I ran the width-12 c/4 orthogonal knightt search. The results are attached to this post, although they are probably not very useful to anyone. I looked through the ships a little and managed to construct the following small ships based on new components:
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x = 56, y = 80, rule = B3/S23
b2o47bo$3o47b2o2b2o$bo15b2o31bo2bo$2b2ob2o10b3obo10b2o19bo$7bo5bob3o
13b3o$2b2o7bobo6bobo9bo20b3o$3bo6bobo10bo9b2ob2o16bo$4bo2bo14b3o13bo5b
o6bobo$5bobobob2o20b2o7bobob3o$4b2o3bo12bo11bo6bobo4b3obo$6bo12bo2bo
12bo2bo9b2o$19b2o2b2o11bobobob2o$19bo15b2o3bo$37bo11$29bo$28b2o$16bo2b
o$16bo2bo4b2obo$14b2obo4b4obobo$19bo3bo2b2obo$13bo2bobo9bo$9bo3bobo3bo
bo$7bo2b2o$5b3o$4bobo$4bob2o$3bo4bo$2b2o2$bo4b2o$5bo$2b3o$4bo$5bo$4b2o
$5bo$5b2o$2bo2b2o$2o3bo$2bo11$16b2obo$12bobo3b2o$10b2o4bo$12bob3o$17b
2o3bobo$16bo4bo2bo$20bo3bo$14bobobobo$5b3o4bobobo$o2b2o4b2obobo5b2o$2o
7bo$o3bo6b3o$5b2o4bo2bo$10b2o2bo$7b3o4bo$14bo$13b2o$11bo2b2o$9b2o$11bo
!
I also found this 70-cell ship that has probably been seen before, but has been overlooked for some reason:
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x = 34, y = 11, rule = B3/S23
6bo$4b2o3bo4b3o$5bobobob2o3b2o$4bo2bo6bo3b2o$3bo6bobo8b2o$2b2o7bo7bo9b
2o$7bo4bo3b2o2bo3bo2bo2bo2bo$2b2ob2o6bo3b2o2bo2b3o6bo$bo9bo9bo8bo2bo$
3o6b2o11b2o3bob2o$b2o8bo14bo!
I am also running the width-12 2c/5 knightt search. So far it has found these two small tagalongs:
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x = 36, y = 44, rule = B3/S23
6bo7bob2obo$5bobo6bobo3bo$4bo3b3o2bobobo7bobo$5bob3o3bobo5bob2o3bo$6b
2o6bobobo3bo2bob3o$14bobobo4bo6bo2bo$2b2obo11b2o3bo$bobo2bo12b2o12bo$
2o3bo24bo3bo$bobobo23b2ob2o$2b2ob2o23bo$5bo25b2ob2o11$26bo2bo$26bo3bo$
25bo2bo2bo$24b3o2$12bo3bob2obobo4bo$11bo4bo4bobo2b2obobo$11bo2b2obobob
o4b2obobo$11b2o9bo2bo4bo$15bob3o2bo3b4o$6bo8bo11b2o$5bobo7bo$4bo3b3o$
5bob3o$6b2o2$2b2obo$bobo2bo$2o3bo$bobobo$2b2ob2o$5bo!
A for awesome wrote:I mark the first cell in the leading row (that is not preprocessed to be empty) as on, and start the search. When that completes, I mark that cell off, set the next one in the row on, and restart the search.
This is what I suspected. Do you do this for every cell in the entire diagonal row (as opposed to the first half-diagonal)? Do you also do this in every phase?