o$3o2b2o$b2ob2o$2b2o2bo$2b2o$2ob3o$2bob2o$2bob2o$3b4o$4bo$2b3o2$2b4o$3bo$
3bob3o$3b2o3bo$5bobo$6bo$3b2o2bo$2bobo$3bo2$4b2o$3b2o$3b2o$3bo$bo2bo$bo2bo$3o$bo$ob4o$4b2o$b3obo$3b2o$2bob2o$3b3o$2bo3bo$2b4o$4b3o$bo$o2bo$ob2o$4b2o$5bo$2b2o$5b3o$4bo2bo$3b4o$bo2bo$b3
o$2o2b2o$2o2bo$3bo2bo$b2obo$o2bo$5b2o$6b2o$2b4o$3bobo$4bo$3bo$5bo$5b2o$5b2o$5bob2o$7b2o$6bo$6bo2$3bob2o$3bo3bo$5o2b2o$bo2b2o$o2bobo$2b3o$3bo3bo$3bobo$3b2o$3b2obo2$b4obo$b2obo$3bo$3bo$
4bobo$4b2ob2o2$3b3obo$3bob3o$5b2o$4b3o$4b3o$3b2ob2o$6bo$4b3o$5bo$3b3o$3b3obo$4b3obo$4bobo$2bob3o$3bobo$3b4o$2bob2o$2b6o$2b2o2bo$7b2o$3bo3bo$2bob2obo$3bob2obo$3b2ob3o$5b2o$4b2o$2b2o$3b
ob2o$3o2b2o$b4ob2o$2obob2o$2b2o$2bo2bo$5o$bob5o$bob5o$bobobo$ob4o$4bobo$b5o$b2o2bo$3bobobo$5bobo$4bob2o$2bobobo$2b2o$2b2o$bo4b2o$4b2o2bo$3b5o$2b2obobo$2bobo2b2o$o5b3o$3b2obo$2ob2o2bo! - ↑ found by the dreamweaver, who specified that it is not guaranteedly minimal-length for a width-11 since the search split and only one branch was necessary to search to find it, but shows that 11 is the minimum
shares frontend with the longest width-10 (10*65) partial
5bobo$5b3o$4bob2o$2b4o2bo$2b4o$6bobo$9bo$5bobo$4b4o$3bobobo$3b2o$5bobo$5b4o$4bobo$4b2obobo$4b2o$4b5o$3b2o$4bo3bo$2b2ob4o$2bobob2o$3bobobo$3b2o$2b2
obo$b2o2b2o$7bo$3bo$2bo3b3o$2bob2obobo$2bobobob2o$4b2o2bo$6b4o$4b2obo$4b3o$5b2o2$3b2obo$2bo3b3o$3b2obobo$3b2obobo$3b2obobo$o2b5o$7b2o$2b3o2bo$2bo4
bo$3bo3bo$3b2o2b2o$2bo2b3obo$b2obo$b2obo$o4bo$b2ob2o$3b5o$b4obo$bo2bo2bo$9o$bob4obo$2bo2bo2b2o$2bo2bobo$5bo3bo$2bobo$bobo$b3o2b4o$2obobob2o$3b4obo! - ↑ was first found by lordlouckster in [9] then noted minimal in [10]
- ↑ 7*39 partial
2b4o$2b4o3$4b2o$4bo2$b3o$bobo$3b3o$2b2obo$2bobo2$bobobo$2b2o2$bobo$obobo$bobo$o$3bo$3b2o$4bo
$3b3o$o3bo$bobobo$3o3bo$2bo$bo2b2o$b2o2$b2ob2o$3o3bo$bob3o$bob2o$bobob2o$b2ob2o$2bo2bo$3b2o! - ↑ 13*143 partial
2bo7bo$b3obobob3o$ob4ob4obo$5bobo$4b2ob2o$4bo3bo$5bobo$4b5o$2b3o3b3o$3bobobobo$3b2obob2o$bob2o3b2obo$4bo3bo$4bo3bo$3b2o3b2o$5bobo$3b2o3b2o$2b2o5b2o$3
b2obob2o$2bo2b3o2bo$4b2ob2o3$3b2obob2o$4bo3bo$3bobobobo$3b2o3b2o$4bobobo$3bo5bo$4bo3bo$4b5o2$5b3o$4b2ob2o$4b2ob2o$4b2ob2o$2bob2ob2obo$2bo3bo3bo$3bobo
bobo$2b2o5b2o$2b2ob3ob2o$b4obob4o$3b7o$bo2bobobo2bo$b5ob5o$2b3o3b3o$3b2o3b2o$bob2o3b2obo$2bobo3bobo$6bo$4bobobo$3bob3obo$3bo2bo2bo$2bobo3bobo$2bobobo
bobo$bo9bo$o2b2o3b2o2bo$2b2obobob2o$3b2o3b2o3$2b2o5b2o$bob2o3b2obo$2b3o3b3o$b2ob2ob2ob2o$4b5o$5b3o$3bobobobo$b2o3bo3b2o$b11o$bo3bobo3bo2$4bo3bo$4bo3b
o$3bo2bo2bo$3bo5bo$4bobobo$2b2obobob2o$2bobo3bobo$b3obobob3o$3obobobob3o$bo3b3o3bo$2bobo3bobo2$3bo5bo$4b2ob2o$6bo2$2b3o3b3o$2b2o2bo2b2o$b4obob4o$bo3b
obo3bo$3b3ob3o$4bo3bo$3b2obob2o$6bo$3bobobobo$5bobo$3bo5bo$4b2ob2o$2b9o$b3o5b3o$3bo5bo2$5bobo$3ob5ob3o$b2o7b2o$bob2o3b2obo$2o9b2o$b4obob4o$6bo$3bo5bo
$5b3o$b2o3bo3b2o$ob4ob4obo$4ob3ob4o$bo3bobo3bo$2b3obob3o$6bo$5bobo$3b3ob3o$2bobo3bobo$b2obo3bob2o$5bobo$2b3o3b3o$4bobobo$3b2o3b2o$2bobo3bobo$2bob2ob2
obo$2obo2bo2bob2o$b2obobobob2o$2obo2bo2bob2o$2bo2b3o2bo$b4o3b4o$4bo3bo$bo2b5o2bo$b2o2bobo2b2o$2b9o$3bo5bo$5b3o$obobo3bobobo$2obobobobob2o$bobob3obobo! - ↑ 14*194 partial
6b2o$5bo2bo$4bo4bo$6b2o$6b2o2$3b3o2b3o$4b6o$4bob2obo$3b2o4b2o$3b2ob2ob2o$5bo2bo$3b3o2b3o$3b3o2b3o$5bo2bo$4b2o2b2o2$3b2ob2ob2o$6b2o$5b4o$5b4o2$4bo4
bo$3bo2b2o2bo$4bo4bo$4bo4bo$6b2o$5b4o2$4bo4bo$2b2obo2bob2o$2bob2o2b2obo$5bo2bo$2b3ob2ob3o$2b2o2b2o2b2o$3b2ob2ob2o$b2o8b2o$5b4o$3b8o$3bobo2bobo$3b2
o4b2o$3b8o$2bo8bo$2b3o4b3o$4bob2obo$4b2o2b2o$4b2o2b2o$4b2o2b2o$6b2o$5bo2bo$4bo4bo$4bo4bo$3bo6bo$5b4o$4b6o2$3bo2b2o2bo$4bob2obo$4b2o2b2o$3bobo2bobo
$3b2o4b2o$2b2o2b2o2b2o$4bo4bo$3b3o2b3o$o2bo6bo2bo$b3o2b2o2b3o$bob2ob2ob2obo$6b2o$4bo4bo$2bo8bo$2b4o2b4o$b2o2bo2bo2b2o$3b3o2b3o$3bobo2bobo$2b3ob2ob
3o$4bob2obo$4bo4bo2$6b2o$4bo4bo$3b2o4b2o$3b2ob2ob2o$5b4o$5b4o$4b2o2b2o$2bobo4bobo$6b2o$3bo2b2o2bo$4bob2obo$4bo4bo$4bo4bo$6b2o2$5bo2bo$3b3o2b3o$2b3
ob2ob3o$2bobo4bobo$4b6o$4b6o$4bo4bo$4bo4bo2$3bo6bo$bob2ob2ob2obo$3b3o2b3o$bo3b4o3bo$2bobo4bobo$2bo8bo$6b2o$5bo2bo$2bo3b2o3bo$3b8o$4b2o2b2o$4bob2ob
o2$4b2o2b2o$4b2o2b2o$4b2o2b2o2$2bob2o2b2obo$3bo6bo$2bobob2obobo$6b2o$3b2o4b2o$3b3o2b3o$3b2o4b2o$4b2o2b2o$5b4o$3bob4obo$4b2o2b2o$2b3o4b3o$3b3o2b3o$
bob3o2b3obo$2bo2bo2bo2bo$3bob4obo$3b8o$6b2o$3bo6bo$6b2o$2b10o$3b2ob2ob2o$2bo3b2o3bo$4b6o$3b2o4b2o$4bo4bo$3b2o4b2o$3b2o4b2o$3bob4obo$3bobo2bobo$3b2
o4b2o$3b2ob2ob2o$3b2ob2ob2o$2b2ob4ob2o$2b3o4b3o$3bob4obo$2bobob2obobo$b2o8b2o$2bobo4bobo2$2bobob2obobo$b2o8b2o$2b3o4b3o$2b2o6b2o2$3bob4obo$2bo2b4o
2bo$2b2o6b2o$b2o8b2o$2bob2o2b2obo$3bo6bo$b4o4b4o$2b2o2b2o2b2o$o3b6o3bo$o2b2o4b2o2bo$bo3b4o3bo$2o4b2o4b2o$bobo2b2o2bobo$4bob2obo$3b2ob2ob2o$4b2o2b2
o$2b2o6b2o$3b2ob2ob2o$bobobo2bobobo$obo2bo2bo2bobo$b3o2b2o2b3o$o2bo6bo2bo$2bo2bo2bo2bo$3b3o2b3o$bo2b6o2bo$b3o6b3o$b2o8b2o$2b2ob4ob2o$4b6o$3bob4obo! - ↑ 99 cells
same result for width 11
smallest at width 13 seems to be 109 cells - ↑ 96 cells, less short but smaller is 90 cells
- ↑ 25.0 25.1 25.2 25.3 25.4 25.5 unique thinnest
- ↑ 10*30 partial
5b2o$4b3o$7b2o$4b3obo$4bo3bo$5b3o$7bo$6bo$3bo3b2o$3b2o$3b6o$4bobob2o$5b5o$4bo$5bo$3b5o$2bobo3bo$5b2
o2bo$b2o2bo$2b2o2bo$obobo$3obobo$b2obob2o$o2b6o$b2ob2o2b2o$2bo4b2o$bob3ob2o$2b2o3bobo$3b3o3bo$ob2o! - ↑ 19*86 partial
b4o9b4o$2b2o11b2o$2bobo9bobo$b5o7b5o$4bo9bo$b2o13b2o$bobo11bobo$2bob2o7b2obo$3b
obo2b3o2bobo$3b3o7b3o$3b2o9b2o$3bob2o5b2obo$8b3o$9bo$7bobobo$5b2o2bo2b2o$5bo2b3
o2bo$4bo2bo3bo2bo$4bob2o3b2obo$3bob2ob3ob2obo$6b7o$8bobo$3bo2bob3obo2bo$3b4obob
ob4o$4b3o5b3o$4b2ob2ob2ob2o$6b2o3b2o$6b2o3b2o$6b3ob3o$5bobo3bobo$4bo2b5o2bo$4b2
o7b2o$3b3o7b3o$4b5ob5o$6bob3obo$4bo2bobobo2bo$4b2obobobob2o$3bobo2b3o2bobo$4b4o
bob4o$4b2obo3bob2o$3b2o2bo3bo2b2o$3bob3o3b3obo$4b2o7b2o$4b2ob2ob2ob2o$6b2o3b2o$
4b2o2bobo2b2o$4bo9bo$4bobo5bobo$5b2o5b2o$3b3o2bobo2b3o$2bo2b2o5b2o2bo$3bo3bo3bo
3bo$2o3bo7bo3b2o$bo3b2o5b2o3bo$2ob3o7b3ob2o$bob3o3bo3b3obo$b3obobobobobob3o$2bo
4bobobo4bo$2b4o3bo3b4o$2b3o9b3o$4b5ob5o$2b2o3bo3bo3b2o$2bo2b4ob4o2bo$bobob2obob
ob2obobo$3bobob5obobo$bobo2bobobobo2bobo$o2bobo2bobo2bobo2bo$b2o2bo3bo3bo2b2o$2
o4bobobobo4b2o$ob2o2b2obob2o2b2obo$6b7o$4b3o5b3o$4b2o7b2o$4b5ob5o$2bo3bobobobo3
bo$4bo2b5o2bo$b4obo5bob4o$4bo2bobobo2bo$bo3bobo3bobo3bo$b2obobob3obobob2o$b2obo
b3ob3obob2o$b2o2b3o3b3o2b2o$2bob2o3bo3b2obo$4b2o2b3o2b2o$b3o11b3o$3bo3bo3bo3bo! - ↑ 7*51 partial
3b2o$3bo2bo$bo2bo$2b3obo$2o2b2o$o$b2o$bo$bob2o$2bobo$4bo2$3bobo$3b3o$4bo$3b2o$2b2o$2bo$bo2$bobo$o3bo$bobobo$o3bo$2b2o$2b2o$2b
o$4b2o$b3ob2o$2b3obo$2b3o$bobobo$2bo$2b3o$2b3o$4bo$4bo$3bobo$b2o$ob2o$3bo$4b2o$4ob2o$7o$2bo$2bob2o$2bo$2b5o$2b5o$b2ob2o$o4bo! - ↑ 11*61 partial
3b2ob2o$2b3ob3o$2b3ob3o$2b2o3b2o$2bobobobo$3bobobo$3b2ob2o$3b5o$3bo3bo$b3obob3o$b3o3b3o$2bo5bo$2b2o3b2o$bobo3bobo2$4b3o$4bobo$4b3o$4bobo$4bobo$4b3o
$5bo$5bo$2bob3obo$2b2o3b2o$2b7o$5bo$4b3o$3bobobo$4b3o$2b2obob2o$2bobobobo$4bobo$2bob3obo$3b5o$2bob3obo$b2o5b2o$4bobo$2b2o3b2o$4b3o$2b2obob2o$bobo3b
obo$2bobobobo$b3o3b3o$3b2ob2o$4bobo$5bo2$b3obob3o$b3o3b3o$4bobo$3b2ob2o$bo7bo$o3bobo3bo$b4ob4o$4b3o$2bobobobo$5bo$bo2b3o2bo$2obobobob2o$b2obobob2o! - ↑ 12*91 partial
5b2o$5b2o$4bo2bo$5b2o$4b4o$3bo4bo$4bo2bo$3b6o2$2b2o4b2o$2bobo2bobo$b2ob4ob2o$b2o6b2o$b2o6b2o$3b6o$3b6o2$5b2o$3bo4bo$3bo4bo$2bobo2
bobo$2bobo2bobo$5b2o$3b2o2b2o$2o8b2o$b3o4b3o$b2o6b2o$2o3b2o3b2o$2b8o$bo8bo2$4b4o$5b2o$4b4o2$4bo2bo$4b4o$3bob2obo$2bo2b2o2bo$b2o2b
2o2b2o$5b2o$3b2o2b2o$2bobo2bobo2$2b2o4b2o$3b6o$b2ob4ob2o$2bobo2bobo$bob2o2b2obo$4b4o3$2bob4obo$bob6obo$b2ob4ob2o$b3ob2ob3o$3b2o2b
2o$b4o2b4o$3b2o2b2o$4bo2bo$4bo2bo$b4o2b4o$bo8bo2$o4b2o4bo$2b8o$3b6o$2o2b4o2b2o$o10bo$b3o4b3o$b3o4b3o$5b2o$2b8o$2b2o4b2o$3b2o2b2o$
5o2b5o$ob2o4b2obo$3b6o$2bobo2bobo$3b2o2b2o$4bo2bo$2b2o4b2o$3b2o2b2o$4bo2bo2$3bob2obo$2b2o4b2o$4bo2bo$2bobo2bobo$4ob2ob4o$o4b2o4bo! - ↑ 8*51 partial
3b2o$3b2o$2bo2bo$2b4o3$b2o2b2o$2bo2bo$ob4obo2$bo4bo$b6o$bo4bo$2b4o$2b4o$2b4o2$3b2o$3b3o$b2o3bo$2bobobo$3bob2o$2b2obo$2bob2o$4b2o$2bo2bo2$2b
5o$bob2o$2ob2o$2bobo$2b4o2$b2o2b2o$bo2b3o$2bobo$3bo3bo$bo2b2obo$bob3o$2b3o$3b2o$2bo$b3o$4b2o$2bo2bo$2b2ob2o$2b3ob2o$2bob4o$bo3bo$b3obo$6bo! - ↑ 15*168 partial
2b2o7b2o$bo2bo5bo2bo$o4bo3bo4bo2$5bo3bo$4b3ob3o$4b3ob3o$2bo9bo$2b4o3b4o$3b2ob3ob2o$6b3o$5bobob
o$5b5o$4b2o3b2o$4b2o3b2o$4b2o3b2o$4bo5bo$6b3o$3bobo3bobo$4b2o3b2o$3bo7bo$4bob3obo$5b5o$6bobo2$
6bobo$5b2ob2o$2o3b2ob2o3b2o$2b2obo3bob2o$3ob7ob3o$2b11o$2bo2b2ob2o2bo$5bobobo$6bobo2$5b2ob2o2$
7bo$6b3o$4b7o$5b2ob2o$5b2ob2o$5b2ob2o$5bo3bo$4bobobobo$4bo2bo2bo$7bo$7bo$4bob3obo$3b2o5b2o$6b3
o$7bo$b3o2b3o2b3o$bo11bo$3b9o$b2ob2obob2ob2o$b2obobobobob2o$2bo2bo3bo2bo$3bo3bo3bo$4b7o$3b2ob3
ob2o$b2obo5bob2o$2b2ob5ob2o$bobo2b3o2bobo$5b5o$5bobobo$2bob7obo$2bo2b2ob2o2bo$3b3o3b3o2$3b2o5b
2o$5bobobo$5b2ob2o$3b3o3b3o$3bo7bo$3bo7bo$4b2o3b2o$4b2o3b2o$3bo3bo3bo$b2o2bo3bo2b2o$2bobo5bobo
$2bobo2bo2bobo$4bo5bo$2b2o7b2o$3bo7bo$4b2obob2o$3bob2ob2obo$2bo2bobobo2bo$2bo9bo$bobo3bo3bobo$
b3o7b3o$bobo3bo3bobo$5bo3bo$4bob3obo$5bo3bo$6bobo$2b3o5b3o$2b2obo3bob2o$bo11bo$3bobo3bobo$4b2o
3b2o$3b4ob4o$2b3obobob3o$2b2obo3bob2o$2bo9bo$6bobo$4b3ob3o$2b2ob2ob2ob2o$2b3o2bo2b3o$b6ob6o$bo
bo2b3o2bobo$2bo9bo$2bo9bo$bobo7bobo$o13bo$bob2o5b2obo$3bo7bo$4o7b4o$2bo9bo$2bob2o3b2obo$bob2o5
b2obo$2bo9bo$2bobobobobobo$3bobo3bobo$3b9o2$2bob3ob3obo$2bo4bo4bo$3bo7bo$2o11b2o$ob4o3b4obo$bo
11bo$2b11o$bo3b2ob2o3bo$2b4o3b4o$2bo2bo3bo2bo$b2o3bobo3b2o$bo2bobobobo2bo$2bobo5bobo$b3o7b3o$3
b3o3b3o$5b2ob2o$3bobo3bobo$2b2o7b2o$3b2obobob2o$2bob7obo$2b2o2b3o2b2o$4b2o3b2o$2bo3bobo3bo$3b2
o5b2o$2bob2obob2obo$2bob7obo$2b2o7b2o$bo11bo$5bo3bo$6b3o$2b3obobob3o$3b2o5b2o$b2obo5bob2o$b2o2
b5o2b2o$b2o2bo3bo2b2o2$3obo5bob3o$b4o2bo2b4o$o3b2o3b2o3bo$o3bobobobo3bo$3bo2bobo2bo$4ob5ob4o!
13*71 partial
b3o5b3o$o2bobobobo2bo$obobo3bobobo$b2obo3bob2o$3b3ob3o$3b3ob3o2$5b3o$4b2ob2o$4b5o$4bo3bo$4bobobo$5bobo$2bob2ob2obo$2bo2bobo2bo$2bob
2ob2obo$2bobo3bobo$3b2o3b2o$2b9o$bo2b5o2bo$2b2o5b2o$bo2bo3bo2bo$bob2o3b2obo$bobo5bobo$3obo3bob3o$bobo2bo2bobo$2b2o2bo2b2o$2b2obobob
2o$2bo2b3o2bo$4bo3bo$4b2ob2o$b3o5b3o$2b2o5b2o$2b2o5b2o$2bo7bo$4bo3bo$3b3ob3o$4bo3bo$3bo2bo2bo$5bobo2$3b2o3b2o$2b4ob4o$4b5o$3b3ob3o$
b3o5b3o$2bo2b3o2bo$b2o3bo3b2o$2bob2ob2obo$3b2obob2o$2bo3bo3bo$2b2o5b2o$bobob3obobo$2b2o2bo2b2o$b3o2bo2b3o$4b5o$2b4ob4o$b2ob5ob2o$b2
ob2ob2ob2o$o2bobobobo2bo$2b2o2bo2b2o$b2obo3bob2o$b3o5b3o$bobo2bo2bobo$3bo2bo2bo$2b4ob4o$bo9bo$bo9bo$b2o2bobo2b2o$2o4bo4b2o$4b2ob2o! - ↑ 16*286 partial
3b2o6b2o$2b4o4b4o$3b2o6b2o$2bo2bo4bo2bo$3b2o6b2o$7b2o$5b6o$5b6o$4bo6bo$4bo6bo$2bob3o2b3obo$b4o6b4o$3b
3o4b3o$3b2o2b2o2b2o$b2o2b6o2b2o$3b2o6b2o$2bo3bo2bo3bo$4bo2b2o2bo$3bo8bo$2b2obob2obob2o$bob4o2b4obo$ob
2o8b2obo$bo12bo$4bo6bo$3b3o4b3o$2bob3o2b3obo$4bobo2bobo$6bo2bo$5bo4bo$5bo4bo$2bo2bob2obo2bo$bob4o2b4o
bo$bo2bobo2bobo2bo$4bo6bo$3b2obo2bob2o$5bo4bo2$4b3o2b3o$3bo8bo$2bo10bo$2bo2bo4bo2bo$2bo2bo4bo2bo$2bob
o6bobo$5bob2obo$5b6o$6bo2bo$6bo2bo$6b4o$6b4o$6b4o2$5b2o2b2o2$5bob2obo$4b2o4b2o$3b4o2b4o$2o4b4o4b2o$4o
bob2obob4o$2bobo2b2o2bobo$6b4o$2bob2ob2ob2obo$3bo3b2o3bo$3bo3b2o3bo$3bo2b4o2bo$2b2o8b2o$2bob2o4b2obo$
3bobob2obobo$3bo3b2o3bo$3bo2bo2bo2bo$7b2o$6bo2bo$7b2o$6b4o$6bo2bo$4b2o4b2o$7b2o$6bo2bo2$6bo2bo$7b2o$4
b2ob2ob2o$4b8o$3b3ob2ob3o$3bo8bo$5b6o$4bob4obo$7b2o$4b2o4b2o$6bo2bo$6b4o$5bo4bo$5b6o$5b6o$4bo6bo$4b2o
4b2o$3bobo4bobo$3b3o4b3o$4bo6bo$2b2o2bo2bo2b2o$bo12bo$b2o10b2o2$3b3o4b3o$3b3o4b3o$3b3o4b3o$3b2o6b2o$2
b3ob4ob3o$3b10o$4b2o4b2o$4bob4obo$5b6o$2bo2b6o2bo$b4o6b4o$2bobobo2bobobo$2bob2o4b2obo$2o3bob2obo3b2o$
3obobo2bobob3o$3bobo4bobo$3bo8bo$3b2o6b2o$3b3o4b3o$4b2ob2ob2o$4bob4obo2$4bobo2bobo$2b3ob4ob3o$2b2ob2o
2b2ob2o$3bo8bo$2b2ob2o2b2ob2o$5b2o2b2o$4bo2b2o2bo$4b2ob2ob2o$2bobo2b2o2bobo$2bobob4obobo$2b2obob2obob
2o$6b4o$b3ob6ob3o$3bobob2obobo$4bobo2bobo$4bo6bo$4bobo2bobo$5b2o2b2o$6b4o2$6b4o2$5bob2obo$5b2o2b2o$5b
2o2b2o$7b2o$4bo6bo$6b4o$6b4o$7b2o$7b2o$4bo6bo$4bo6bo$7b2o$5b2o2b2o$5bo4bo$3b10o$3b10o$4bo2b2o2bo$5b2o
2b2o$5b2o2b2o$5b2o2b2o2$4b2o4b2o2$3bo8bo$4b3o2b3o$2b2obo4bob2o$3bo2bo2bo2bo2$2bobo6bobo$2b4o4b4o$3bob
o4bobo$2bo2bo4bo2bo$2bo2bo4bo2bo$2bobo6bobo$3bo8bo$3b2o6b2o$5bo4bo$2b4o4b4o$2b2o8b2o$3b2o6b2o$2bobo6b
obo$5bo4bo$4b3o2b3o$3b3o4b3o$2b3o2b2o2b3o$3b2o6b2o$4bo6bo$3bobob2obobo$3bobob2obobo$b14o$5bob2obo$bob
obo4bobobo$bob3o4b3obo$obob2o4b2obobo$3b10o$3bo2b4o2bo$4bobo2bobo$3bob6obo$5bob2obo$7b2o$6bo2bo$3bo3b
2o3bo$3b3ob2ob3o$3b3o4b3o$5bo4bo$b2o10b2o$b2o10b2o$3b3o4b3o$3b2o6b2o$3bobo4bobo$5bo4bo$2bob8obo$b4ob4
ob4o$4bo6bo$7b2o$5bo4bo$2bob3o2b3obo$3bo3b2o3bo$3bo8bo$2bob8obo$2b3obo2bob3o$2b3ob4ob3o$5b6o$4b2o4b2o
$6b4o$3b2obo2bob2o$4bo2b2o2bo$7b2o$2b3o2b2o2b3o$2bobobo2bobobo$2b4ob2ob4o$2b3o2b2o2b3o$2b3o2b2o2b3o$b
ob3o4b3obo$3b3o4b3o$7b2o2$4b2ob2ob2o$2b5o2b5o$2bo2bo4bo2bo$3b2o6b2o$2bobob4obobo$3b3o4b3o$4bo6bo$5b2o
2b2o$5b2o2b2o$3bobob2obobo$3b2o2b2o2b2o$3b2ob4ob2o$3bobob2obobo$b4o6b4o$2b2o2bo2bo2b2o$b2obobo2bobob2
o$2bo2bob2obo2bo$2bob2ob2ob2obo$3bo8bo$6b4o$4bo2b2o2bo$3b2o2b2o2b2o$2bob8obo$4obo4bob4o$4bo6bo$bob3o4
b3obo$2bob2ob2ob2obo$5bob2obo$4bobo2bobo$3bo8bo$2b3o2b2o2b3o$3b2ob4ob2o$2b5o2b5o$b4ob4ob4o$b3o2bo2bo2
b3o$3b3o4b3o$2b3obo2bob3o$3bobo4bobo$3bobob2obobo$bo2bobo2bobo2bo$2b2o3b2o3b2o$o6b2o6bo$b2o3bo2bo3b2o!
14*98 partial
6b2o$5b4o3$5bo2bo$4bo4bo$4bo4bo$6b2o$4b2o2b2o$3bo2b2o2bo$4bob2obo$4b2o2b2o$4b2o2b2o$5bo2bo2$4b2o2b2o$5bo2bo$4b2o2b2o$3bo6bo$3bob4obo$3b2o4b2o$
6b2o$4b6o$4bo4bo$2b3ob2ob3o$3bob4obo$2b3o4b3o$b4o4b4o$2b2o6b2o$2bo8bo$obobo4bobobo$3b3o2b3o$2bo3b2o3bo$4b6o$3bo6bo$3b2o4b2o$4b2o2b2o2$4bob2obo
$5b4o$4b6o$6b2o$2bo3b2o3bo$2b3o4b3o$bo3bo2bo3bo$bo2b2o2b2o2bo$2o10b2o$b2o3b2o3b2o$3bo6bo$3b8o$5bo2bo$4bob2obo$3bo2b2o2bo$2bob2o2b2obo$2b3ob2ob
3o$3bo6bo$2b4o2b4o$4b2o2b2o$2bobob2obobo$b3o2b2o2b3o2$2bobo4bobo$4b2o2b2o$4bob2obo$4bo4bo$5bo2bo$3bob4obo$3bo6bo2$2bo2bo2bo2bo$6b2o$2b2obo2bob
2o$3bob4obo$o2bob4obo2bo$b2ob2o2b2ob2o$4b2o2b2o$4b6o$2b3ob2ob3o$b3obo2bob3o$2b2obo2bob2o$b2obo4bob2o$3bobo2bobo$bobobo2bobobo$5bo2bo$2o2b6o2b2
o$3bobo2bobo$5bo2bo$bob3o2b3obo$b2o3b2o3b2o$o4bo2bo4bo$3o2b4o2b3o$2bo3b2o3bo$3b2o4b2o$6b2o$3b2ob2ob2o$bo4b2o4bo$2o2bob2obo2b2o$o2bo2b2o2bo2bo! - ↑ 23*60 partial
10bobo$8b2obob2o$7b2obobob2o$6bob2obob2obo$6bo3bobo3bo$5b3o2bobo2b3o$5bob2obobob2obo$5b4o5b4o$8bob3obo$4bob2
o3bo3b2obo$7bobobobobo$3bob4ob3ob4obo$3b2o3bo5bo3b2o$2b3o3b3ob3o3b3o$5bo2bobobobo2bo$5bo3b2ob2o3bo$5bo2bobob
obo2bo$5bob2ob3ob2obo$4b3obob3obob3o$3b3o3bobobo3b3o$2bob2ob2o2bo2b2ob2obo$bob2ob3o5b3ob2obo$o3bo4b5o4bo3bo$
b2o2bo2bo5bo2bo2b2o$2bo4bob2ob2obo4bo$2bo5bo5bo5bo$2b5o9b5o$4b3ob7ob3o$3bo5b5o5bo$3b3o2bo5bo2b3o$7bo3bo3bo$2
b6ob2ob2ob6o$10b3o$3bo15bo$2bob2obo2b3o2bob2obo$3bo2b3o5b3o2bo$10bobo$4bob3obobob3obo$6bobo5bobo$7bob2ob2obo
$3b3ob2ob3ob2ob3o$2b2o2b2ob5ob2o2b2o$6bobo5bobo$3b3o2bo2bo2bo2b3o$3bobo3bobobo3bobo$3bo3b2o2bo2b2o3bo$2bo3b2
obobobob2o3bo$2b5o4bo4b5o$7bo3bo3bo$b4o3bobobobo3b4o$bo5b2ob3ob2o5bo$2bo2bo3bo3bo3bo2bo$3bobo5bo5bobo$o4b2ob
3ob3ob2o4bo$3o4b2ob3ob2o4b3o$2bo3bo2b2ob2o2bo3bo$10b3o$bob4o2bo3bo2b4obo$2bobo13bobo$b2o2bob2ob3ob2obo2b2o! - ↑ 24*140 partial
7bo2b4o2bo$6b2ob6ob2o$5b2obo6bob2o$5b5ob2ob5o$5bo2b2ob2ob2o2bo$8b2o4b2o$6b2ob2o2b2ob2o$6b2ob2
o2b2ob2o$5b2ob2ob2ob2ob2o$4bob2obob2obob2obo$4b3obo6bob3o$5b5o4b5o$7b4o2b4o$4b5obo2bob5o$3bob
o2b2o4b2o2bobo$4bo2bo8bo2bo$3bobo12bobo$3b5obo4bob5o$4b2obo8bob2o$2b2obobo8bobob2o$3b2ob3o6b3
ob2o$7b3o4b3o$7b2o6b2o$5b5o4b5o$3b2ob2o8b2ob2o$3bob5o4b5obo$7b2o6b2o$5b2obo6bob2o$4b4o8b4o$2b
2o3bo8bo3b2o$3b2o4b6o4b2o$2b7ob4ob7o$3bo2bo3bo2bo3bo2bo$5bo3b2o2b2o3bo$5bobo2bo2bo2bobo$4bob4
ob2ob4obo$10bo2bo$6bobobo2bobobo$7b3ob2ob3o$8b3o2b3o$5b2o2b2o2b2o2b2o$5bo4b4o4bo$6bo3bo2bo3bo
$6b2ob2o2b2ob2o$4b2o4bo2bo4b2o$5b2obo2b2o2bob2o$2bobo3bo6bo3bobo$9bo4bo$b2o2b3o8b3o2b2o$2bobo
2bobob2obobo2bobo$4b3o3bo2bo3b3o$3o3bob8obo3b3o$4b4o8b4o$5b2o10b2o$2b2o2b3ob4ob3o2b2o$bobo4bo
2b2o2bo4bobo$b2o6bob2obo6b2o$2bo6b2o2b2o6bo$2bobo2bo8bo2bobo$3b2o4b2o2b2o4b2o$3b2o2b4o2b4o2b2
o$2bobo2bo2bo2bo2bo2bobo$2bobo2bobo4bobo2bobo$3bo4bo6bo4bo$4bo4b6o4bo$2bo3b2o3b2o3b2o3bo$3bo4
b3o2b3o4bo$bob4obo6bob4obo$bo20bo$2b2o4bo6bo4b2o$4bob3o6b3obo$4b5o6b5o$4b2o2bobo2bobo2b2o$6bo
bobo2bobobo$3bo4bo2b2o2bo4bo$5bo2bobo2bobo2bo$5b3o8b3o$4bo2b3ob2ob3o2bo$3b2o4b6o4b2o$3bob6o2b
6obo$6bobo6bobo$3b2o3b3o2b3o3b2o$3bob5o4b5obo$3b2ob2o8b2ob2o$2b3o14b3o$b2ob2obo8bob2ob2o$2bob
2ob2o6b2ob2obo$2bo2bobo8bobo2bo$b2obo3bo6bo3bob2o$bobo16bobo$o3bob2o8b2obo3bo$bo5bo8bo5bo$3bo
b2o10b2obo$bo2b2obo8bob2o2bo$2b3o2bo8bo2b3o$bo2bo2b2ob4ob2o2bo2bo$5bob3o4b3obo$2bo7b4o7bo$b2o
4b2o6b2o4b2o$o2bo3b2o6b2o3bo2bo$6bob3o2b3obo$2bo3bo2bob2obo2bo3bo$2b2o2b4ob2ob4o2b2o$3bo2bo10
bo2bo$2bo2bob10obo2bo$3b3o2bo2b2o2bo2b3o$b2o2bo2bo6bo2bo2b2o$bobobob3ob2ob3obobobo$6bobo2b2o2
bobo$8bob4obo$3b2ob2o8b2ob2o$b3o2b2ob2o2b2ob2o2b3o$3o3bo4b2o4bo3b3o$bo2b4obo4bob4o2bo$3b2o2bo
bob2obobo2b2o$bobobo2b2o4b2o2bobobo$3b2o2b4o2b4o2b2o$2b2o2bo10bo2b2o$2bo2b2o2b2o2b2o2b2o2bo$b
3o4bobo2bobo4b3o$2b2obo12bob2o$b2o2bo4bo2bo4bo2b2o$bobob2obobo2bobob2obobo$3b5o3b2o3b5o$b6obo
bo2bobob6o$3bo2b2o2bo2bo2b2o2bo$3bobobo3b2o3bobobo$2bobo2b2ob4ob2o2bobo$2b2o2b2obo4bob2o2b2o$
3b2ob4o4b4ob2o$3bo4b3o2b3o4bo$2b2o2b3o6b3o2b2o$4bo14bo$4b3o3b4o3b3o$6bobobo2bobobo$2bobo3b2ob
2ob2o3bobo$2bo4bobob2obobo4bo$bobobo5b2o5bobobo$o5bobo2b2o2bobo5bo$obobob2o2bo2bo2b2obobobo! - ↑ 11*101 partial
3bo3bo$3b5o$2b2obob2o$3bobobo$2bobobobo$3bo3bo$4bobo$4b3o$3obobob3o$4bobo$4b3o2$3bobobo$3b5o$4bobo$3bo3bo$3b2ob2o2$4b3
o$5bo$3b5o$3b5o$3bo3bo$bobo3bobo$2b2o3b2o$b3obob3o$b4ob4o$4bobo2$5bo$2bo5bo$2b2obob2o$bob5obo$4bobo$bo2b3o2bo$2b2obob2
o$bob2ob2obo$b4ob4o$bo7bo$bobo3bobo$3bo3bo$3b2ob2o$3b2ob2o$4bobo$5bo2$4b3o$3bo3bo$2b2o3b2o$2b3ob3o$3b2ob2o$4bobo$3bo3b
o$3bo3bo$4bobo$3b5o$5bo$2bo2bo2bo$3b2ob2o$2b2o3b2o$2bo5bo$3b2ob2o$3b2ob2o$3b5o$3b5o$4bobo$b3obob3o$2b2obob2o$2bobobobo
$ob2o3b2obo$obo5bobo$4bobo$3bo3bo$5bo$2b3ob3o$2b2o3b2o$2bo5bo$bo3bo3bo$2b7o$2b7o$3b5o$4bobo2$3bo3bo$2b7o$bobobobobo$b9
o$2b3ob3o$b2o5b2o$5bo$bo7bo$2o2bobo2b2o$bo2b3o2bo$2b7o$bo7bo$2ob2ob2ob2o$bobo3bobo$b2obobob2o$o3b3o3bo$bo3bo3bo$4bobo! - ↑ 12*120 partial
4b4o$5b2o$4bo2bo$2b2o4b2o$3bo4bo$2bo6bo$b2o6b2o$b10o2$3bo4bo$4bo2bo$2b3o2b3o$3bob2obo$2bo6bo$3b2o2b2o$3
bo4bo$bo8bo$4b4o$b2obo2bob2o$2bobo2bobo$bobob2obobo2$o4b2o4bo$bo2bo2bo2bo$2b2ob2ob2o$4b4o2$3b6o$3b2o2b2
o$4ob2ob4o$o2b2o2b2o2bo$b10o$ob3o2b3obo2$2b2o4b2o$bob2o2b2obo$bo8bo$4bo2bo$3b2o2b2o$4bo2bo$2b2o4b2o$b4o
2b4o$o2b6o2bo$2o2b4o2b2o$bob6obo$2bo6bo$3bo4bo2$3b2o2b2o$3b2o2b2o$3b2o2b2o$4bo2bo$3bo4bo$4b4o$3bo4bo$3b
ob2obo$3b2o2b2o$3b2o2b2o$5b2o$4bo2bo$4b4o$2b3o2b3o$3bob2obo$3b6o$3b6o$b4o2b4o2$2bobo2bobo$2bo2b2o2bo$2b
8o$b2o6b2o$2bob4obo$4b4o2$bo8bo$ob8obo$3bo4bo$4bo2bo$4bo2bo$5b2o$4bo2bo$2bo2b2o2bo$3b2o2b2o$3b6o$3b2o2b
2o$2b8o$bo8bo$obobo2bobobo$bobo4bobo$bo2bo2bo2bo$2b2o4b2o$2b3o2b3o$3b2o2b2o$2b8o$2bobo2bobo$b2o6b2o$b2o
6b2o$bob6obo$4bo2bo$3b2o2b2o$2bob4obo$3bo4bo$bob2o2b2obo$bo3b2o3bo$bo2b4o2bo$bo2b4o2bo$2bo6bo2$2bobo2bo
bo$b10o$2b3o2b3o$bo8bo$bo2b4o2bo$bo2bo2bo2bo$b4o2b4o$2obo4bob2o$obob4obobo$bo2bo2bo2bo$12o$b2o2b2o2b2o! - ↑ 7*34 partial
4b2o$3b4o2$5b2o$5bo$5bo$3bo$2b3o$2b4o$3bo2$2bo$ob2o$bo2b3o$2o$4bo$5bo$2b2obo$5b2o$3
b2obo$3b3o$2bob2o$3bo$3b2o$2b3o$5o$o2b2o$b2o2bo$bob3o$3b2o$2bobo$2bo3bo$bo$ob2ob2o! - ↑ 12*70 partial
5b2o$4b4o$5b2o$4bo2bo$4bo2bo$3b6o$2b2o4b2o$3b6o$3b2o2b2o$3b6o$4b4o2$4b4o$4bo2bo$5b2o$3b6o$4bo2bo$4bo2bo$4b4o$4bo2bo$4bo2bo$5b2o$4b
4o$4b4o$bobo4bobo$3bo4bo$b3o4b3o$2b2o4b2o$b2o6b2o$ob3o2b3obo$b2o2b2o2b2o$12o$2b8o$3b6o2$2b2o4b2o$bobo4bobo$2ob2o2b2ob2o$bo2bo2bo2b
o$b3o4b3o$b2obo2bob2o$3b2o2b2o$3bob2obo$2bo2b2o2bo$5b2o$2b8o$4bo2bo$5b2o$b2obo2bob2o$2bo6bo$3bob2obo$3bo4bo$2bo2b2o2bo$4bo2bo2$3b2
o2b2o$3bob2obo$5b2o2$2b8o$bo3b2o3bo$bo3b2o3bo$bo2bo2bo2bo$2bo2b2o2bo$2bo2b2o2bo$b4o2b4o$b2obo2bob2o$b2obo2bob2o$2bob4obo$3bob2obo! - ↑ 13*61 partial
b4o3b4o$b4o3b4o$2b2o5b2o$bob2o3b2obo$bo3bobo3bo$2bo2bobo2bo$3b3ob3o$b2o7b2o$b4o3b4o$2bo7bo$2b
2o5b2o$bo2bo3bo2bo$bo2b2ob2o2bo$bo4bo4bo$b5ob5o$4b2ob2o$4bo3bo$3b2o3b2o$3bo5bo$4b2ob2o$5b3o$4
bobobo$3b2obob2o$4b2ob2o$3b2obob2o$2bob2ob2obo$3bo5bo$2bo2bobo2bo$b3obobob3o$3b2o3b2o$bo3bobo
3bo2$3bo5bo$b2obo3bob2o$b2ob2ob2ob2o$b2ob2ob2ob2o$b3o5b3o$3bo5bo$4bo3bo$bo2bo3bo2bo$2b2o5b2o2
$2bob5obo$b3ob3ob3o$3bo5bo$2b4ob4o$3bobobobo$bo2b5o2bo$5bobo$b2ob2ob2ob2o$5bobo$2b2o2bo2b2o$b
4obob4o$2bob5obo$3ob5ob3o$2obob3obob2o$bo2b5o2bo$2b4ob4o$b2ob5ob2o$bobo2bo2bobo$ob2obobob2obo! - ↑ 12*48 partial
4b4o$2b8o$4b4o$b2obo2bob2o$3bo4bo$3bob2obo$2b2o4b2o$2b2o4b2o$3b2o2b2o$4bo2bo$3b6o$5b2o$2bo6bo$2o8b2o$bobo4bobo2$3b2o2b2o$b2o6b2o$2bo6bo$3bo4bo$bo3b2o3bo2$2o8b2o$12o$b10o$2b2o4b2o$
3bo4bo$4b4o$4bo2bo$2b2ob2ob2o$2bo6bo$3bob2obo$ob2o4b2obo$ob3o2b3obo$b10o$2bo2b2o2bo$2obob2obob2o$b4o2b4o$bob6obo$5b2o$bo8bo$3bob2obo$2b2o4b2o$5o2b5o$4o4b4o$bo3b2o3bo$3b6o$b2o6b2o!
14*54
6b2o$4b2o2b2o$3b8o$3bobo2bobo$3b2o4b2o$4b6o$4b6o$4b2o2b2o$4b2o2b2o$5b4o$5b4o$4bo4bo$2b3o4b3o$2b2o6b2o$2b3o4b3o$3b2o4b2o$3b3o2b3o2$3bo6bo$b2obo4bob2o$b4o4b4o$2ob2o
4b2ob2o$2b3o4b3o$2bo2b4o2bo$3bo2b2o2bo$2bo2bo2bo2bo$4b6o$bo4b2o4bo$5bo2bo$3b3o2b3o$4b2o2b2o$4bo4bo$2bo2bo2bo2bo$2bo2bo2bo2bo$2bo2bo2bo2bo$2b2obo2bob2o$5b4o$3bo6bo
$4b2o2b2o$2b2obo2bob2o$bobob4obobo$bo4b2o4bo$b5o2b5o$4bob2obo$3b2ob2ob2o$2b3o4b3o$3b3o2b3o$2ob8ob2o$o3b2o2b2o3bo$2bob2o2b2obo$2bo2b4o2bo$3bo2b2o2bo$o12bo$bob8obo!
16*70
6b4o$4b8o$6b4o$3b2obo2bob2o$5bo4bo$5bob2obo$4b2o4b2o$4b2o4b2o$5b2o2b2o$6bo2bo$5b6o$7b2o$4bo6bo$2b2o8b2o$3bobo4bobo2$
5b2o2b2o$4bo6bo$3b2o6b2o$3b2o6b2o$2bo2b2o2b2o2bo$b2o2b2o2b2o2b2o$3b3ob2ob3o$7b2o$3b2o2b2o2b2o$3b3ob2ob3o$3b2o6b2o$3b
obo4bobo$3b3o4b3o$2bobob4obobo$3bob2o2b2obo$5b6o$4bo6bo$3bo3b2o3bo$2b2o2bo2bo2b2o$4b3o2b3o$3b2o6b2o$3b3ob2ob3o$7b2o$
4b2o4b2o$3bo2bo2bo2bo$3b2o2b2o2b2o$5b2o2b2o$4bo2b2o2bo$5b6o$4b3o2b3o$bob2obo2bob2obo$o3bobo2bobo3bo$2o3bob2obo3b2o$2
b3o2b2o2b3o$4b3o2b3o$3bo2bo2bo2bo$3bob2o2b2obo$2bob8obo$b2o3bo2bo3b2o$b2o4b2o4b2o$bo2b2o4b2o2bo$bobobob2obobobo$2b2o
8b2o$5bo4bo$b2o3b4o3b2o$2b12o$b4o6b4o$ob3o6b3obo$3b2o6b2o$b2o3bo2bo3b2o$b14o$b2o2b6o2b2o$2b2obo4bob2o$2bob2ob2ob2obo! - ↑ 19*47 partial
2b15o$b4o4bo4b4o$5b2obobob2o$b2obob2o3b2obob2o$2b2o2b2o3b2o2b2o$bo4b3ob3o4bo$4bobob3obobo$6bob3obo$bobo2b3ob3o2bobo$b3obo2bobo2bob3o$b2o2bobo3bobo2b2o$3bob
2o5b2obo$6b3ob3o$5bobo3bobo$2bo2bo2bobo2bo2bo$bo2bobo5bobo2bo$b2ob2o7b2ob2o$b4ob7ob4o$bob2obob3obob2obo$2bo6bo6bo$b2ob11ob2o$bo2bo9bo2bo$3b2ob7ob2o$b3o2b2o
3b2o2b3o$bo2bobo5bobo2bo$b2o2bobo3bobo2b2o$b2o5bobo5b2o$3bo2bobobobo2bo$bob5o3b5obo$7bo3bo$2o4bo5bo4b2o$b3o11b3o$bo3bob2ob2obo3bo$bob2o2bo3bo2b2obo$2bo3bo5b
o3bo$b3obo7bob3o$b3o11b3o$2bo4bo3bo4bo$7ob3ob7o$bob4o5b4obo$2ob5o3b5ob2o$5bobo3bobo$3b2o3bobo3b2o$3b3o2bobo2b3o$3bob2o2bo2b2obo$3b3o2bobo2b3o$3o3b3ob3o3b3o! - ↑ 20*30 partial
8b4o$6b8o$5b3o4b3o$8bo2bo$3bo3bob2obo3bo$4b2o2bo2bo2b2o$2b2o2bo2b2o2bo2b2o$2b2ob2obo2bob2ob
2o$3bob10obo$3bo3bo4bo3bo$3bobo2bo2bo2bobo$5bo8bo$5b3ob2ob3o$5b4o2b4o$5bobo4bobo$7b6o$6bo6b
o$2b3ob3o2b3ob3o$4bob2ob2ob2obo$b3ob3ob2ob3ob3o$bob3o8b3obo$2b2o2b2o4b2o2b2o$5b2o6b2o$3bobo
bo4bobobo$b3obobob2obobob3o$bo2bo3bo2bo3bo2bo$o5bobo2bobo5bo2$ob3obo6bob3obo$bo4b3o2b3o4bo! - ↑ 44.0 44.1 44.2 44.3 44.4 44.5 44.6 44.7 44.8 44.9 though preceding width has been disproven, this was not found with qfind so is not guaranteed to be of minimal height
- ↑ 17*49 partial
7b3o$6bo3bo$6bo3bo$4bob5obo$4bobo3bobo2$6b2ob2o$3bo9bo$3bo2b2ob2o2bo$5bobobobo$5b2o3b2o$4b3o3b3o3$7bobo$8bo$8bo$5b3ob3o2$4b4ob4o$3b4o
3b4o$4b2o5b2o$8bo$7bobo$7bobo$3bobo5bobo$3bobo5bobo$3b2o7b2o$6b2ob2o$4bo2bobo2bo$5bobobobo$2bo11bo$b3o9b3o2$b3o9b3o$2b3o2b3o2b3o$b2o
bo2bobo2bob2o$3obo2b3o2bob3o$4bo2bobo2bo$7b3o$5bo5bo$4b2o5b2o$2bobo2b3o2bobo$bo5b3o5bo$b3o9b3o$ob3ob2ob2ob3obo2$2bo2b2o3b2o2bo$o15bo! - ↑ 46.0 46.1 15*44 partial
6b3o$5bo3bo$5bo3bo$3bob5obo$3bobo3bobo2$5b2ob2o$2bo9bo$2bo2b2ob2o2bo$4bobobobo$4b2o3b2o
$3b3o3b3o3$6bobo$7bo$7bo$4b3ob3o2$3b4ob4o$2b4o3b4o$3b2o5b2o$7bo$6bobo$6bobo$2bobo5bobo
$2bobo5bobo$2b2o7b2o$5b2ob2o$3bo2bobo2bo$4bobobobo$bo11bo$3o9b3o2$3o9b3o$2b2ob2ob2ob2o$
2bo3bobo3bo$obo2b2ob2o2bobo$3ob2o3b2ob3o$3bobo3bobo$3bo3bo3bo$3bo3bo3bo$7bo$2bobo5bobo! - ↑ 16*34 partial (becomes width-18 on generation 2)
b2o10b2o$2o12b2o$4bo6bo$5bo4bo3$b5o4b5o$2b2ob6ob2o$6bo2bo$3bo2bo2bo2bo$3bo2bo2bo2bo2$5b2o2b2o$5b2o2b2o$4b2o4b2o$3bo8bo$2bo10bo$2b2obo4bob2o$2bo3b
4o3bo$o2b3o4b3o2bo$o4bob2obo4bo2$2o2bo6bo2b2o$3o10b3o$2bo2bo4bo2bo$bo2b2o4b2o2bo$4bobo2bobo$o14bo$2o12b2o$o5b4o5bo$b5o4b5o$bo12bo$5bo4bo$b5o4b5o! - ↑ 19*42 partial
2b2o11b2o$bo15bo$5bo7bo$5bo7bo$2b5o5b5o$3bo11bo$2o2b3o5b3o2b2o$8bobo$bobo4bobo4bobo$5b3o3b3o$5bobo3bobo$5bo7bo$
8bobo$3b3o7b3o$5bo2bobo2bo$4bo2bo3bo2bo$6bo5bo$6bo5bo$4b2o2bobo2b2o$7b2ob2o$3bo3bo3bo3bo$2b3obobobobob3o$3bo2bo
bobobo2bo2$bobo11bobo$4b3o5b3o$bobobob2ob2obobobo$3bo2bo5bo2bo$3bo2bo5bo2bo$6bo5bo$2bobo9bobo$7bo3bo$bo3bo2bobo
2bo3bo$2bob2o7b2obo$6bo5bo$5b2obobob2o$4bo3bobo3bo$3b2obo5bob2o$3bo4bobo4bo$2bo3bobobobo3bo$b2o13b2o$ob6o3b6obo! - ↑ 10*32 partial
4b2o$4bo2bo$5bo2bo$4bo$3b2obobo$3bo$3b2o2bo$3bo$4bo2bo$5b2o2$2b3o$bo2b5o$b4o3bo$2b2obo2bo$3bobo$2bo
2b2o$bo4bo2$bo2b2obo$5bobo$2b5o$bo$b3obo2b2o$4bo$o3bo$2b2o2bo$3b2o2b2o$bo6bo$2bo3b2o$2b3o$bo3bo2bo! - ↑ seemingly first found in [18]
- ↑ 10*42 partial
4bo2b2o$3bob2obo$2bo2b3o$5b2o$5bo$4bo2$3b4o$3o$2bo$5bob2o$3b2obobo$7bo$2b3obo$2b5o$b3o2bo$4b2o$6bo$6bo$3bo2bo$3bo2bo$5b3
o$2bo3bo$2bobo$7bo$3bobo2bo$4b2o$3b2ob2o$3bo5bo$3bo4bo$5bo$2bo$2bo$6b2o$3b3o$3bo3bo$6b3o$2bo6bo$3b5obo$2b2o4bo$b9o$o6b3o! - ↑ 17*48 partial
5b3ob3o$4b2o5b2o$3bo3bobo3bo$2bo11bo$5bo5bo$bo2bo7bo2bo$bo2bo7bo2bo$bo13bo$bo3bo5bo3bo$4bobo3bobo2$7bobo$7bobo$8bo$5bob3obo$
6bobobo$2bo4b3o4bo$bo13bo$4bo7bo$bob2obo3bob2obo$2bobo7bobo$4bo3bo3bo$4bo7bo$b2obo7bob2o$4b2o5b2o$2o2bo7bo2b2o$obo2bob3obo2b
obo$b4o3bo3b4o$2b3o2b3o2b3o$4bo7bo$4bo3bo3bo$2bobo2b3o2bobo2$6b5o$2bo3bobobo3bo$bob2o7b2obo$2bob2ob3ob2obo$3bobo2bo2bobo$o2b
o3b3o3bo2bo$2o2bo7bo2b2o$b2o2bo5bo2b2o$obo3b2ob2o3bobo$2o3b2o3b2o3b2o$2b2obo5bob2o$b3ob3ob3ob3o$2bo11bo$bo3bo5bo3bo$b3o9b3o! - ↑ 18*41 partial
3b2o8b2o$2bo12bo$b4o8b4o$bo14bo$5bo6bo$3bo2bo4bo2bo$3bob2o4b2obo$3b2obo4bob2o$4b3o4b3o$5bo6bo2$3
b3o6b3o$3b5o2b5o2$obo4bo2bo4bobo$ob3obo4bob3obo$3b3o6b3o2$4b3o4b3o$6bo4bo$3bo3b4o3bo$2bo12bo$3b3
obo2bob3o$3bo10bo$2b2o10b2o$bo14bo$2bo3bo4bo3bo$6b2o2b2o$3obo8bob3o$b2o2b3o2b3o2b2o$6bob2obo$4bo
3b2o3bo$5bo6bo$5b8o$4b2o6b2o$3b2obo4bob2o$3bobo6bobo$3bobo6bobo$3b3o6b3o$5bo2b2o2bo$2bo4bo2bo4bo! - ↑ 20*62 partial
8b4o$7b6o$6b2o4b2o$7bo4bo$7bo4bo$7bob2obo$9b2o$5bo8bo$5b2o6b2o$5bo3b2o3bo2$9b2o$6b2o4b2o$4bo10bo$4bo10bo2$8bo2bo$6bobo2bob
o$7b2o2b2o$4b2o8b2o$5bo3b2o3bo$5bo3b2o3bo$3bo12bo$2bo14bo2$bo2b4o4b4o2bo$4b2obo4bob2o$4bo3b4o3bo$bobobob6obobobo$5bobob2ob
obo$7bo4bo$3bo3bo4bo3bo$4bo10bo$5bo2b4o2bo$6bo6bo$7bo4bo$7bo4bo$7bo4bo2$3b2o3bo2bo3b2o$2bo2b3o4b3o2bo$6bo6bo$2bo4bo4bo4bo$
2bo4bo4bo4bo$7bo4bo$2bo3bo6bo3bo$b5obo4bob5o$2b2o2b2o4b2o2b2o$3b4o6b4o$b3o2bo6bo2b3o$ob2obo8bob2obo$2o7b2o7b2o$3bo2bo6bo2b
o$2b2o3bo4bo3b2o$2bob2o2bo2bo2b2obo$2bobob2ob2ob2obobo$3b5o4b5o$4bo10bo$4bo3b4o3bo$3b2o2b2o2b2o2b2o$bo3bo8bo3bo$bo7b2o7bo! - ↑ there is also a width-18 version which has the same backend as the w17o (and as such can be considered its even variant)
- ↑ 10*33 partial
5bo$4bobo$5bo$5bo$5bo$4bo2bo2$5bob2o$5bobobo$6b3o$6b2o$5bo$4b2o$4b2o$4bo2bo$4bo2bo$7bo$3bob3o$3b
obobo$3b3o2bo$4b2o$4bobo$3bo2bo$3bo2bo$2b2o$2b2o3bo$2bobob2o$2b4o$bobobo2bo$o4bo2bo$5o3bo2$o8bo!
looks alike the Statue of Liberty - ↑ this one has a smaller population but a backspark that increases its bounding box
- ↑ not sure of minimality of length, also is 466 cells and beaten in population by a 299-cell w23o (by dreamweaver)
- ↑ 24*19 partial
10b4o$8bobo2bobo$8b8o$8b8o$4b4ob6ob4o$4b6ob2ob6o$2bobob2obo4bob2obobo$2b3obo2bo4bo2bob3o$2bobobo2bo4bo2bobobo$b2obob4o4b4obob2o$ob3obo2bo4
bo2bob3obo$2bobob4ob2ob4obobo$3obobo3b4o3bobob3o$6bo3b4o3bo$bo6bo2b2o2bo6bo$b2obobo2b6o2bobob2o$b2o3bobo2b2o2bobo3b2o$bobo6b4o6bobo$10b4o! - ↑ 20*46 partial
7b6o$5bob2o2b2obo$3bobob6obobo$bob3ob6ob3obo$bob14obo$ob4obob2obob4obo$b5ob6ob5o$b18o$b4obo6bob4o$3b3o8b3o$bobobo8bobobo$bob3o8b3obo$2b2o5b2o5b2o
$ob5o2b2o2b5obo$obobobobo2bobobobobo$2bobobob4obobobo$4bob8obo$2b5ob4ob5o$2bobob2o4b2obobo$3b5ob2ob5o$2b5o6b5o$2bob4o4b4obo$4b2o8b2o$2b3obobo2bo
bob3o$3b4o2b2o2b4o$b8o2b8o$4bobob4obobo$3b4ob4ob4o$bob2obob4obob2obo$bob14obo$bob5o4b5obo$4b4o4b4o$b7o4b7o$4bo2b2o2b2o2bo$2b3obo6bob3o$4bobo6bob
o$2b2o12b2o$2b16o$2bobo2b2o2b2o2bobo$2bo2bobob2obobo2bo$4b2ob6ob2o$b2o3b3o2b3o3b2o$2b4o3b2o3b4o$4o2bo2b2o2bo2b4o$ob3ob8ob3obo$2bobob2ob2ob2obobo! - ↑ 57 cells, smallest known is 41 cells at width 8, first found by [22]
- ↑ 235 cells, shortest width-15 is 146 cells
other such tables alike this
references
- ↑ wwei47 (May 14, 2024). Re: Thread for your miscellaneous posts and discussions, in which the scheme for non-orthogonal width notation was specified
- ↑ 2.0 2.1 2.2 2.3 2.4 wwei47 (May 21, 2024). Re: Thread for your LLS/JLS/WLS search dumps, in which various results were found for diagonal spaceships in B36/S245
- ↑ wwei47 (May 24, 2024). Re: Thread for your LLS/JLS/WLS search dumps, in which a minimal-width[2] c/5 diagonal in B36/S245 was found
- ↑ DroneBetter (March 3, 2024). Re: B36/S245, in which the currently smallest-known c/5d (146 cells) was found
- ↑ 5.0 5.1 lordlouckster (August 29, 2022). Message in #bots-and-mute-this on the Conwaylife Lounge Discord server, in which the thinnest symmetrical c/5d in B36/S245 was found
- ↑ wwei47 (June 1, 2024). Re: B36/S245, in which [5]'s minimal-width symmetric c/5 diagonal was noted to be minimal
- ↑ May13 (March 3, 2024). Re: B36/S245, in which a symmetrical width-19 c/5d was found
- ↑ LaundryPizza03 (December 21, 2020). Re: B36/S245, in which a (2,1)c/6 was found (the first knightship)
- ↑ lordlouckster (August 15, 2022). Message in #bots-and-mute-this on the Conwaylife Lounge Discord server, in which the first 2c/7 in B36/S245 was found at w16e
- ↑ wwei47 (June 1, 2024). Re: B36/S245</ref>
this spaceship (with a forked tail) is in fact shorter, but higher-population - ↑ LaundryPizza03 (March 25, 2024). Re:B3/S12 (Flock), noting Lapin Acharné's 2c/8
- ↑ 12.0 12.1 12.2 12.3 wwei47 (May 13, 2024). Re: B3/S12 (Flock), in which bounds upon c/3 widths were found with JLS
- ↑ 13.0 13.1 13.2 13.3 13.4 13.5 wwei47 (May 14, 2024). Re: B3/S12 (Flock), in which considerably improved bounds were found with ikpx2
- ↑ 14.0 14.1 May13 (May 17, 2024). Re: B3/S12 (Flock), in which a width-71 gutter-preserving c/3 was found with LSSS (which also works in Pedestrian Flock)
- ↑ 15.0 15.1 amling (May 18, 2024). Re: amling questionable searches/ideas firehose, in which dark magic was utilised to achieve the impossible of finding a minimal-width w38a c/3
- ↑ wwei47 (April 27, 2024). Re:RLE copy/paste thread - everyone else, in which minimal-width c/3's were found in HighFlock with JLS
- ↑ wwei47 (June 9, 2024). Re: Thread for your LLS/JLS/WLS search dumps, in which the existence of a width-11 c/5 in HighFlock was disproven with gfind
- ↑ lordlouckster (December 15, 2022). Message in #naturalistic on the Conwaylife Lounge Discord server, in which the thinnest odd-symmetric 2c/5 in B36/S12 was found
- ↑ wwei47 (June 5, 2024). Re: Thread for your LLS/JLS/WLS search dumps, in which a negative gfind search was completed for B38/S12 c/4 w12a (meaning the w13a from wwei's B3/S12 search is minimal-width in B38/S12 as well)
- ↑ wwei47 (June 7, 2024). Re: Thread for your LLS/JLS/WLS search dumps, in which a negative gfind search was completed for B38/S12 c/5 w13a
- ↑ wwei47 (April 25, 2024). Re:RLE copy/paste thread - everyone else, in which width-15 c/3's were found in Holstein (per personal correspondence, with JLS and also disproving lower widths)
- ↑ anonymousdeveloper (March 4, 2021). Message in #naturalistic on the Conwaylife Lounge Discord server, in which the smallest width-8 2c/4 in Geology was found (with rlifesrc, per personal correspondence)
- ↑ lordlouckster (December 9, 2023). Message in #naturalistic on the Conwaylife Lounge Discord server, in which the first (2,1)c/5 in Geology was found
- ↑ saka (March 4, 2021). Message in #naturalistic on the Conwaylife Lounge Discord server, in which the smallest w11o c/7 in Geology was first found
- ↑ H. H. P. M. P. Cole (May 31, 2024). Re: Spaceships in Life-like cellular automata, in which a c/7 w15g in Geology was disproven (with qfind, per personal correspondence)
- ↑ LaundryPizza03 (September 11, 2020). Re: B3578/S24678, in which the smallest w14e 2c/7 was first found (apparently they didn't remember to do w13o otherwise they would have a considerably smaller one)
verified with qfind, next shortest w14e is this one - ↑ saka (March 5, 2021). Message in #naturalistic on the Conwaylife Lounge Discord server (further down they explain it was found with qfind)