c/3 Against-the-Grain Greyships
(By Keith Amling, Hartmut Holzwart, and Jason Summers)
On August 31, 2023 Keith Amling constructed the first c/3 grayship where the stripes are perpendicular to the direction of travel ("against-the-grain"). Such grayships were previously only known to travel at speed c/2 with period 4.
A c/3 against-the-grain greyship must have period at least 6, which is typically far too high to reliably search at. Fortunately in this case, Amling's amazing search tools and a neat trick by Hartmut Holzwart and Jason Summers allowed this to be completed almost entirely with period-3 components. In a moment I will endeavor to explain how this is accomplished in detail, with a bit of history thrown in, but first let's see the actual ship:
Code: Select all
#C A c/3 against-the-grain greyship
#C By Keith Amling, August 31, 2023
#C Using ideas and components by Hartmut Holzwart and Jason Summers
#C This is a significant reduction to Amling's original ship
#C https://conwaylife.com/forums/viewtopic.php?p=166141#p166141
#C https://conwaylife.com/forums/viewtopic.php?p=129400#p129400
x = 277, y = 239, rule = B3/S23
116b2o41b2o$113b2ob2o41b2ob2o$113b2o3bo39bo3b2o$109b3o2bo47bo2b3o$109b
2o2b3o45b3o2b2o$109b3o53b3o$110bo55bo$111bo2bo47bo2bo$110b2ob2o2bo41bo
2b2ob2o$114b2ob2o39b2ob2o$113bob2o2bo37bo2b2obo$117bobo37bobo$117b2o
39b2o$116b2o41b2o$114bo2bo41bo2bo$114bo47bo$113bo3bo41bo3bo$113bo3bo
41bo3bo$116bo43bo$113b2o3bo39bo3b2o$112bo3b4o37b4o3bo$113bo4b2o37b2o4b
o2$113b2o47b2o$114bo47bo$114bo47bo$112b2o49b2o$111b2ob2o45b2ob2o$110bo
55bo$114bo47bo2$111b3o49b3o$106b2ob2o55b2ob2o$106b2o4b2o49b2o4b2o$106b
3ob2o53b2ob3o$106b2o2b2o53b2o2b2o$107bo61bo2$110b3o51b3o$111bo53bo$
108b2o3b2o47b2o3b2o$108b2o3b2o47b2o3b2o$109b5o49b5o$111bo53bo$111bo53b
o$110b3o51b3o3$109bo3bo49bo3bo$108b3ob3o47b3ob3o$106b2o7b2o43b2o7b2o$
106b2o7b2o10b3o17b3o10b2o7b2o$109b2ob2o9bob2o3bo15bo3b2obo9b2ob2o$109b
o3bo8b3o3bobo15bobo3b3o8bo3bo$110bobo8bo3bo4b2o13b2o4bo3bo8bobo$108bob
obobo7bo7b3o11b3o7bo7bobobobo$107bo2bobo2bo12bobo15bobo12bo2bobo2bo$
106bo9bo10b2o19b2o10bo9bo$105bo2bo5bo2bo8bo3bo15bo3bo8bo2bo5bo2bo$105b
o3bo3bo3bo12bo15bo12bo3bo3bo3bo$73bo33bob2ob2obo11bob2o7bo7b2obo11bob
2ob2obo33bo$69b3ob3o29bo2bobobobo2bo9bo9bobo9bo9bo2bobobobo2bo29b3ob3o
$68bo6b2o28bo3b2ob2o3bo9b3o6bo3bo6b3o9bo3b2ob2o3bo28b2o6bo$69b2o3bo2bo
59b3o59bo2bo3b2o$79b3o22b2o11b2o5bobo23bobo5b2o11b2o22b3o$75bo2bobo42b
2obob2o5b2o3b2o5b2obob2o42bobo2bo$75bo2bobo2b2obo16bo15bo2bo3bobo2b3o
3bobo3b3o2bobo3bo2bo15bo16bob2o2bobo2bo$74bobobo2b2o2b3o15bobo11bobo8b
ob2obo3bobo3bob2obo8bobo11bobo15b3o2b2o2bobobo$57bo18bobobo3bo3bo19b2o
3b2o13bobo6bobo6bobo13b2o3b2o19bo3bo3bobobo18bo$53b3ob3o27bo15b2obob2o
3b2obob2o8bobo2bobobobobobo2bobo8b2obob2o3b2obob2o15bo27b3ob3o$52bo6b
2o21bo24bo2bobo2bo9b2obobo15bobob2o9bo2bobo2bo24bo21b2o6bo$53b2o3bo2bo
21b2o23b3ob3o10b2obo4b2o7b2o4bob2o10b3ob3o23b2o21bo2bo3b2o$63b3o17b2o
21b3o5b3o14b2o11b2o14b3o5b3o21b2o17b3o$59bo2bobo19bo6b2o12bo2bo5bo2bo
9b2o3bo4b3o4bo3b2o9bo2bo5bo2bo12b2o6bo19bobo2bo$59bo2bobo2b2obo15bob2o
b2o11b2obo7bob2o6b3o2bo6b3o6bo2b3o6b2obo7bob2o11b2ob2obo15bob2o2bobo2b
o$58bobobo2b2o2b3o14b2obo3bo10b2o3bo3bo3b2o11bo5bo3bo5bo11b2o3bo3bo3b
2o10bo3bob2o14b3o2b2o2bobobo$60bobobo3bo3bo9b3obob3o2bo12b2o7b2o8b2o2b
ob7ob7obo2b2o8b2o7b2o12bo2b3obob3o9bo3bo3bobobo$71bo12bobo3bo3bo9b6o3b
6o5b3o2b4obo7bob4o2b3o5b6o3b6o9bo3bo3bobo12bo$66bo16bo2bobo3bobo8bo3bo
7bo3bo5bob3o6bobobo6b3obo5bo3bo7bo3bo8bobo3bobo2bo16bo$67b2o17bobo18b
2o5b2o9bo2bo6b3ob3o6bo2bo9b2o5b2o18bobo17b2o$67b2o15bo3b2o19bo3bo21bo
5bo21bo3bo19b2o3bo15b2o$68bo6b2o7bo3b2ob2o11b2obobo3bobob2o7bo3b2o4bo
3bo4b2o3bo7b2obobo3bobob2o11b2ob2o3bo7b2o6bo$70bob2ob2o9bob2obo12bo4b
2ob2o4bo12bo13bo12bo4b2ob2o4bo12bob2obo9b2ob2obo$70b2obo3bo13bobo13b3o
3b3o12b2obob2obo3bob2obob2o12b3o3b3o13bobo13bo3bob2o$66b3obob3o2bo9b4o
2b2o11bo2bo3bo2bo9b2obobobo3bobo3bobobob2o9bo2bo3bo2bo11b2o2b4o9bo2b3o
bob3o$68bobo3bo3bo7b3obo15bob2o3b2obo8bobo3bobo3bobo3bobo3bobo8bob2o3b
2obo15bob3o7bo3bo3bobo$67bo2bobo3bobo6b2o6b2o10b2obo5bob2o8b3o2bo2b2o
2bo2b2o2bo2b3o8b2obo5bob2o10b2o6b2o6bobo3bobo2bo$70bobo13bo6b2o10bo11b
o14bo3bobobo3bo14bo11bo10b2o6bo13bobo$68bo3b2o11b2o5bobo12bobo3bobo8b
2o5b2o2b7o2b2o5b2o8bobo3bobo12bobo5b2o11b2o3bo$68bo3b2ob2o14bo32b2o9bo
5bo9b2o32bo14b2ob2o3bo$70bob2obo9b2o4bo14bo2bo3bo2bo8b3o9b3o9b3o8bo2bo
3bo2bo14bo4b2o9bob2obo$75bobo7b2o4bo14bob2o3b2obo10b2o4b4obob4o4b2o10b
ob2o3b2obo14bo4b2o7bobo$71b4o2b2o5bobo6b3o10b2o7b2o8b2obo2b3o2b2ob2o2b
3o2bob2o8b2o7b2o10b3o6bobo5b2o2b4o$70b3obo8bo12bo7b4o2bobo2b4o4bo2bobo
b2o3bobobobo3b2obobo2bo4b4o2bobo2b4o7bo12bo8bob3o$69b2o6b2o4bo8b2obo7b
2obobobobobobob2o3b2obobobo2bob2obob2obo2bobobob2o3b2obobobobobobob2o
7bob2o8bo4b2o6b2o$70bo6b2o4bo7bo10b2o3b2obobob2o3b2obobobobobob2obo5bo
b2obobobobobob2o3b2obobob2o3b2o10bo7bo4b2o6bo$69b2o5bobo6b3o6b2o6bo2b
2obobobobob2o2bobobobobobobo11bobobobobobobo2b2obobobobob2o2bo6b2o6b3o
6bobo5b2o$75bo12bo3bo3bo5bobobobobobobobobobobobobobobobobo3bo3bobobob
obobobobobobobobobobobobobo5bo3bo3bo12bo$69b2o4bo8b2obo5bo5b2obobobobo
bobobobobobobobobobobobobobo3bobobobobobobobobobobobobobobobobobob2o5b
o5bob2o8bo4b2o$69b2o4bo7bo12bo3bobobobobobobobobobobobobobobobobobobo
3bobobobobobobobobobobobobobobobobobobo3bo12bo7bo4b2o$68bobo6b3o6b2o5b
o2b3obobobobobobobobobobobobobobobobobobob2ob2obobobobobobobobobobobob
obobobobobobob3o2bo5b2o6b3o6bobo$67bo12bo3bo3bo4b2obobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob2o
4bo3bo3bo12bo$67bo8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobob
o2bob3obo2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo$67bo
7bo12bo3bobobobobobobobobobobobobobobobobobobobobo11bobobobobobobobobo
bobobobobobobobobobobobo3bo12bo7bo$69b3o6b2o5bo2b3obobobobobobobobobob
obobobobobobobobobo2bob11obo2bobobobobobobobobobobobobobobobobobobob3o
2bo5b2o6b3o$72bo3bo3bo4b2obobobobobobobobobobobobobobobobobobobobobo
19bobobobobobobobobobobobobobobobobobobobobob2o4bo3bo3bo$68b2obo5bo5b
2obobobobobobobobobobobobobobobobobobobobo2bob19obo2bobobobobobobobobo
bobobobobobobobobobobob2o5bo5bob2o$41b2ob3o8b3ob2o6bo12bo3bobobobobobo
bobobobobobobobobobobobobobobo27bobobobobobobobobobobobobobobobobobobo
bobo3bo12bo6b2ob3o8b3ob2o$41b2o4b2o4b2o4b2o9b2o5bo2b3obobobobobobobobo
bobobobobobobobobobobo2bob27obo2bobobobobobobobobobobobobobobobobobobo
b3o2bo5b2o9b2o4b2o4b2o4b2o$40bo2bobo3bo2bobob3o9bo3bo4b2obobobobobobob
obobobobobobobobobobobobobobo35bobobobobobobobobobobobobobobobobobobob
obob2o4bo3bo9b3obobo2bo3bobo2bo$47b3o2bob2ob2o2b2o6bo5b2obobobobobobob
obobobobobobobobobobobobobo2bob35obo2bobobobobobobobobobobobobobobobob
obobobob2o5bo6b2o2b2ob2obo2b3o$49b2o8bob3obo6bo3bobobobobobobobobobobo
bobobobobobobobobobo43bobobobobobobobobobobobobobobobobobobobobo3bo6bo
b3obo8b2o$49bo4bobo4bob4o2bo2b3obobobobobobobobobobobobobobobobobobobo
2bob43obo2bobobobobobobobobobobobobobobobobobobob3o2bo2b4obo4bobo4bo$
50b2o2b3o2bo6bo2b2obobobobobobobobobobobobobobobobobobobobobo51bobobob
obobobobobobobobobobobobobobobobobob2o2bo6bo2b3o2b2o$52b3ob3o3bo3bobob
obobobobobobobobobobobobobobobobobobobo2bob51obo2bobobobobobobobobobob
obobobobobobobobobobobo3bo3b3ob3o$53b2obo5bo3bobobobobobobobobobobobob
obobobobobobobobobo59bobobobobobobobobobobobobobobobobobobobobobo3bo5b
ob2o$51bo4bo11bobobobobobobobobobobobobobobobobobobo2bob59obo2bobobobo
bobobobobobobobobobobobobobobo11bo4bo$52bobo10b2obobobobobobobobobobob
obobobobobobobobo67bobobobobobobobobobobobobobobobobobobob2o10bobo$65b
2obobobobobobobobobobobobobobobobobo2bob67obo2bobobobobobobobobobobobo
bobobobobob2o$17bo12bo35bobobobobobobobobobobobobobobobobobo75bobobobo
bobobobobobobobobobobobobobo35bo12bo$9b2o4b4o9b4o6bo6bo21b2obobobobobo
bobobobobobobobobo2bob75obo2bobobobobobobobobobobobobobob2o21bo6bo6b4o
9b4o4b2o$8b2o4b2o3bo7b2o3bo4bobo4b4o18b3obobobobobobobobobobobobobobo
83bobobobobobobobobobobobobobob3o18b4o4bobo4bo3b2o7bo3b2o4b2o$8b2ob2o
4bobo5bo2bo3bo3bo3bo2bo3b2o11b3o4b4obobobobobobobobobobobo2bob83obo2bo
bobobobobobobobobobob4o4b3o11b2o3bo2bo3bo3bo3bo2bo5bobo4b2ob2o$5bob2o
2bobob4o5bo2bo6bo8bo5bo8b2obo8bobobobobobobobobobobobo91bobobobobobobo
bobobobobo8bob2o8bo5bo8bo6bo2bo5b4obobo2b2obo$b3ob2o4bo4b2o6bo7bo2b2o
2bobobob2obobo4bobo3bob2o5bobobobobobobobobobo2bob91obo2bobobobobobobo
bobobo5b2obo3bobo4bobob2obobobo2b2o2bo7bo6b2o4bo4b2ob3o$o6bob5obo3bo6b
o7bob2obo5b2o4b2obob5o2bobobo2bobobobobobobobobobo99bobobobobobobobobo
bo2bobobo2b5obob2o4b2o5bob2obo7bo6bo3bob5obo6bo$b2o3bo4bo2bo4b2o3bo5b
2ob2o6bobo3b2o2b2o5b2o2bo2b2obobobobobobobobobo2bob99obo2bobobobobobob
obobob2o2bo2b2o5b2o2b2o3bobo6b2ob2o5bo3b2o4bo2bo4bo3b2o$22bobobo3bob2o
bob3o4bob3o3bobob2o4b2obo2bobobobobobobobobo107bobobobobobobobobo2bob
2o4b2obobo3b3obo4b3obob2obo3bobobo$19bo3bo3b2o8bobobo2bobo2bo15bob2obo
bobobobobo2bob107obo2bobobobobobob2obo15bo2bobo2bobobo8b2o3bo3bo$23bob
ob2o3b2obo3bob2obo3b5o12b2o3bobobobobobo115bobobobobobo3b2o12b5o3bob2o
bo3bob2o3b2obobo$18b5o2bo3b2ob2o5b2obo5bo2bo17b2obobobo2bob115obo2bobo
bob2o17bo2bo5bob2o5b2ob2o3bo2b5o$17b2o5bo8b4obobobobo8b3o3b4o7bobobobo
123bobobobo7b4o3b3o8bobobobob4o8bo5b2o$24bo4bo2bobobo2bo2bob2ob2o2b2o
4b3ob2o3b3obobo2bob123obo2bobob3o3b2ob3o4b2o2b2ob2obo2bo2bobobo2bo4bo$
21b5o2b2obo2b3o2bo2bo4b5ob2o2bo6b3obobobo131bobobob3o6bo2b2ob5o4bo2bo
2b3o2bob2o2b5o$19bo3bo4b2o5bobo8b2o2b2o3bo2b2o2bobo3bo2bob131obo2bo3bo
bo2b2o2bo3b2o2b2o8bobo5b2o4bo3bo$17b3o8b2o2bobo10b2o8b2o5bobobo143bobo
bo5b2o8b2o10bobo2b2o8b3o$13b2ob2o3bo5bo18bo3bo3b3o2b2obo6b139o6bob2o2b
3o3bo3bo18bo5bo3b2ob2o$13b2o2bo2bo5b2o17b2o4bo4bobobobo2bobo141bobo2bo
bobobo4bo4b2o17b2o5bo2bo2b2o$12bo2bo41b2obobo4b143o4bobob2o41bo2bo$56b
2o2bo4bobo141bobo4bo2b2o$33b3ob2obo9b2o4b3o4b2o4bob135obo4b2o4b3o4b2o
9bob2ob3o$29bob2o4b2ob2o8b2ob2o7bo3b2obo137bob2o3bo7b2ob2o8b2ob2o4b2ob
o$28b3o3bo3b2o2bo7b2o2bo2bo4bobob2obo2b133o2bob2obobo4bo2bo2b2o7bo2b2o
3bo3b3o$27bo3bo4bo17b2obo2bo3bo2bobobo133bobobo2bo3bo2bob2o17bo4bo3bo$
28bo8bo5b2o3b2o2b6o2bo6bobobob131obobobo6bo2b6o2b2o3b2o5bo8bo$36b2o2bo
2bob5o2b2o3b3o5bobobobo133bobobobo5b3o3b2o2b5obo2bo2b2o$40b2obo2bo14b
2ob2obobobobob127obobobobob2ob2o14bo2bob2o$43bob5o9b2o3b2obobobobo129b
obobobob2o3b2o9b5obo$40b2obobobo2bo6b3o2bo2b3obobobo2b125o2bobobob3o2b
o2b3o6bo2bobobob2o$47b2obo2b3ob2ob2ob3obobobobobo125bobobobobob3ob2ob
2ob3o2bob2o$46b2o2bobo7bo6bobobobobob123obobobobobo6bo7bobo2b2o$44bo4b
o4b2obobo6bo2bobobobo125bobobobo2bo6bobob2o4bo4bo$43b2obo2bob2o13b2obo
bobobobob119obobobobobob2o13b2obo2bob2o$42bo2bo2b2o19bobobobobo121bobo
bobobo19b2o2bo2bo$43bo4b2o19bobobobobo2b117o2bobobobobo19b2o4bo$59b3o
5bobobobobobobo117bobobobobobobo5b3o$58bo7b3o2bobobobobob115obobobobob
o2b3o7bo$56b3o4bo2bo2b2o2bobobobo117bobobobo2b2o2bo2bo4b3o$52b3obobob
5obo5bo2bobobobob111obobobobo2bo5bob5obobob3o$51bo9bo2bobo4b2o2bobobob
o113bobobobo2b2o4bobo2bo9bo$52bo2bo10bob4o3bobobobo2b109o2bobobobo3b4o
bo10bo2bo$56bo9bo4bo2b2obobobobo109bobobobob2o2bo4bo9bo$54b2o11bo6b2ob
obobobob107obobobobob2o6bo11b2o$69b2o5bo2bobobo109bobobo2bo5b2o$74bo2b
obobobobob103obobobobobo2bo$75bo5bobobo105bobobo5bo$81bobobo2b101o2bob
obo$81bobobobo101bobobobo$78b2obobobobob99obobobobob2o$78b2obobobobo
101bobobobob2o$81bobobobobob95obobobobobo$80bo2bobobobo97bobobobo2bo$
78b3o2bobobobo2b93o2bobobobo2b3o$82b2obobobobo93bobobobob2o$85bobobobo
b91obobobobo$81bo3bobobobo93bobobobo3bo$81bo2b3o2bobobob87obobobo2b3o
2bo$82bo3b2obobobo89bobobob2o3bo$89bobobo2b85o2bobobo$86b2obobobobo85b
obobobob2o$85bo3bobobobob83obobobobo3bo$85bo2bo2bobobo85bobobo2bo2bo$
84b2o2bo2bobobobob79obobobobo2bo2b2o$83bob2o2bobobobobo81bobobobobo2b
2obo$82bo3bob3o2bobobo2b77o2bobobo2b3obo3bo$82bo7bob2obobobo77bobobob
2obo7bo$85bo2bob2obobobobob75obobobobob2obo2bo$82b2o9bobobobo77bobobob
o9b2o$81bo13bobobobob71obobobobo13bo$81b2o7bobobo2bobobo73bobobo2bobob
o7b2o$82b3o5bo6bobobo2b69o2bobobo6bo5b3o$82bo2bo3bobo5bobobobo69bobobo
bo5bobo3bo2bo$86bo4bo2b2obobobobob67obobobobob2o2bo4bo$94b2obobobobo
69bobobobob2o$81b2obobo10bobobobobob63obobobobobo10bobob2o$81b2o3bo9bo
2bobobobo65bobobobo2bo9bo3b2o$80bo2bo10b3o2bobobobo2b61o2bobobobo2b3o
10bo2bo$86b5o7b2obobobobo61bobobobob2o7b5o$85bobob2o10bobobobob59obobo
bobo10b2obobo$84b2o4bo6bo3bobobobo61bobobobo3bo6bo4b2o$84b3o3b2o5bo2b
3o2bobobob55obobobo2b3o2bo5b2o3b3o$83bo3bobo2bo5bo3b2obobobo57bobobob
2o3bo5bo2bobo3bo$82bo2bob5o13bobobo2b53o2bobobo13b5obo2bo$84bo4bob2o9b
2obobobobo53bobobobob2o9b2obo4bo$81b4obob2o2b2o7bo3bobobobob51obobobob
o3bo7b2o2b2obob4o$80b2o8bo10bo2bo2bobobo53bobobo2bo2bo10bo8b2o$100b2o
2bo2bobobobob47obobobobo2bo2b2o$91b2o6bob2o2bobobobobo49bobobobobo2b2o
bo6b2o$87b3ob2o5bo3bob3o2bobobo2b45o2bobobo2b3obo3bo5b2ob3o$83bob2obo
9bo7bob2obobobo45bobobob2obo7bo9bob2obo$82b3o4bo11bo2bob2obobobobob43o
bobobobob2obo2bo11bo4b3o$81bo3bo12b2o9bobobobo45bobobobo9b2o12bo3bo$
82bo14bo13bobobobob39obobobobo13bo14bo$97b2o7bobobo2bobobo41bobobo2bob
obo7b2o$98b3o5bo6bobobo2b37o2bobobo6bo5b3o$98bo2bo3bobo5bobobobo37bobo
bobo5bobo3bo2bo$102bo4bo2b2obobobobob35obobobobob2o2bo4bo$110b2obobobo
bo37bobobobob2o$97b2obobo10bobobobobob31obobobobobo10bobob2o$97b2o3bo
9bo2bobobobo33bobobobo2bo9bo3b2o$96bo2bo10b3o2bobobobo2b29o2bobobobo2b
3o10bo2bo$102b5o7b2obobobobo29bobobobob2o7b5o$101bobob2o10bobobobob27o
bobobobo10b2obobo$100b2o4bo6bo3bobobobo29bobobobo3bo6bo4b2o$100b3o3b2o
5bo2b3o2bobobob23obobobo2b3o2bo5b2o3b3o$99bo3bobo2bo5bo3b2obobobo25bob
obob2o3bo5bo2bobo3bo$98bo2bob5o13bobobo2b21o2bobobo13b5obo2bo$100bo4bo
b2o9b2obobobobo21bobobobob2o9b2obo4bo$97b4obob2o2b2o6b3ob2obobobob19ob
obobob2ob3o6b2o2b2obob4o$96b2o8bo5b2ob2o3bob2obobo21bobob2obo3b2ob2o5b
o8b2o$112b2o2bo2bo3bobobobob15obobobobo3bo2bo2b2o$107b2o2bo2bo7bo2bobo
bo17bobobo2bo7bo2bo2b2o$103b3ob2o18bobo2b13o2bobo18b2ob3o$99bob2obo15b
2o7bobo13bobo7b2o15bob2obo$98b3o4bo8b2o4bob3ob2obobob11obobob2ob3obo4b
2o8bo4b3o$97bo3bo12b2ob2o4b2o4bobo6bo6bobo4b2o4b2ob2o12bo3bo$98bo14bo
3b2o8bobobobobo5bobobobobo8b2o3bo14bo$117b2o7bo4bobo2b2ob2o2bobo4bo7b
2o$127b2obo15bob2o!
The trick is in the conversion of vertical stripes to horizontal, and then horizontal stripes to vertical, allowing the outer edges of the ship to primarily be supported by period-3 with-the-grain components.
How can a greyship change its stripes?
You may be familiar with the classic 2c/3 signal traveling along a diagonal seam between horizontal and vertical stripes. What you may not realize is that the standard 2c/3 signal is actually made up of two "half signals". On July 24, 1997 Dean Hickerson found a strange p9 signal injector that seemed to inject two signal-like perturbations each period:
Code: Select all
#C A strange p9 signal injector by Dean Hickerson, July 24, 1997
x = 28, y = 29, rule = B3/S23
obo3b2o$2obobo2bo$3bob2obo$3o2bo2bob2o$o2bo3b2obo$b2o8bo$7b4o$b2o3bo$b
o2bo2b6o$3b2obo6bo$4bobo2b5o$2bobobobo7bo$2b2o2bobo2b6o$6bobobo$7b2obo
2b6o$10bobo6bo$10bobo2b5o$11b2obo7bo$14bo2b6o$14bobo8bo$13b2obo2b7o$
16bobo$16bobo2b5o$17b2obo4bo$20bo2bo$20bobob4o$19b2obo4bo$23b3o$25b2o!
These two perturbations are actually oppositely oriented half signals. Unlike a proper signal, a half signal modifies the wire it travels on; it moves the seam between horizontal and vertical stripes to a new location. Below is a comparison of a standard signal and a half signal:
Code: Select all
#C A standard signal (left) and a half signal (right).
#C Notice that the half signal moves the seam between
#C horizontal and vertical stripes upward by 2 cells.
x = 98, y = 40, rule = B3/S23
6b2o2b2o2b2o50b2o2b2o2b2o$6b2o2b2o2b2o50b2o2b2o2b2o2$4b14o46b12o$3bo
14bo44bo12bo$3bobob12o44bob12o$2obobo15bo38b2obo15bo$2obobo2b14o38b2ob
o2b14o$3bobobo55bobo$3bobobo2b14o39bobo2b14o$2obobobobo14bo35b2obobobo
14bo$2obobobobo2b13o35b2obobobo2b13o$3bobobobobo15bo35bobobobo15bo$3bo
bobobobo2b14o35bobobobo2b14o$2obobobobobobo46b2obobobobobo$2obobobobob
obo2b14o30b2obobobobobo2b14o$3bobobobobobobo14bo32bobobobobobo14bo$3bo
bobobobobobo2b13o32bobobobobobo2b13o$4b2obobobobobobo15bo28b2obobobobo
bobo15bo$7bobobobobobo2b14o31bobobobobobo2b14o$7bobobobobobobo45bobobo
bobobobo$6b2obobobobobobo2b14o28b2obobobobobobo2b14o$9bobobobobobobo
14bo30bobobobobobobo14bo$9bobobobobobobo2b13o30bobobobobobobo2b13o$10b
2obobobobobobo15bo28b2obobobobobobo15bo$13bobobobobobo2b14o31bobobobob
obo2b14o$13bobobobobobobo45bobobobobobobo$12b2obobobobobobo2b2o2b2o2b
2o32b2obobobobobobo2b2o2b2o2b2o$15bobobobobobobobo2b2o2b2o35bobobobobo
bobobo2b2o2b2o$15bobobobobobob2o44bobobobobobob2o$16b2obobobobo48b2obo
bobobo$19bobobobo51bobobobo$19bobobobob2o48bobobobob2o$18b2obobobob2o
47b2obobobob2o$21bobobo53bobobo$21bobobo53bobobo$22b2obob2o51b2obob2o$
25bob2o54bob2o$25bo57bo$24b2o56b2o!
Like a standard signal, these half signals can be mirrored across the diagonal stripe seam. Two oppositely oriented half signals are sufficient to put the seam back where it started. This is displayed below, with the half signals separated by a noticeable distance:
Code: Select all
#C Two oppositely oriented half signals do not move
#C the seam between horizontal and vertical stripes.
x = 40, y = 40, rule = B3/S23
6b2o2b2o2b2o$6b2o2b2o2b2o2$4b14o$3bo14bo$3bobo2b11o$2obobobo13bo$2obob
obo2b12o$3bobobobo$3bobobobo2b12o$2obobobobobo12bo$2obobobobobob12o$3b
obobobobo15bo$3bobobobobo2b14o$2obobobobobobo$2obobobobobobo2b14o$3bob
obobobobobo14bo$3bobobobobobobo2b13o$4b2obobobobobobo15bo$7bobobobobob
o2b14o$7bobobobobobobo$6b2obobobobobobo2b14o$9bobobobobobobo14bo$9bobo
bobobobobo2b13o$10b2obobobobobobo15bo$13bobobobobobo2b14o$13bobobobobo
bobo$12b2obobobobobobo2b2o2b2o2b2o$15bobobobobobobobo2b2o2b2o$15bobobo
bobobob2o$16b2obobobobo$19bobobobo$19bobobobob2o$18b2obobobob2o$21bobo
bo$21bobobo$22b2obob2o$25bob2o$25bo$24b2o!
By manually advancing only the second (i.e., upper left most) half signal by 9 generations, the two now-adjacent half signals become one standard signal! But we don't need or want a proper signal here. For making greyships, the movement of the seam is the desirable outcome, it allows the seam to move with the potential ship, so we want subsequent half signals to have the same orientation.
This seam-moving half signal idea was first developed in a discussion between Hartmut Holzwart and Jason Summers from November 2005 to January 2006 after Holzwart incidentally found a 2c/4 seam-moving reaction in an ordinary against-the-grain greyship search. By placing half signals at varying distances, different seam-moving speeds can be achieved. Different placements also need to be used depending on whether the conversion is vertical-to-horizontal (v-to-h) or horizontal-to-vertical (h-to-v). Here are the placements for 2c/6 movement:
Code: Select all
#C 2c/6 stripe converters (travel direction is upward)
#C top left: v-to-h converter
#C bottom left: h-to-v converter, homogeneous
#C bottom middle: h-to-v converter, heterogeneous
#C bottom right: h-to-v converter, heterogeneous
x = 155, y = 89, rule = B3/S23
4bo3bo3bo3bo3bo3bo3bo3bo$3bobobobobobobobobobobobobobobobob2o$3bobobob
obobobobobobobobobobobobobo$b2o2bobobobobobobobobobobobobobobobo$o4bob
obobobobobobobobobobobobobobob2o$b4o2bobobobobobobobobobobobobobobo2bo
$7bobobobobobobobobobobobobobobobo$b6o2bobobobobobobobobobobobobobob2o
$o10bobobobobobobobobobobobobo$b10o2bobobobobobobobobobobobob2o$15bobo
bobobobobobobobobob2o$b14o2bobobobobobobobobobo$o18bobobobobobobobobo$
b18o2bobobobobobobobob2o$23bobobobobobobob2o$b22o2bobobobobobo$o26bobo
bobobo$b26o2bobobobob2o$31bobobob2o$b30o2bobo$o34bo$b34o2$3b2o2b2o2b2o
2b2o2b2o2b2o2b2o2b2o$3b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o12$3b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o26b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o30b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o$3b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o26b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2$b34o22b34o26b34o$o34bo20b
o34bo24bo34bo$b32o2bo21b33obo25b33obo$33bobob2o52bob2o56bob2o$b31obobo
b2o18b31obobob2o22b30o2bobob2o$o32bobo20bo32bobo24bo30bobobo$b30o2bobo
21b30o2bobo25b31obobo$31bobobob2o48bobobob2o52bobobob2o$b28o2bobobob2o
18b29obobobob2o22b29obobobob2o$o28bobobobo20bo30bobobo24bo30bobobo$b
27obobobobo21b27obobobobo25b26o2bobobobo$29bobobobob2o46bobobobob2o48b
obobobobob2o$b26o2bobobobob2o18b26o2bobobobob2o22b27obobobobob2o$o26bo
bobobobo20bo26bobobobobo24bo26bobobobobo$b24o2bobobobobo21b25obobobobo
bo25b25obobobobobo$25bobobobobobob2o44bobobobobob2o48bobobobobob2o$b
23obobobobobobob2o18b23obobobobobobob2o22b22o2bobobobobobob2o$o24bobob
obobobo20bo24bobobobobobo24bo22bobobobobobobo$b22o2bobobobobobo21b22o
2bobobobobobo25b23obobobobobobo$23bobobobobobobob2o40bobobobobobobob2o
44bobobobobobobob2o$b20o2bobobobobobobob2o18b21obobobobobobobob2o22b
21obobobobobobobob2o$o20bobobobobobobobo20bo22bobobobobobobo24bo22bobo
bobobobobo$b19obobobobobobobobo21b19obobobobobobobobo25b18o2bobobobobo
bobobo$21bobobobobobobobob2o38bobobobobobobobob2o40bobobobobobobobobob
2o$b18o2bobobobobobobobob2o18b18o2bobobobobobobobob2o22b19obobobobobob
obobob2o$o18bobobobobobobobobo20bo18bobobobobobobobobo24bo18bobobobobo
bobobobo$b16o2bobobobobobobobobo21b17obobobobobobobobobo25b17obobobobo
bobobobobo$17bobobobobobobobobobob2o36bobobobobobobobobob2o40bobobobob
obobobobob2o$b15obobobobobobobobobobob2o18b15obobobobobobobobobobob2o
22b14o2bobobobobobobobobobob2o$o16bobobobobobobobobobo20bo16bobobobobo
bobobobobo24bo14bobobobobobobobobobobo$b14o2bobobobobobobobobobo21b14o
2bobobobobobobobobobo25b15obobobobobobobobobobo$15bobobobobobobobobobo
bob2o32bobobobobobobobobobobob2o36bobobobobobobobobobobob2o$b12o2bobob
obobobobobobobobob2o18b13obobobobobobobobobobobob2o22b13obobobobobobob
obobobobob2o$o12bobobobobobobobobobobobo20bo14bobobobobobobobobobobo
24bo14bobobobobobobobobobobo$b11obobobobobobobobobobobobo21b11obobobob
obobobobobobobobo25b10o2bobobobobobobobobobobobo$13bobobobobobobobobob
obobob2o30bobobobobobobobobobobobob2o32bobobobobobobobobobobobobob2o$b
10o2bobobobobobobobobobobobob2o18b10o2bobobobobobobobobobobobob2o22b
11obobobobobobobobobobobobob2o$o10bobobobobobobobobobobobobo20bo10bobo
bobobobobobobobobobobo24bo10bobobobobobobobobobobobobo$b8o2bobobobobob
obobobobobobobo21b9obobobobobobobobobobobobobo25b9obobobobobobobobobob
obobobo$9bobobobobobobobobobobobobobob2o28bobobobobobobobobobobobobob
2o32bobobobobobobobobobobobobob2o$b7obobobobobobobobobobobobobobob2o
18b7obobobobobobobobobobobobobobob2o22b6o2bobobobobobobobobobobobobobo
b2o$o8bobobobobobobobobobobobobobo20bo8bobobobobobobobobobobobobobo24b
o6bobobobobobobobobobobobobobobo$b6o2bobobobobobobobobobobobobobo21b6o
2bobobobobobobobobobobobobobo25b7obobobobobobobobobobobobobobo$7bobobo
bobobobobobobobobobobobob2o24bobobobobobobobobobobobobobobob2o28bobobo
bobobobobobobobobobobobob2o$b4o2bobobobobobobobobobobobobobobob2o18b4o
2bobobobobobobobobobobobobobobob2o22b4o2bobobobobobobobobobobobobobobo
b2o$o4bobobobobobobobobobobobobobobobo20bo4bobobobobobobobobobobobobob
obobo24bo4bobobobobobobobobobobobobobobobo$obo2bobobobobobobobobobobob
obobobobo20bobo2bobobobobobobobobobobobobobobobo24bobo2bobobobobobobob
obobobobobobobobo$bobobobobobobobobobobobobobobobobobob2o18bobobobobob
obobobobobobobobobobobobob2o22bobobobobobobobobobobobobobobobobobob2o$
2b2obobobobobobobobobobobobobobobobob2o19b2obobobobobobobobobobobobobo
bobobob2o23b2obobobobobobobobobobobobobobobobob2o$6bo3bo3bo3bo3bo3bo3b
o3bo27bo3bo3bo3bo3bo3bo3bo3bo31bo3bo3bo3bo3bo3bo3bo3bo!
Notice that there is only one 2c/6 v-to-h converter, but there are three h-to-v converters. The bottom left is the "expected" h-to-v converter, where individual half signals all have the same orientation. By contrast, the other two h-to-v converters each have three times as many half signals as the first fitting on the same seam, two with the same orientation and one with the opposite orientation. There's nothing special about any of these h-to-v converters in particular. Amling's ship just happens to use the middle converter.
Of course, it isn't enough to just have these stripe converters. We need to connect them somehow. The difficulty is that these stripe converters are period 6, and 2c/6 searches have little chance of succeeding both because 2c/6 components are rarer than period-3 components and because p6 searches inherently take longer than p3 searches. On May 1, 2021 Holzwart managed to find the symmetric back end shown in the final spaceship, but the back end is almost always the easy part.
Using powerful new search tools, Keith Amling was able to reduce the side and front connection problems from p6 to p3 and then solved them at the lower period. On close inspection, you should be able to see that virtually no part of the connecting components has period 6. It isn't just the period reduction that's impressive here. It would still be quite difficult to complete the p3 parts using previous tools even if the period reduction were given.