Also if your goal is to maximize the ratio of head velocity to tail velocity, then an appropriately modified HBK could take the cake - it's allowed to sit still for as long as it takes the signal to travel. Put one in front at the breakneck speed of (6,3)c/245912, and have it leave its oblique trail of blinkers instead of cleaning it up. Then put one in the back with the top-right piece moved arbitrarily far from the HBs (I think that works?) and which cleans up the blinkers from the front one, and you have a growing spaceship whose rear moves whatever factor you want slower than its head. Plus, it's oblique!
But it won't be the fastest-growing because the head isn't c/2 anymore.
I guess you could have two c/2 orthogonal puffers and a signal that ping-pongs between their debris, which is slower depending on how far apart they are. That could be arbitrarily slow and have a c/2 head.
Edit: it actually has existed for a long time, in jslife-interactions. (Everything in that folder is awesome).
Code: Select all
x = 219, y = 150, rule = B3/S23
73b6o$73bo5bo$73bo39b3o$35b2o25b2o10bo4bo16b2o14b5o$33bo4bo22b2ob3o9b
2o4b5o8b2ob4o9b2ob3o$32bo29b5o15bo4bo8b6o10b2o$32bo5bo11b4o9b3o16bo14b
4o$22b3o7b6o6bo5bo3bo28bo3bo$21b5o16bo3bo3bo34bo7b2o36b3o$20b2ob3o15bo
9bo15bo23bo40b2o$10bo2bo7b2o18bo4bo6b2o11b3o6b2o13bo6bo9b2o17bobo$9bo
31b5o11b3o5b2o2bo5b2o13bo8bo12b2o14bo$9bo3bo20b3o13b2o3b2o3bo5b3o21b8o
bo7b2o3b2o4bo9bo$9b4o21bo2bo11b2ob3obo2bo7b2o26b2o8bob2o8bobo4bo2bo$
20bo16bo12b9o45b3o10bobo5bo$18b2obo7bo3b4o14b4o21bo41bo$10b3o10bo4bo3b
o42bo15b2o$9b5o9bo5bobo3bo39b3o12b2ob2o$8b2ob4o5bob2o7bo59b4o57bo$9b2o
5b2o2bo11bo22b6o31b2o3b6o47bobo$21bo10bo2bo19bo5bo35bo5bo47b2o$33bo21b
o41bo$17b2o37bo4bo36bo4bo$15bo4bo37b2o24bo15b2o$14bo68bo$14bo5bo62b3o$
14b6o20bo15b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o6bo7b2o14b2o14b2o$40b
2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o4bobo7b2o14b2o14b2o$175b2o$
40b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o$14b6o20bo
15b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o$14bo5bo$14bo
201bo$15bo4bo72bo15bo15bo15bo15bo15bo15bo25b3o$17b2o73bobo13bobo13bobo
13bobo13bobo13bobo13bobo10b2o2b2o8bob2o$33bo58bobo13bobo13bobo13bobo
13bobo13bobo13bobo10bo4bo9b3o$21bo10bo2bo57bo15bo15bo15bo15bo15bo15bo
12b4o10b2o$9b2o5b2o2bo11bo24b2o29bobo$8b2ob4o5bob2o7bo24b2ob4o25bo115b
2o$9b5o9bo5bobo3bo21b6o25bo35b2o77bobo$10b3o10bo4bo3bo25b4o18b2o40bo4b
o76bo$18b2obo7bo3b4o42b2o40bo56b2o$20bo16bo14b2o21b3o2bo40bo5bo49bobo$
9b4o21bo2bo12bo4bo8bo9bo3bo37b2o3b6o52bo$9bo3bo20b3o12bo13b3o12bo36b4o
$9bo31b5o3bo6bo6bo2bo6bo4bo35b2ob2o$10bo2bo7b2o18bo4bo2b8o7b3o6bo2bo
38b2o77b3o$20b2ob3o15bo12b2o7b2o9bo69bo49bo$21b5o16bo3bo14bobo59bo6b2o
11bobo49bo$22b3o7b6o6bo16bobo55b6o8bo9bobo8b2o$32bo5bo11b2o17bo44b8o3b
o5b2ob2o2b2o4bo8bobo11b2o$32bo16b2ob2o15bo44bo8b2o7b3o3b2o15bo9bo4bo$
33bo4bo11b4o10b3o47bo6b3o40bo$35b2o14b2o10b5o47bo5b2o41bo5bo$62b2ob3o
49b2o45b6o16b3o$63b2o121bo$121b4o62bo$120b6o10b2o$119b2ob4o9b2ob3o19b
4o$120b2o14b5o18b6o8b2o$137b3o18b2ob3obo6bo2bo$159b2o3b2o6bo2b4o$174bo
2bob2o7b2o$162b2o6b3o3b2o3bo6b2o$160bo9b2o5b2ob2o$159bo17b3o2bo11bo$
159bo3bo18bo9bo3bo$159b4o9b3o6bo9bo$171b5o15bo4bo$170b2ob3o9b2o4b5o$
171b2o10bo4bo$182bo$182bo5bo$182b6o3$174b6o$174bo5bo$174bo$163b2o10bo
4bo$162b2ob3o9b2o4b5o$163b5o15bo4bo$151b4o9b3o6bo9bo$151bo3bo18bo9bo3b
o$151bo17b3o2bo11bo$152bo9b2o5b2ob2o$154b2o6b3o3b2o3bo6b2o$166bo2bob2o
7b2o$151b2o3b2o6bo2b4o$129b3o18b2ob3obo6bo2bo$112b2o14b5o18b6o8b2o$
111b2ob4o9b2ob3o19b4o$112b6o10b2o$113b4o62bo$55b2o121bo$54b2ob3o49b2o
45b6o16b3o$27b2o14b2o10b5o47bo5b2o41bo5bo$25bo4bo11b4o10b3o47bo6b3o40b
o$24bo16b2ob2o15bo44bo8b2o7b3o3b2o15bo9bo4bo$24bo5bo11b2o17bo44b8o3bo
5b2ob2o2b2o4bo8bobo11b2o$14b3o7b6o6bo16bobo55b6o8bo9bobo8b2o$13b5o16bo
3bo14bobo59bo6b2o11bobo49bo$12b2ob3o15bo12b2o7b2o9bo69bo49bo$2bo2bo7b
2o18bo4bo2b8o7b3o6bo2bo38b2o77b3o$bo31b5o3bo6bo6bo2bo6bo4bo35b2ob2o$bo
3bo20b3o12bo13b3o12bo36b4o$b4o21bo2bo12bo4bo8bo9bo3bo37b2o3b6o52bo$12b
o16bo14b2o21b3o2bo40bo5bo49bobo$10b2obo7bo3b4o42b2o40bo56b2o$2b3o10bo
4bo3bo25b4o18b2o40bo4bo76bo$b5o9bo5bobo3bo21b6o25bo35b2o77bobo$2ob4o5b
ob2o7bo24b2ob4o25bo115b2o$b2o5b2o2bo11bo24b2o29bobo$13bo10bo2bo57bo15b
o15bo15bo15bo15bo15bo12b4o$25bo58bobo13bobo13bobo13bobo13bobo13bobo13b
obo10bo4bo$9b2o73bobo13bobo13bobo13bobo13bobo13bobo13bobo10b2o2b2o$7bo
4bo72bo15bo15bo15bo15bo15bo15bo$6bo$6bo5bo$6b6o20bo15b2o14b2o14b2o14b
2o14b2o14b2o14b2o14b2o14b2o14b2o14b2o$32b2o14b2o14b2o14b2o14b2o14b2o
14b2o14b2o14b2o14b2o14b2o14b2o$167b2o$32b2o14b2o14b2o14b2o14b2o14b2o
14b2o14b2o14b2o4bobo7b2o14b2o14b2o$6b6o20bo15b2o14b2o14b2o14b2o14b2o
14b2o14b2o14b2o6bo7b2o14b2o14b2o$6bo5bo62b3o$6bo68bo$7bo4bo37b2o24bo
15b2o$9b2o37bo4bo36bo4bo$25bo21bo41bo$13bo10bo2bo19bo5bo35bo5bo47b2o$b
2o5b2o2bo11bo22b6o31b2o3b6o47bobo$2ob4o5bob2o7bo59b4o57bo$b5o9bo5bobo
3bo39b3o12b2ob2o$2b3o10bo4bo3bo42bo15b2o$10b2obo7bo3b4o14b4o21bo41bo$
12bo16bo12b9o45b3o10bobo5bo$b4o21bo2bo11b2ob3obo2bo7b2o26b2o8bob2o8bob
o4bo2bo$bo3bo20b3o13b2o3b2o3bo5b3o21b8obo7b2o3b2o4bo9bo$bo31b5o11b3o5b
2o2bo5b2o13bo8bo12b2o14bo$2bo2bo7b2o18bo4bo6b2o11b3o6b2o13bo6bo9b2o17b
obo$12b2ob3o15bo9bo15bo23bo40b2o$13b5o16bo3bo3bo34bo7b2o36b3o$14b3o7b
6o6bo5bo3bo28bo3bo$24bo5bo11b4o9b3o16bo14b4o$24bo29b5o15bo4bo8b6o10b2o
$25bo4bo22b2ob3o9b2o4b5o8b2ob4o9b2ob3o$27b2o25b2o10bo4bo16b2o14b5o$65b
o39b3o$65bo5bo$65b6o!
A c/2 head, and you can move the top puffer any even number of cells vertically to get a slower tail speed. Already a solved problem without needing to resort to a Gemini

Physics: sophistication from simplicity.