Spaceship Discussion Thread

Bullet51 · Post by **Bullet51** » January 4th, 2025, 5:20 am

Is a pipsquirter spark from a 2c/5 orthogonal spaceship useful?

x = 15, y = 55, rule = B3/S23
3b3o$3bo2bo$2b2o$4bo$4bobo$3b2obobo$3b2obob2o$4b3o2bo$5b2o2b2o$5b2o$6b
obob2o$8bo2$9bo$7bobo$7bo2bo$10b2o$10b2o$5b2o3b2o$4bob2ob2o$4bo2bobo$
6b3o$7bobo$7b2o$7bo2bo$8bobo$6b4o$5b3o$4bo2bo$4b3o$4b3obo$4b6o$6bo3bo$
7b4o$7b2obo$6bo3b2o$5bobo2b3o$7b2obo$12bo$7b2o3bo$7b3o$7b5o$10bo$7b3o
2$9bo$6bo2bo$7b2o$5b3o3b2o$8b4ob2o$5bob2o4b2o$6b3o3b2o$3o9b3o$2bo9b2o$
bo! [[ STOP 12 ]]

EDIT: This 2c/5 spaceship has a larger spark and admits a tagalong:

Code: Select all

x = 24, y = 184, rule = B3/S23
15bo$14bobo$13b2ob2o$13b2o$15bo$15b4o$15bo2b2o$16b2o2bo$17b5o$19bobo$
18b2obo$19bobo$16b2obo$19bo$18b3o2$21bo$21b3o$18bo$16b2o$16bo3bo$16bob
ob2o$20b2o$18bo$17bo2b2o$20bo$19bo$16b2o$15bo2bo$15bobo2$13bo3bo$12b2o
3bo$11b2o2bo$10bo4bo$14bo$12b2o2$11bo$10b2obo$9bo3bo$8bo2bo$7bob2o$7bo
2bo$9b3o$7bo2b2o$7bo2bo$6bo$10bo$6bob2o$7bo$8b2o$5b5o2$4bo2bo$5bo2bo$
8bo$5b2ob2o$5b2ob2o$3bo2bobo$2bo2bob2o$3bo$4bo2$b2ob2o$o3b3o$3bo3bo$3b
2ob2o$3bob3o$5bo2bo$bo3bo$2bo$5bobo$3b2o2b2o$2bo3b2o$b3obo2bo$b2obo$8b
2o$4b3o2$7bo$6bobo$6bobo$9bo$8bo$7bob4o$10bo2bo$9b2o2$7b2obobo$12bo$7b
o$10bo$9bo3bo$10bob2o$8bo4bo$11bo$9bobo$11b2o$10b3o$10bobo$9b2ob2o$10b
obo$9b2ob2o$9bobobo$8bo5bo$10bobo$10bobo2$7b9o2$6bo2bo3bo2bo2$6b2ob5ob
2o$6bob2o3b2obo2$7bo3bo3bo$11bo$7b2ob3ob2o$9bo3bo$10b3o$9bo3bo$9bo$14b
o$9bobob2o$11bo$8bo3bo$13bo$7b2obo$11b3o$7bo$7bo3bo$7bo4bo$7bo$8bo3bo$
8bo2b2obo$11bo2bo$12bo2bo$10bo4b2o$10bo4bo$14b2o2$10b3o$9bo3bo$8bo5bo$
8b7o$10bobo$9b2ob2o$10bobo$7b2obobob2o$5b2obobobobob2o$5b2obobobobob2o
$4bobobobobobobobo$7b2obobob2o$5b2obobobobob2o$5bobo2bobo2bobo$3bo2bo
3bobo3bo2bo$3bob2ob3ob3ob2obo$7bobo3bobo$4b2o2b2o3b2o2b2o$4b2obo7bob2o
$4b3o9b3o$5b2o9b2o$7bo7bo$8b2o3b2o$7b2obobob2o$5bo11bo$6bob3ob3obo$6bo
9bo$7b9o$7bobo3bobo$10b3o5$10b2o$8bob2o$6b2o3b2o$5bo3bo$6bobo$6b2o$5bo
$5bo!

HartmutHolzwart · Post by **HartmutHolzwart** » January 8th, 2025, 6:50 pm

MathAndCode wrote: January 1st, 2025, 2:21 am

HartmutHolzwart wrote: January 28th, 2022, 2:55 amOn a different matter. I finally managed to complete a stretcher for the c/4 wick recently mentioned:

The solution is in no way optimzed, but it shows quite well how the branching approach works.

The twenty outermost columns on each side are unecessary.

Code: Select all

x = 163, y = 170, rule = B3/S23
24bo113bo$23bobo5b4o93b4o5bobo$22bo6b3ob3o8bo73bo8b3ob3o6bo$5b3o5b2o6b
2obo3bo4bo2bo6bobo71bobo6bo2bo4bo3bob2o6b2o5b3o$6bo5bo2b2ob3obob2o5bo
2bob2o3b2o5b3ob3o53b3ob3o5b2o3b2obo2bo5b2obob3ob2o2bo5bo$b3o6bo5bobo2b
2obob2o3bo2bob2o2bobobo6bo3bob2o45b2obo3bo6bobobo2b2obo2bo3b2obob2o2b
obo5bo6b3o$8bo2bo4bo7bobob3o3bo2b3obo7bobo5bobo43bobo5bobo7bob3o2bo3b
3obobo7bo4bo2bo$bobo3b2o2bob5o4b5o11bobob2obo3bo7b2o45b2o7bo3bob2obob
o11b5o4b5obo2b2o3bobo$4bo2b3o3bo2bob2o4bo2bo15bo2b6o4bo49bo4b6o2bo15b
o2bo4b2obo2bo3b3o2bo$4o3bo6bo10b4o7bo8bobo3b2o3b2obo43bob2o3b2o3bobo8b
o7b4o10bo6bo3b4o$2o3bo7bo10bo10b2o18b4ob2o39b2ob4o18b2o10bo10bo7bo3b2o
$6obobo3b2o12b2o5bo15bo2bob2o5bo4b2o25b2o4bo5b2obo2bo15bo5b2o12b2o3bo
bob6o$6ob2obo39b3o4bo4bo3bob5o17b5obo3bo4bo4b3o39bob2ob6o$o3bo2b2obo32b
3o2bo3b2o5bob2o2b2obobo2bo15bo2bobob2o2b2obo5b2o3bo2b3o32bob2o2bo3bo$
4bo3b2o35bo5bo9bo2bo33bo2bo9bo5bo35b2o3bo$3b2o2b2o28bo3b4o2b2o19b2o5b
2o9b2o5b2o19b2o2b4o3bo28b2o2b2o$8b2o22b2ob3o3b2o21bo3b2ob3obob2o5b2ob
ob3ob2o3bo21b2o3b3ob2o22b2o$b3ob2o3bo21b2ob2o2bo24bobobo5bo13bo5bobob
o24bo2b2ob2o21bo3b2ob3o$bo7bo19b3o3bo4b4o23bo4b2obo3bo3bo3bob2o4bo23b
4o4bo3b3o19bo7bo$2o2b2obo23bo2bo5b2o2bo13bo3b2o2bo2bo2b4o3bo3bo3b4o2b
o2bo2b2o3bo13bo2b2o5bo2bo23bob2o2b2o$2o3bo22b2obobob2o7b2o12bob2obo2b
3o5b2o11b2o5b3o2bob2obo12b2o7b2obobob2o22bo3b2o$bob2o26bob4o21b2obo4b
o9b3o5b3o9bo4bob2o21b4obo26b2obo$bo3bo20bobo2b5o9bo14b2o39b2o14bo9b5o
2bobo20bo3bo$6bo15bo3b3obobo28b2o37b2o28bobob3o3bo15bo$3bo3bo14bo7b2o
24bobobo15bo2b2ob2o2bo15bobobo24b2o7bo14bo3bo$21bobo2b2o2b2o17bob2obo
3b2o2bo11b2obo2bobo2bob2o11bo2b2o3bob2obo17b2o2b2o2bobo$6b2obo15b3o20b
2o2bob2o3b2obo11b2o2bo5bo2b2o11bob2o3b2obo2b2o20b3o15bob2o$9bo15b2o21b
4o2bo4b2obo12bo2bo5bo2bo12bob2o4bo2b4o21b2o15bo$27bo21bo2bo3b2o17bob2o
b3ob2obo17b2o3bo2bo21bo$8b3o15bo2bo16bo10bo18b3ob3ob3o18bo10bo16bo2bo
15b3o$7b4o16bobo16bo3b4obobo19bobobobobo19bobob4o3bo16bobo16b4o$7b4o18b
o16bo3b2o4bo19b2obobobob2o19bo4b2o3bo16bo18b4o$26b2ob2o15bo2b2o24bo4b
obo4bo24b2o2bo15b2ob2o$5bo19bob2o15b2ob3obo23bobobobobobobo23bob3ob2o
15b2obo19bo$4b3o19b2o15bobobo3b2o23bo3bobo3bo23b2o3bobobo15b2o19b3o$7b
o12b3o4b2obo12bo4b2obo22b2obo7bob2o22bob2o4bo12bob2o4b3o12bo$4b4o19bo
2bo18bobo22b5o5b5o22bobo18bo2bo19b4o$5bo14bo2bo6bo15b2o3bo22b5o5b5o22b
o3b2o15bo6bo2bo14bo$22bo2b3o18bo4bo23bob2ob3ob2obo23bo4bo18b3o2bo$4bo
b4o11b5obobo12b2obo28bobobo5bobobo28bob2o12bobob5o11b4obo$10bo16b3o12b
obob2o2bo22bo15bo22bo2b2obobo12b3o16bo$4bobobobo14b2ob2o13b2o4b3o23b4o
5b4o23b3o4b2o13b2ob2o14bobobobo$5b3o2bo18b2o11bo6b3o22bo3bo2bo2bo3bo22b
3o6bo11b2o18bo2b3o$8b3o31bo4bo31bobobo31bo4bo31b3o$7bobo19b2o13b2ob2o
25b2o2b2obob2o2b2o25b2ob2o13b2o19bobo$4b2o2b3o35bobo29b2o3b2o29bobo35b
3o2b2o$4b2o2bobo17b3o11b2o35b2ob2o35b2o11b3o17bobo2b2o$11bo14bob2o11b
4o73b4o11b2obo14bo$8bo2bo12bob2o13bob2o36bo36b2obo13b2obo12bo2bo$40bo
bo35b3ob3o35bobo$5bo2bo11b3o3bo14b2o37b3o37b2o14bo3b3o11bo2bo$4bobob2o
16bo15bo36b5o36bo15bo16b2obobo$3bo16bo2bob2o15b2o35bo3bo35b2o15b2obo2b
o16bo$6bo15bo3bo14bobo34bo5bo34bobo14bo3bo15bo$4b2o18bob3o50bo3bo50b3o
bo18b2o$6bo2b3o15b2o11bo37b2obob2o37bo11b2o15b3o2bo$6bo3bo17bo12b3o34b
2o3b2o34b3o12bo17bo3bo$4b2ob2o18bo15b2obo32b2ob2o32bob2o15bo18b2ob2o$
26b3o18bo67bo18b3o$28b2o17b2o32bo32b2o17b2o$4b3o20b3o16b3o29b3ob3o29b
3o16b3o20b3o$4b3o22bo16bo33b3o33bo16bo22b3o$8bo18bob2o15bo32b5o32bo15b
2obo18bo$6b3o20bo17b2o30bo3bo30b2o17bo20b3o$8b2o19b2o15bo31bo5bo31bo15b
2o19b2o$7bo38bo32bo3bo32bo38bo$10bo17bo49b2obob2o49bo17bo$8b2o19bo15b
3o30b2o3b2o30b3o15bo19b2o$10bo18bo17b3o29b2ob2o29b3o17bo18bo$10bo33b4o
bo63bob4o33bo$9bo34b3o34bo34b3o34bo$7bob2o38b3o26b3ob3o26b3o38b2obo$7b
o2bo34bo2b3o29b3o29b3o2bo34bo2bo$7bo38b4o29b5o29b4o38bo$11b2o35b2o29b
o3bo29b2o35b2o$6bo3b3o65bo5bo65b3o3bo$5b2ob2obo37bo29bo3bo29bo37bob2o
b2o$5b2o43b2o26b2obob2o26b2o43b2o$6b2o41b3o26b2o3b2o26b3o41b2o$6b2ob2o
39bo28b2ob2o28bo39b2ob2o$7bo3bo37bo63bo37bo3bo$5bo5bo36b2o31bo31b2o36b
o5bo$5bo5bo66b3ob3o66bo5bo$7bobo2bo35bo31b3o31bo35bo2bobo$7bo41b2o28b
5o28b2o41bo$7b2o70bo3bo70b2o$10b2o66bo5bo66b2o$10bo68bo3bo68bo$78b2ob
ob2o$6b3o69b2o3b2o69b3o$5bo73b2ob2o73bo$6b2o147b2o$81bo$78b3ob3o$80b3o
$79b5o$79bo3bo$78bo5bo$79bo3bo$78b2obob2o$78b2o3b2o$79b2ob2o2$81bo$78b
3ob3o$80b3o$79b5o$79bo3bo$78bo5bo$79bo3bo$78b2obob2o$78b2o3b2o$79b2ob
2o2$81bo$78b3ob3o$80b3o$79b5o$79bo3bo$78bo5bo$79bo3bo$78b2obob2o$78b2o
3b2o$79b2ob2o2$81bo$78b3ob3o$80b3o$79b5o$79bo3bo$71bo6bo5bo6bo$70b3o6b
o3bo6b3o$70b3o5b2obob2o5b3o$78b2o3b2o$72b3o4b2ob2o4b3o$75bo11bo$75b3o
3bo3b3o$71bo3bobo2bobo2bobo3bo$71bo2bo2b2obobob2o2bo2bo$70bobob2obobo
3bobob2obobo$71bob2ob2o3bo3b2ob2obo$77bo2b3o2bo$74bo2bobo3bobo2bo$73b
o3bob2ob2obo3bo$73bob3o3bo3b3obo$76bo9bo$72b3o13b3o$77b2ob3ob2o$77b2o
bobob2o$76b2o7b2o$76bo2b2ob2o2bo$76bobobobobobo$75b2o3bobo3b2o$75bo3b
o3bo3bo$74bobo2b2ob2o2bobo$75bo11bo$77bo7bo$75bobo7bobo$75bobo7bobo2$
75bo11bo$73b3o11b3o$72bo4b2ob3ob2o4bo$72b2o4bobobobo4b2o$76bo3bobo3bo
$73bo3bo7bo3bo$72bobo3bo5bo3bobo$72bo3b3o5b3o3bo$79b2ob2o$78bo5bo!

As I wrote, it wasn’t optimized… Minor remark: As shown, gen 4 for is different from gen 0, so gen 4 actually is the reduced spaceship.

dexter1 · Post by **dexter1** » January 8th, 2025, 6:56 pm

This is a new orthogonal c/5 ship i discovered by continuing the earlier qfind -w13 gutter search. I found an idle memory node and figured i might do another 24 hour run. It popped up one hour after the start of the batch run, along with more copies of Kermit.

Code: Select all

x = 25, y = 9, rule = B3/S23
4bo15bo$3b3o13b3o$9b3ob3o$bo6bobo3bobo6bo$obobo3bo7bo3bobobo$3bob2o2b
3ob3o2b2obo$o23bo$2o4b2o9b2o4b2o$2o4b2o9b2o4b2o!

The ship is tied with spider in terms of fewest amount of alive cells (58), but has a bigger bounding box. It is also non-monotonic.

Proposed name: Tarantula

Edit: The ship can support an 8-cell period-10 tagalong, found on Oct. 6, 2015 by Bullet51 (Edit by Sokwe: as Bullet51 noted, this is now the smallest known 2c/10 spaceship):

Code: Select all

x = 25, y = 17, rule = B3/S23
4bo15bo$3b3o13b3o$9b3ob3o$bo6bobo3bobo6bo$obobo3bo7bo3bobobo$3bob2o2b
3ob3o2b2obo$o23bo$2o4b2o9b2o4b2o$2o4b2o9b2o4b2o2$6b2o$6b2o$8bo$5bobo$
5bo2$6b2o!

... and a larger tagalong found by C_R_116:

Code: Select all

x = 25, y = 29, rule = B3/S23
3b3o13b3o$3bo2bo3b2ob2o3bo2bo$b8obo3bob8o$obobob3obo3bob3obobobo$o23bo
$2bo3bo3b2ob2o3bo3bo$2o4bo11bo4b2o$o6bo9bo6bo$6bo11bo2$6b2o9b2o$5bo2bo
7bo2bo$4bo2b2o7b2o2bo$5b3o9b3o$7bo9bo2$3b5o4bo4b5o$3b2o4b3ob3o4b2o$4bo
5bo3bo5bo$4bobo2bo5bo2bobo$9bo5bo$9b2o3b2o2$6b3o7b3o$8bo7bo$5bo3bo5bo
3bo$5bo4bo3bo4bo$5bo13bo$5b5o5b5o!

C_R_116 · Post by **C_R_116** » January 8th, 2025, 8:24 pm

dexter1 wrote: January 8th, 2025, 6:56 pm ... and a larger tagalong found by C_R_116:
Code: Select all
in

Here are some more tagalongs:

Code: Select all

x = 110, y = 60, rule = B3/S23
4bo15bo11bo15bo12bo15bo11bo15bo$3b3o13b3o9b3o13b3o10b3o13b3o9b3o13b3o$
9b3ob3o21b3ob3o22b3ob3o21b3ob3o$bo6bobo3bobo6bo5bo6bobo3bobo6bo6bo6bob
o3bobo6bo5bo6bobo3bobo6bo$obobo3bo7bo3bobobo3bobobo3bo7bo3bobobo4bobob
o3bo7bo3bobobo3bobobo3bo7bo3bobobo$3bob2o2b3ob3o2b2obo9bob2o2b3ob3o2b
2obo10bob2o2b3ob3o2b2obo9bob2o2b3ob3o2b2obo$o23bo3bo23bo4bo23bo3bo23bo
$2o4b2o9b2o4b2o3b2o4b2o9b2o4b2o4b2o4b2o9b2o4b2o3b2o4b2o9b2o4b2o$2o4b2o
9b2o4b2o3b2o5bo9bo5b2o4b2o4b2o9b2o4b2o3b2o4b2o9b2o4b2o2$6b2o9b2o15bo2b
o5bo2bo19bo5bo18b2o9b2o$6b2o9b2o18b2o3b2o22b2o3b2o18b2o9b2o$6b2o9b2o
18bo5bo21bo2bobo2bo17b2o9b2o$7b2o7b2o49b2ob2o19bo11bo$8b2o5b2o18bob2o
3b2obo17b2o3bobo3b2o13b2obo9bob2o$7bo2bo3bo2bo15bo3bo5bo3bo15b2o3bobo
3b2o13b2o3bo5bo3b2o$7bobo5bobo15bo4bo3bo4bo18bo5bo15bo5bo5bo5bo$6b2o9b
2o13bo3bob2ob2obo3bo17b2obob2o20bo7bo$7bo9bo14bo3bob2ob2obo3bo$7bo9bo
18bo7bo21bobobobo20b3o3b3o$40bo20b2o2bo7bo2b2o14bo3bobo3bo$5b2o11b2o
13b2ob2o5b2ob2o12bo2bo2bo5bo2bo2bo13bobobobobobo$4b2o13b2o12b2o11b2o
15bo2bobobobo2bo17b2obobob2o$4b2ob2o7b2ob2o13bob2o2bo2b2obo15b2o11b2o
16bob2ob2obo$6b2ob2o3b2ob2o15bo2bo5bo2bo14b2o13b2o13bobo7bobo$6bo2bobo
bobo2bo16bo9bo18b2o7b2o16bob2o5b2obo$7b3obobob3o48bo5bo19b4o3b4o$7b2ob
2ob2ob2o45bo2bo5bo2bo18b7o$36b3o3b3o17bo3bo5bo3bo18bobobo$32bo3bo2bobo
2bo3bo13bo2bo7bo2bo17bo2bo2bo$11b3o17b3ob11ob3o11bo2bob2obob2obo2bo14b
2o2bobo2b2o$10bobobo50bo7bo18b4o3b4o$9bo5bo18bo11bo15bo13bo19b3o$9bo5b
o18bo2bo5bo2bo16bob2ob3ob2obo20b3o$10b2ob2o18b2o3bo3bo3b2o21bo$8b3o3b
3o16b2o3b5o3b2o19b2ob2o20bobobobobobo$8b2o5b2o17b2o9b2o18bobo3bobo17b
2o3bobo3b2o$7bob2o3b2obo18b2obobob2o19bobob3obobo21bobo$10bo3bo22bo5bo
22bo5bo18b3o7b3o$5b3o9b3o15b2ob2ob2ob2o18b2o2b3o2b2o15bo13bo$5b2ob3o3b
3ob2o14bobob2ob2obobo21b3o20bo11bo$6b4o5b4o14b2ob2o5b2ob2o19bo3bo$7b3o
5b3o15b2obo7bob2o13b4o2b2ob2o2b4o$34bobo7bobo17b3obobob3o$35bo9bo18bo
2bo3bo2bo$34bo11bo14b2obo9bob2o$33bo3b3ob3o3bo18bo5bo$32bo4bo5bo4bo17b
o5bo$32b2o3bo5bo3b2o$33bob2o7b2obo$34b3obo3bob3o$31bo2b2o3bobo3b2o2bo$
32b3o4bobo4b3o$34b2o2b2ob2o2b2o$35b2ob2ob2ob2o$38b2ob2o$37b2o3b2o$40bo
$37bo5bo$38b2ob2o!

Two non-tagalong spaceships also appeared in my search (Edit by Sokwe: these were first found by Paul Tooke between Nov. 2004 and Jan. 2005):

Code: Select all

x = 42, y = 48, rule = B3/S23
7bo3bo17bo5bo$6b7o15bobo3bobo$5bo3bo3bo17bobo$4bob2obob2obo10bo2bobo3b
obo2bo$3bo11bo9b2ob2o5b2ob2o$b3o2bo5bo2b3o8b5o3b5o$6bo5bo13b3obo3bob3o
$o3bo3bobo3bo3bo7b2o2bo3bo2b2o$bo2bo2b2ob2o2bo2bo9b2o7b2o$2b2o4bobo4b
2o13b2ob2o$3bobo2bobo2bobo14b2ob2o$2bobobobobobobobo14bobo$2b2ob2obobo
b2ob2o10b2o2bobo2b2o$4bo3bobo3bo12b2o2bobo2b2o$5b3o3b3o12bo2bobobobo2b
o$5b2o5b2o11bobo3b3o3bobo$2b3o9b3o7b6o5b6o$2b2obobo3bobob2o7bo15bo$2b
3obobobobob3o8bob2o7b2obo$4bo3bobo3bo14bo5bo$4bo4bo4bo12bo9bo$5bo3bo3b
o13b2o7b2o$2bob2ob5ob2obo9b2o9b2o$2bo2bo7bo2bo10b2o7b2o$6bobobobo14b2o
7b2o$5bo2bobo2bo14b2o5b2o$3b6ob6o$2bo4bo3bo4bo11bobo3bobo$2bobob2o3b2o
bobo8bo2bobo3bobo2bo$3b2obo5bob2o9b2o11b2o$5bobo3bobo12b3o7b3o$6b3ob3o
13bo2bo5bo2bo$8bobo13b2o4bo3bo4b2o$b3o3b2ob2o3b3o11bo2bo2bo$b2ob2ob2ob
2ob2ob2o5bo5bob3obo5bo$3bobobo3bobobo8b2ob2o2bobo2b2ob2o$25bob5ob5obo$
25b3o2bo3bo2b3o$27b2o7b2o$28b2o5b2o$29bo5bo2$27b2obo3bob2o2$27b3o2bo2b
3o$26bobo2bobo2bobo$25bo5bobo5bo$25bo4b2ob2o4bo!

confocaloid · Post by **confocaloid** » January 11th, 2025, 2:35 am

Attached is a constant-population p5 orthogonal c/5 convoy, with 1316294 alive cells in every phase, consisting of 16717 spiders and 2981 tarantulas. All tarantulas are in the same phase:

p5-c5o-constant-population-1316294.mc: (3.35 KiB) Downloaded 203 times

Of course, it's possible to make a much smaller constant-population convoy by putting one copy of every phase, but that feels less interesting:

Code: Select all

x = 68, y = 73, rule = B3/S23
11bo7bo26bo15bo$5b2obobob2o3b2obobob2o19b3o13b3o$2b3obob3o9b3obob3o22b
3ob3o$2bo3bobo5bobo5bobo3bo14bo6bobo3bobo6bo$6b2o6bobo6b2o17bobobo3bo
7bo3bobobo$3b2o9bobo9b2o17bob2o2b3ob3o2b2obo$3b2ob2o15b2ob2o14bo23bo$
7bo15bo18b2o4b2o9b2o4b2o$42b2o4b2o9b2o4b2o8$11b2o5b2o25b3o13b3o$3b4obo
bobo5bobobob4o17b3o4bo3bo4b3o$2b3obobob2obo3bob2obobob3o17bo4b3ob3o4bo
$2bo3bobo13bobo3bo14bo6bob2ob2obo6bo$3bob3o5b2ob2o5b3obo15b5ob2o2bobo
2b2ob5o$3b2o21b2o15bob3o3b2o3b2o3b3obo$3b5o15b5o14b2o3bobo2bo3bo2bobo
3b2o$6b2o15b2o16bo6b2o9b2o6bo$42b2o4b2o9b2o4b2o7$46bo15bo$4b2o5b2o5b2o
5b2o18bobo13bobo$2bo3bo3bo2bo3bo2bo3bo3bo22b3ob3o$2bo3bobob3o5b3obobo
3bo16b3o13b3o$2bo5b2o2b3ob3o2b2o5bo14bo3bob2o7b2obo3bo$2b2ob3o15b3ob2o
13b2o3b4o2bobo2b4o3b2o$2bo25bo20bob3ob3obo$3bo3bo15bo3bo14b3o2bob4o3b
4obo2b3o$4bo2bo15bo2bo14bo5bo2bo7bo2bo5bo$42bo5b2o9b2o5bo7$46bo15bo$5b
o5b2o5b2o5bo20bo5bo3bo5bo$3bo2b2ob2o2bo3bo2b2ob2o2bo17bobo4bo3bo4bobo$
b3o4bobo3bobo3bobo4b3o16b3ob3o3b3ob3o$b2o2bo2b3ob2o3b2ob3o2bo2b2o12b3o
5bo7bo5b3o$b3o2b3o4bo3bo4b3o2b3o12b2o3bo5bobo5bo3b2o$2bobo2bo15bo2bobo
15bo2bo5bobo5bo2bo$3bo23bo14b2o5bo3bobo3bo5b2o$41bo5bo13bo5bo$48b2o9b
2o8$6bo3b3o5b3o3bo20b3o13b3o$3b2ob5ob2o3b2ob5ob2o17bo2bo3b2ob2o3bo2bo$
bob2obo5bobobobo5bob2obo13b8obo3bob8o$o3bobo3b5ob5o3bobo3bo11bobobob3o
bo3bob3obobobo$4b3o5b2o3b2o5b3o15bo23bo$bo2bob3o13b3obo2bo14bo3bo3b2ob
2o3bo3bo$3bo23bo14b2o4bo11bo4b2o$42bo6bo9bo6bo$48bo11bo!
#C [[ SHOWGENSTATS ]]

What is the smallest constant-population convoy of spiders and tarantulas where the tarantulas appear in only two different phases?
What is the smallest constant-population convoy of spiders and tarantulas where the spiders appear in only two different phases?

JP21 · Post by **JP21** » January 11th, 2025, 11:57 am

useless c/5 spider and tarantula interaction:

Code: Select all

x = 46, y = 52, rule = B3/S23
24bo7bo$18b2obobob2o3b2obobob2o$15b3obob3o9b3obob3o$15bo3bobo5bobo5bob
o3bo$19b2o6bobo6b2o$16b2o9bobo9b2o$16b2ob2o15b2ob2o$20bo15bo3$23b3o13b
3o$23bo2bo3b2ob2o3bo2bo$21b8obo3bob8o$20bobobob3obo3bob3obobobo$20bo
23bo$22bo3bo3b2ob2o3bo3bo$20b2o4bo11bo4b2o$20bo6bo9bo6bo$26bo11bo15$9b
o7bo$3b2obobob2o3b2obobob2o$3obob3o9b3obob3o$o3bobo5bobo5bobo3bo$4b2o
6bobo6b2o$b2o9bobo9b2o$b2ob2o15b2ob2o$5bo15bo3$24b3o13b3o$24bo2bo3b2ob
2o3bo2bo$22b8obo3bob8o$21bobobob3obo3bob3obobobo$21bo23bo$23bo3bo3b2ob
2o3bo3bo$21b2o4bo11bo4b2o$21bo6bo9bo6bo$27bo11bo!

Bullet51 · Post by **Bullet51** » January 13th, 2025, 7:48 am

2c/6 spaceship:

Code: Select all

x = 90, y = 23, rule = B3/S23
31bo16bo14b2o17b2o$23b2o6b2o14b5o8bo5bo10b2o3bo2b2obo$20b2ob2o5b2obo
13b2ob4ob3obo6bo10bo7b5o$17bobo3bo21bo3bo3b2o2bob2o2bo5b2o3bo2bo2bob2o
$4bobo9bobo6bo2b2o9bo4b2o3b4o4b2obo3b2o3b2o3bo3bobo$4bo10b4obo7bobo6b
2obobo3bobo3b5o2bobo2bo10bo3bo$b3o10bo2bo2bobo4b2obo2bo3b2o3bo2bobo6bo
4b2o3b10obo$b2obo5b2o2bobo3bob2obobo3bobo6b2o17bo4bo$o2b2o4bobo3bo5bo
4b2o2b2ob2ob2o21b2o4b2ob2o2bob2o$o2b2o2b3o2bo13b2o3bo2bob2obo2bo2bo14b
obo2bo3bo$o2bobo3bo2b2o12bobo2b2obo3bo3bobo16bo4bo2bo$5b3obo3bo14bo12b
o27bo2b3o$o2bobo3bo2b2o12bobo2b2obo3bo3bobo16bo4bo2bo$o2b2o2b3o2bo13b
2o3bo2bob2obo2bo2bo14bobo2bo3bo$o2b2o4bobo3bo5bo4b2o2b2ob2ob2o21b2o4b
2ob2o2bob2o$b2obo5b2o2bobo3bob2obobo3bobo6b2o17bo4bo$b3o10bo2bo2bobo4b
2obo2bo3b2o3bo2bobo6bo4b2o3b10obo$4bo10b4obo7bobo6b2obobo3bobo3b5o2bob
o2bo10bo3bo$4bobo9bobo6bo2b2o9bo4b2o3b4o4b2obo3b2o3b2o3bo3bobo$17bobo
3bo21bo3bo3b2o2bob2o2bo5b2o3bo2bo2bob2o$20b2ob2o5b2obo13b2ob4ob3obo6bo
10bo7b5o$23b2o6b2o14b5o8bo5bo10b2o3bo2b2obo$31bo16bo14b2o17b2o!

confocaloid · Post by **confocaloid** » January 13th, 2025, 9:08 am

What are lowest-constant-population "completions" of p5 orthogonal c/5 spaceships by collections of p5 oscillators?
Here are some (likely suboptimal) solutions:

Spider is "completed" into a constant-population pattern (160 alive cells in every generation):

Code: Select all

x = 63, y = 28, rule = B3/S23
11bo35bo$9b3o35b3o$8bo41bo$8b2o39b2o$7b2o$5b3o44bobo$3b2o2b2o42b4o$4b
3o44bobo$3b2o$2b2o52bobo$3bo51b4o$3o52bobo$o$59b2o$59bo$60b3o$62bo4$4b
2o4b2o13bo7bo13b2o4b2o$4bobo2bobo7b2obobob2o3b2obobob2o7bobo2bobo$6bo
2bo6b3obob3o9b3obob3o6bo2bo$5bo4bo5bo3bobo5bobo5bobo3bo5b2o2b2o$5b6o9b
2o6bobo6b2o8b3o2b3o$6b4o7b2o9bobo9b2o7bo2bo$17b2ob2o15b2ob2o$21bo15bo!
#C [[ SHOWGENSTATS ]]

Kermit is "completed" into a constant-population pattern (177 alive cells in every generation):

Code: Select all

x = 75, y = 21, rule = B3/S23
bo19bo$2o19b2o$o2bo4b2o3b2o4bo2bo$4bob2obo3bob2obo$3bo15bo9b2o4b2o2b2o
8bo9bo$5b4o5b4o11bobo2bobo2bo2bo6b3o7b3o$9b2ob2o17b4o5bobo9bo9bo$29bo
2b2o2bo14b2o8b2o$10bobo16bo2b2o2bo5bobo17b2o$9bo3bo17bo2bo18b2obo6b3o$
5b5o3b5o26bobo6bo2bo5b2o2b2o$4b2o2b2o3b2o2b2o34bob2o7b3o$4bo5bobo5bo
27bob2o16b2o$2b4o2bobobobo2b4o36b2o8b3o$9bo3bo34bobo6bo8b2o2b2o$49b2o
7b3o7b3o$60bo9b2o$71b2o$71bo$72b3o$74bo!
#C [[ SHOWGENSTATS ]]

Tarantula is "completed" into a constant-population pattern (181 alive cells in every generation):

Code: Select all

x = 60, y = 30, rule = B3/S23
2o4b2o$obo2bobo$2bo2bo$bo4bo$b6o7b2o10bo$2b4o9bo8b3o$12b2o9bo$24bo$10b
obo11bo$19b2o$8bobo7bo4bo$21b2o$6bobo8bo$6bo10bo10bo$4bo13bo7b3o$4b2o
9b3o7bo$13b3o9b2o$12bo11b2o$12b2o8b3o$11b2o7b2o2b2o$9b3o9b3o15bo15bo$
7b2o2b2o7b2o16b3o13b3o$8b3o7b3o23b3ob3o$7b2o7b2o2b2o14bo6bobo3bobo6bo$
6b2o9b3o15bobobo3bo7bo3bobobo$7bo8b2o20bob2o2b3ob3o2b2obo$4b3o8b2o18bo
23bo$4bo11bo18b2o4b2o9b2o4b2o$13b3o19b2o4b2o9b2o4b2o$13bo!
#C [[ SHOWGENSTATS ]]

moebius · Post by **moebius** » January 16th, 2025, 10:59 am

Hi all,

I was thinking about getting my spaceship search programs (knight*) up and running again, so I was checking out the general state of affairs in spaceship searches. I was checking out the "Spaceship Search Status Page" and I noticed there was a discussion about a year ago about whether there were height 10 2c/5 spaceships.

I was looking through my files and it turns out that back in 2017 I ran 2c/5 searches at heights of 47 and 48 phases (my program measures height in phases, so 47 would be 2 phases 10 high and 3 phases 9 high) and I got output ships.

The 47 height search gave:

Code: Select all

x = 40, y = 115, rule = B3/S23
4bo3bo11b2o12bo3bo$4bo3bo10b6o9bo3bo$3bobo12bo3bo10bobo$2b3o2b2o9bo4b
2o7b3o2b2o$18bo2bo$5b2o28b2o$5b2o13b2o13b2o$4bo15b2o12bo$20bo$2b2o2bo
11b3o11b2o2bo$b2o13b2ob2o10b2o$o15bo2bo10bo$b2o13b2ob2o10b2o$6bo11b3o
15bo$bo14b2o13bo$o15b3o11bo$bo2bo3bo7b2obo11bo2bo3bo$2b3obobo9b3o11b3o
bobo$4bobo13bo13bobo$4bob2o14bo11bob2o$3b2obo11bo3bo10b2obo$4bobo9b2o
16bobo$b2obo2bo8bo5bo8b2obo2bo$bo2bo11b3o12bo2bo$b4o15bobo8b4o$19b3o$
7bo10b3o16bo$6b3o7b2ob2o15b3o$16b2o$2b2o3bobo8b2o12b2o3bobo$bob2obo9bo
3b2o9bob2obo$bo3b2o8bo4bo10bo3b2o$bobobo10bobo12bobobo$2b2obob2o8bo14b
2obob2o$5bo16bo12bo$5b2o14b3o11b2o$6b2o28b2o$7bo9b2o3bobo12bo$8bo7bob
2obo16bo$8bo7bo3b2o16bo$6bo9bobobo15bo$5b3o9b2obob2o11b3o$6b2o12bo15b
2o$5bo14b2o13bo$4bo16b2o11bo$3bobo16bo10bobo$2b2o19bo8b2o$3bobo17bo9bo
bo$4bo16bo12bo$5bo14b3o12bo$6b2o13b2o13b2o$5b3o12bo14b3o$6bo12bo16bo$
8bo9bobo17bo$8bo8b2o19bo$7bo10bobo16bo$6b2o11bo16b2o$5b2o13bo14b2o$5bo
15b2o13b2o$2b2obob2o11b3o14bo$bobobo15bo16bo$bo3b2o16bo14bo$bob2obo16b
o12bo$2b2o3bobo12bo12b3o$21b2o13b2o$6b3o11b2o13bo$7bo12bo13bo$17b2obob
2o9bobo$b4o11bobobo11b2o$bo2bo11bo3b2o11bobo$b2obo2bo8bob2obo12bo$4bob
o10b2o3bobo10bo$3b2obo29b2o$4bob2o13b3o11b3o$4bobo15bo13bo$2b3obobo29b
o$bo2bo3bo7b4o18bo$o15bo2bo17bo$bo14b2obo2bo13b2o$6bo12bobo13b2o$b2o
15b2obo13bo$o18bob2o9b2obob2o$b2o16bobo9bobobo$2b2o2bo10b3obobo7bo3b2o
$16bo2bo3bo7bob2obo$4bo10bo16b2o3bobo$5b2o9bo$5b2o14bo14b3o$16b2o19bo$
2b3o2b2o6bo$3bobo10b2o13b4o$4bo3bo8b2o2bo9bo2bo$4bo3bo22b2obo2bo$19bo
14bobo$20b2o11b2obo$20b2o12bob2o$34bobo$17b3o2b2o8b3obobo$18bobo10bo2b
o3bo$19bo3bo6bo$19bo3bo7bo$36bo$31b2o$30bo$31b2o$32b2o2bo2$34bo$35b2o$
35b2o2$32b3o2b2o$33bobo$34bo3bo$34bo3bo!

For the 48 high search note that the 2nd ship has gutter symmetry:

Code: Select all

x = 100, y = 116, rule = B3/S23
5b2o13b2o12bo3bo26b2o12bo3bo$4b6o9b6o9bo3bo10b3o12b6o9bo3bo10b3o$3bo3b
o10bo3bo10bobo12bo2bob2o8bo3bo10bobo12bo2bob2o$3bo4b2o8bo4b2o7b3o2b2o
9b3o12bo4b2o7b3o2b2o9b3o$3bo2bo11bo2bo27b5o9bo2bo27b5o$35b2o14b2o27b2o
14b2o$5b2o13b2o13b2o13bobo12b2o13b2o13bobo$5b2o13b2o12bo16bo13b2o12bo
16bo$5bo14bo28bo15bo28bo$3b3o12b3o11b2o2bo10b3o13b3o11b2o2bo10b3o$b2ob
2o10b2ob2o10b2o14b3o11b2ob2o10b2o14b3o$bo2bo11bo2bo10bo15bo14bo2bo10bo
15bo$b2ob2o10b2ob2o10b2o14bo13b2ob2o10b2o14bo$3b3o12b3o15bo10b2o14b3o
15bo10b2o$b3ob2o9b3ob2o9bo29b2o13bo$b2ob3o9b2ob3o8bo15b2o13b3o11bo15b
2o$b2o2bo10b2o2bo10bo2bo3bo8b2ob2obo7b2obo11bo2bo3bo8b2ob2obo$3bo2bo
11bo2bo10b3obobo9bobo12b3o11b3obobo9bobo$4b4o11b4o11bobo13bobo12bo13bo
bo13bobo$6b2o13b2o11bob2o12bob2o13bo11bob2o12bob2o$33b2obo12b2o12bo3bo
10b2obo12b2o$4b2o13b2o13bobo11bobo10b2o16bobo11bobo$3b3o2bo9b3o2bo7b2o
bo2bo9b2obob2o7bo5bo8b2obo2bo9b2obob2o$3bo5bo8bo5bo6bo2bo11bobobob2o7b
3o12bo2bo11bobobob2o$3b2ob3o9b2ob3o7b4o11bobob3o12bobo8b4o11bobob3o$6b
o14bo24b2o2b3o11b3o24b2o2b3o$2bo3bo10bo3bo15bo13b3o9b3o16bo13b3o$b2o
13b2o18b3o12b2obo6b2ob2o15b3o12b2obo$o3bo10bo3bo30b2o9b2o32b2o$b2o2bo
10b2obo12b2o3bobo9bo13b2o12b2o3bobo9bo$b2o3bo10b2o2bo9bob2obo10b4o10bo
3b2o9bob2obo10b4o$3b4o12b2o10bo3b2o9bo2bob3o6bo4bo10bo3b2o9bo2bob3o$4b
o26bobobo9bo4bobo8bobo12bobobo9bo4bobo$19b2o11b2obob2o7bo2bo12bo14b2ob
ob2o7bo2bo$2b3o12b2o2bo13bo11b3ob2o14bo12bo11b3ob2o$bob2o11b2obo15b2o
12bobo14b3o11b2o12bobo$b3o11bo3bo16b2o12b2o29b2o12b2o$bobo12b2o19bo12b
3o9b2o3bobo12bo12b3o$2b2o13bo3bo16bo22bob2obo16bo$b3o17bo16bo22bo3b2o
16bo$bo16b2ob3o12bo15b2o7bobobo15bo15b2o$bo2bo13bo5bo10b3o13b3o8b2obob
2o11b3o13b3o$2bo2bo12b3o2bo12b2o12b2o13bo15b2o12b2o$4b2o13b2o14bo29b2o
13bo$5b2o27bo14bo16b2o11bo14bo$5bobo13b2o10bobo13bo2bo14bo10bobo13bo2b
o$4bo14b4o9b2o14bo19bo8b2o14bo$3bo4bo9bo2bo11bobo11b3o18bo9bobo11b3o$
3bo5bo6b2o2bo13bo13bo17bo12bo13bo$3bo2b2o8b2ob3o13bo13bo2bo12b3o12bo
13bo2bo$4b4o8b3ob2o14b2o11bo16b2o13b2o11bo$5bo12b3o14b3o27bo14b3o$16b
2ob2o15bo13b2o12bo16bo13b2o$16bo2bo18bo12b3o9bobo17bo12b3o$16b2ob2o17b
o13b2o8b2o19bo13b2o$18b3o16bo25bobo16bo$20bo15b2o26bo16b2o$20b2o13b2o
13b3o12bo14b2o13b3o$20b2o13bo14b2o14b2o13b2o12b2o$32b2obob2o10bobo13b
3o14bo12b3o$18bo2bo9bobobo11b3ob2o13bo16bo$18bo4b2o6bo3b2o9bo2bo18bo
14bo$18bo3bo8bob2obo8bo4bobo15bo12bo15b2o$19b6o7b2o3bobo6bo2bob3o13bo
12b3o13b3o$20b2o25b4o15b2o13b2o12b2o$36b3o10bo15b2o13bo$37bo12b2o13bo
13bo14bo$51b2obo7b2obob2o9bobo13bo2bo$31b4o16b3o7bobobo11b2o14bo$31bo
2bo11b2o2b3o8bo3b2o11bobo11b3o$31b2obo2bo8bobob3o8bob2obo12bo13bo$34bo
bo9bobobob2o8b2o3bobo10bo13bo2bo$33b2obo10b2obob2o27b2o11bo$34bob2o10b
obo15b3o11b3o$34bobo12b2o16bo13bo13b2o$32b3obobo11bob2o29bo12b3o$31bo
2bo3bo11bobo8b4o18bo13b2o$30bo17bobo10bo2bo17bo$31bo15b2ob2obo7b2obo2b
o13b2o$36bo9b2o16bobo13b2o13b3o$31b2o30b2obo13bo14b2o$30bo16b2o15bob2o
9b2obob2o10bobo$31b2o14bo16bobo9bobobo11b3ob2o$32b2o2bo9bo15b3obobo7bo
3b2o9bo2bo$47b3o11bo2bo3bo7bob2obo8bo4bobo$34bo12b3o10bo16b2o3bobo6bo
2bob3o$35b2o12bo11bo30b4o$35b2o14bo14bo14b3o10bo$50bobo8b2o19bo12b2o$
32b3o2b2o12b2o7bo35b2obo$33bobo13b5o7b2o13b4o16b3o$34bo3bo9b3o11b2o2bo
9bo2bo11b2o2b3o$34bo3bo9bo2bob2o21b2obo2bo8bobob3o$49b3o12bo14bobo9bob
obob2o$65b2o11b2obo10b2obob2o$65b2o12bob2o10bobo$79bobo12b2o$62b3o2b2o
8b3obobo11bob2o$63bobo10bo2bo3bo11bobo$64bo3bo6bo17bobo$64bo3bo7bo15b
2ob2obo$81bo9b2o$76b2o$75bo16b2o$76b2o14bo$77b2o2bo9bo$92b3o$79bo12b3o
$80b2o12bo$80b2o14bo$95bobo$77b3o2b2o12b2o$78bobo13b5o$79bo3bo9b3o$79b
o3bo9bo2bob2o$94b3o!

I am going to see if I can get my searches to find something interesting.

Have a happy day,

-Tim Coe

Edit:

I noticed that Stanley Dodds posted the 1st, 2nd, and 4th ships from the height 48 run on May 9th 2023 at 8:09AM.

HartmutHolzwart · Post by **HartmutHolzwart** » January 17th, 2025, 8:14 am

We're desperately in need of short wide c/6 space ships!

HartmutHolzwart · Post by **HartmutHolzwart** » January 21st, 2025, 3:11 pm

Tarantula-related c/5o spaceship:

Code: Select all

x = 85, y = 31, rule = B3/S23
4bo75bo$3b3o73b3o$9b3o61b3o$bo6bobo63bobo6bo$obobo3bo67bo3bobobo$3bob
2o2b2o63b2o2b2obo$o10bo3bo53bo3bo10bo$2o4b2o6bo2bo49bo2bo6b2o4b2o$2o4b
2o3bob2o3bo47bo3b2obo3b2o4b2o$11bob2o4bo45bo4b2obo$15b3obo45bob3o$15bo
b3ob3o3b2ob2o21b2ob2o3b3ob3obo$21b2o5bo3bo19bo3bo5b2o$19bo2bob2o2b2o2b
o19bo2b2o2b2obo2bo$19b5ob2obobo23bobob2ob5o$19b2o2bob2o31b2obo2b2o$28b
2o3bo17bo3b2o$29bob2o6bo5bo6b2obo$32bo3b5o3b5o3bo$37bo3bobo3bo$38b2obo
bob2o$40bo3bo2$38b2o5b2o$35b4obo3bob4o$35b2obo2bobo2bob2o$35bobobobobo
bobobo$38bo2bobo2bo$35bob2o2bobo2b2obo$35b2o2bobobobo2b2o$40bo3bo!

CARuler · Post by **CARuler** » January 21st, 2025, 10:24 pm

HartmutHolzwart wrote: January 21st, 2025, 3:11 pm Tarantula-related c/5o spaceship:

Code: Select all

x = 85, y = 31, rule = B3/S23
4bo75bo$3b3o73b3o$9b3o61b3o$bo6bobo63bobo6bo$obobo3bo67bo3bobobo$3bob
2o2b2o63b2o2b2obo$o10bo3bo53bo3bo10bo$2o4b2o6bo2bo49bo2bo6b2o4b2o$2o4b
2o3bob2o3bo47bo3b2obo3b2o4b2o$11bob2o4bo45bo4b2obo$15b3obo45bob3o$15bo
b3ob3o3b2ob2o21b2ob2o3b3ob3obo$21b2o5bo3bo19bo3bo5b2o$19bo2bob2o2b2o2b
o19bo2b2o2b2obo2bo$19b5ob2obobo23bobob2ob5o$19b2o2bob2o31b2obo2b2o$28b
2o3bo17bo3b2o$29bob2o6bo5bo6b2obo$32bo3b5o3b5o3bo$37bo3bobo3bo$38b2obo
bob2o$40bo3bo2$38b2o5b2o$35b4obo3bob4o$35b2obo2bobo2bob2o$35bobobobobo
bobobo$38bo2bobo2bo$35bob2o2bobo2b2obo$35b2o2bobobobo2b2o$40bo3bo!

has a MWSS emulator on the back of it

also, can be called the moth?

Post by **Sokwe** » January 22nd, 2025, 2:39 am

HartmutHolzwart wrote: January 21st, 2025, 3:11 pm Tarantula-related c/5o spaceship:

Nice! Here are some ways it can connect to known components:

Code: Select all

x = 89, y = 92, rule = B3/S23
4bo$3b3o$9b3o$bo6bobo$obobo3bo$3bob2o2b2o$o10bo3bo$2o4b2o6bo2bo$2o4b2o
3bob2o3bo$11bob2o4bo$15b3obo$15bob3ob3o3b2ob2o13b2o3bo$21b2o5bo3bo12bo
bobobo$19bo2bob2o2b2o2bo13b2o4bo11b2o5b2o5b2o5b2o$19b5ob2obobo7b3o5b8o
8bo3bo3bo2bo3bo2bo3bo3bo$19b2o2bob2o11b3o3bo4b3obo8bo3bobob3o5b3obobo
3bo$28b2o3bo7b2obo8b3o6bo5b2o2b3ob3o2b2o5bo$29bob2o2bo2bo18b2o3b2ob3o
15b3ob2o$32bo4b2o18b2o3bo25bo$36bo26bo3bo15bo3bo$36bo27bo2bo15bo2bo10$
4bo$3b3o$9b3o$bo6bobo$obobo3bo$3bob2o2b2o$o10bo3bo$2o4b2o6bo2bo$2o4b2o
3bob2o3bo$11bob2o4bo$15b3obo$15bob3ob3o3b2ob2o$21b2o5bo3bo$19bo2bob2o
2b2o2bo$19b5ob2obobo34b2obo$19b2o2bob2o29b3o2bo3b2ob2o$28b2o3bo17bo3bo
5bob2o5bo$29bob2o6bo5bo6b2ob4o2bo3bo3bo$32bo3b5o3b5o3bo4b3o5bo3bo2bo$
37bo3bobo3bo12b2o4b3o2b2o$38b2obobob2o10bo3bo8bo4b2o$40bo3bo11bobobo
10bobob3o$59bobo15bo$38b2o5b2o27b2o$35b4obo3bob4o24b2o$35b2obo2bobo2bo
b2o$35bobobobobobobobo26b3o$38bo2bobo2bo29bo$35bob2o2bobo2b2obo25bo3bo
$35b2o2bobobobo2b2o24bo4bo$40bo3bo34bo$75b5o13$16bob2o45b2obo$15b2ob2o
3bo2b3o27b3o2bo3b2ob2o$14bo5b2obo5bo3bo17bo3bo5bob2o5bo$15bo3bo3bo2b4o
b2o6bo5bo6b2ob4o2bo3bo3bo$12bo2bo3bo5b3o4bo3b5o3b5o3bo4b3o5bo3bo2bo$
12b2o2b3o4b2o12bo3bobo3bo12b2o4b3o2b2o$8b2o4bo8bo3bo10b2obobob2o10bo3b
o8bo4b2o$7b3obobo10bobobo11bo3bo11bobobo10bobob3o$7bo15bobo33bobo15bo$
9b2o27b2o5b2o27b2o$9b2o24b4obo3bob4o24b2o$35b2obo2bobo2bob2o$6b3o26bob
obobobobobobo26b3o$8bo29bo2bobo2bo29bo$5bo3bo25bob2o2bobo2b2obo25bo3bo
$5bo4bo24b2o2bobobobo2b2o24bo4bo$5bo34bo3bo34bo$5b5o65b5o!

CARuler wrote: January 21st, 2025, 10:24 pm has a MWSS emulator on the back of it

This is actually a surprisingly common odd-symmetric c/5 orthogonal back end. It was first found by Tim Coe on May 2, 1997, with a much smaller support found by Jason Summers on December 12, 2000 (see #3 and #10 in velocity-c5o/ships-c5o-1.rle in the moving objects collection).

moebius wrote: January 16th, 2025, 10:59 am I was checking out the "Spaceship Search Status Page" and I noticed there was a discussion about a year ago about whether there were height 10 2c/5 spaceships.

I was looking through my files and it turns out that back in 2017 I ran 2c/5 searches at heights of 47 and 48 phases (my program measures height in phases, so 47 would be 2 phases 10 high and 3 phases 9 high) and I got output ships....

It's interesting to me how several of these ships involve the same edge component reaching the same central repeating component via three different connecting components:

Code: Select all

x = 40, y = 109, rule = B3/S23
4bo3bo11bo3bo10bo3bo$4bo3bo11bo3bo10bo3bo$3bobo13bobo12bobo$2b3o2b2o9b
3o2b2o8b3o2b2o2$5b2o14b2o13b2o$5b2o14b2o13b2o$4bo15bo14bo2$2b2o2bo11b
2o2bo10b2o2bo$b2o14b2o13b2o$o15bo14bo$b2o14b2o13b2o$6bo15bo13bo$bo15bo
14bo$o15bo14bo$bo2bo3bo8bo2bo3bo7bo3bo$2b3obobo9b3obobo8b2obo$4bobo13b
obo13b2o$4bob2o12bob2o13bo$3b2obo12b2o12bo$4bobo13bo11b2o$b2obo2bo9b2o
bob2o7bo2bo$bo2bo12b2obobo9b2o3bo$b4o11bo4bo11b2obo$17bo3bo12bo$7bo9bo
2bo2bo9bo$6b3o13bobo7bo3bo$21bo2bo7bo3bo$2b2o3bobo9bob2o9bob3o$bob2obo
11bobob2o12b2o$bo3b2o9b2o4b2o7b3ob3o$bobobo10b2obo12b2o$2b2obob2o7b2ob
obo11bo$5bo12b2obo15b3o$5b2o14bo15b3o$6b2o12b2ob2o12bo$7bo13bo11b3o$8b
o23bob2ob2o$8bo22b2obo2bo$6bo16b2o7bobobobo$5b3o13b2o10b2obo$6b2o13bo
14bobo$5bo15bo14bobo$4bo15b3o13bobo$3bobo13b4o14b3o$2b2o14bo19b2o$3bob
o11bo2bo17bo$4bo13bo17b2o$5bo13b4o13bo$6b2o12b3o15bo$5b3o13bo14b2o$6bo
14bo13b2o$8bo12b2o10b2o$8bo14b2o8b2o$7bo25b2o$6b2o27b2o$5b2o14bo14b2o$
5bo14b2ob2o13bo$2b2obob2o12bo14bo$bobobo12b2obo14b2o$bo3b2o9b2obobo16b
o$bob2obo9b2obo18b2o$2b2o3bobo6b2o4b2o13b3o$18bobob2o12bobo$6b3o10bob
2o13bobo$7bo13bo2bo11bobo$22bobo8b2obo$b4o12bo2bo2bo8bobobobo$bo2bo12b
o3bo9b2obo2bo$b2obo2bo8bo4bo10bob2ob2o$4bobo10b2obobo10b3o$3b2obo10b2o
bob2o13bo$4bob2o12bo16b3o$4bobo12b2o16b3o$2b3obobo11bob2o9bo$bo2bo3bo
11bobo9b2o$o17b3obobo6b3ob3o$bo15bo2bo3bo11b2o$6bo9bo15bob3o$b2o14bo
14bo3bo$o21bo9bo3bo$b2o14b2o14bo$2b2o2bo9bo17bo$17b2o14b2obo$4bo13b2o
2bo9b2o3bo$5b2o24bo2bo$5b2o13bo11b2o$21b2o10bo$2b3o2b2o12b2o14bo$3bobo
30b2o$4bo3bo9b3o2b2o8b2obo$4bo3bo10bobo10bo3bo$20bo3bo6bo$20bo3bo7bo$
36bo$32b2o$31bo$32b2o$33b2o2bo2$35bo$36b2o$36b2o2$33b3o2b2o$34bobo$35b
o3bo$35bo3bo!

There are of course several ways to measure spaceship height. Your method seems like it may (or may not?) be slightly different than Keith's moving box method, which is of course different from the all-phases definition. I'm especially curious to know if anyone can confirm my old result that there are no period-5 2c/5 ships that fit in the same height-10 bounding box through its entire period.

Tim, were these searches done with knightt? Are they complete in the sense that all 2c/5 ships of "height 47/48" can be constructed from the ships in the above collections? If so, do you think a similar "height 50" search could be completed? I would assume "height 50" means "(up to) height 10 in each phase". Is this correct?

Zodduniverse · Post by **Zodduniverse** » January 23rd, 2025, 2:08 pm

WhiteHawk wrote: January 21st, 2025, 5:49 pm Can't say either way, but a start with debris clean-up.
Code: Select all

I made a block puffer using a reduced version of the first puffer

Code: Select all

x = 203, y = 140, rule = B3/S23
38b3o13b3o89b3o13b3o$38bo2bo3b2ob2o3bo2bo89bo2bo3b2ob2o3bo2bo$36b8obo
3bob8o85b8obo3bob8o$35bobobob3obo3bob3obobobo83bobobob3obo3bob3obobob
o$35bo23bo83bo23bo$37bo3bo3b2ob2o3bo3bo87bo3bo3b2ob2o3bo3bo$35b2o4bo11b
o4b2o83b2o4bo11bo4b2o$35bo6bo9bo6bo83bo6bo9bo6bo$41bo11bo95bo11bo2$41b
2o9b2o95b2o9b2o$40bo2bo7bo2bo93bo2bo7bo2bo$39bo2b2o7b2o2bo91bo2b2o7b2o
2bo$40b3o9b3o93b3o9b3o$42bo9bo97bo9bo2$38b5o4bo4b5o89b5o4bo4b5o$38b2o
4b3ob3o4b2o89b2o4b3ob3o4b2o$39bo5bo3bo5bo91bo5bo3bo5bo$39bobo2bo5bo2b
obo91bobo2bo5bo2bobo$44bo5bo101bo5bo$44b2o3b2o101b2o3b2o2$41b3o7b3o95b
3o7b3o$43bo7bo99bo7bo$40bo3bo5bo3bo93bo3bo5bo3bo$40bo4bo3bo4bo93bo4bo
3bo4bo$40bo13bo93bo13bo$40b5o5b5o93b5o5b5o8$64b3o$64bo$10bo7bo46bo118b
o7bo$4b2obobob2o3b2obobob2o153b2obobob2o3b2obobob2o$b3obob3o9b3obob3o
147b3obob3o9b3obob3o$bo3bobo5bobo5bobo3bo147bo3bobo5bobo5bobo3bo$5b2o
6bobo6b2o155b2o6bobo6b2o$2b2o9bobo9b2o149b2o9bobo9b2o$2b2ob2o15b2ob2o
149b2ob2o15b2ob2o$6bo15bo68b3o86bo15bo$93bo$92bo2$154bo$154bo$153b2o3b
2o4b3o$151b4o2bo2bo$156bo2bo$149b2obo2bob3o$10bo5b2o5b2o5bo117b3obo3b
o15bo5b2o5b2o5bo$8bo2b2ob2o2bo3bo2b2ob2o2bo34bo3b3o5b3o3bo31bo3b3o5b3o
3bo10bo6b2o15bo2b2ob2o2bo3bo2b2ob2o2bo$6b3o4bobo3bobo3bobo4b3o29b2ob5o
b2o3b2ob5ob2o25b2ob5ob2o3b2ob5ob2o6bo4bo3bo13b3o4bobo3bobo3bobo4b3o$6b
2o2bo2b3ob2o3b2ob3o2bo2b2o27bob2obo5bobobobo5bob2obo21bob2obo5bobobob
o5bob2obo4bo4bo17b2o2bo2b3ob2o3b2ob3o2bo2b2o$6b3o2b3o4bo3bo4b3o2b3o26b
o3bobo3b5ob5o3bobo3bo19bo3bobo3b5ob5o3bobo3bo3bo3bo18b3o2b3o4bo3bo4b3o
2b3o$7bobo2bo15bo2bobo31b3o5b2o3b2o5b3o27b3o5b2o3b2o5b3o8bo2bo2b2o15b
obo2bo15bo2bobo$8bo23bo29bo2bob3o13b3obo2bo21bo2bob3o13b3obo2bo8bo3bo
6b2o8bo23bo$64bo23bo25bo23bo21b2o3$71b2o5b2o43b2o5b2o$63b4obobobo5bob
obob4o27b4obobobo5bobobob4o$62b3obobob2obo3bob2obobob3o25b3obobob2obo
3bob2obobob3o$4bo5b2o5b2o5bo37bo3bobo13bobo3bo25bo3bobo13bobo3bo37bo5b
2o5b2o5bo$2bo2b2ob2o2bo3bo2b2ob2o2bo36bob3o5b2ob2o5b3obo27bob3o5b2ob2o
5b3obo36bo2b2ob2o2bo3bo2b2ob2o2bo$3o4bobo3bobo3bobo4b3o34b2o21b2o27b2o
21b2o34b3o4bobo3bobo3bobo4b3o$2o2bo2b3ob2o3b2ob3o2bo2b2o34b5o15b5o27b
5o15b5o34b2o2bo2b3ob2o3b2ob3o2bo2b2o$3o2b3o4bo3bo4b3o2b3o37b2o15b2o33b
2o15b2o37b3o2b3o4bo3bo4b3o2b3o$bobo2bo15bo2bobo147bobo2bo15bo2bobo$2b
o23bo43bo7bo45bo7bo43bo23bo$64b2obobob2o3b2obobob2o33b2obobob2o3b2obo
bob2o$61b3obob3o9b3obob3o27b3obob3o9b3obob3o$61bo3bobo5bobo5bobo3bo27b
o3bobo5bobo5bobo3bo$65b2o6bobo6b2o35b2o6bobo6b2o$62b2o9bobo9b2o29b2o9b
obo9b2o$62b2ob2o15b2ob2o29b2ob2o15b2ob2o$66bo15bo37bo15bo5$46b4o14b4o
67b4o14b4o$45b6o12b6o65b6o12b6o$43bo3b2o3bo8bo3b2o3bo61bo3b2o3bo8bo3b
2o3bo$42b2obob2obob2o6b2obob2obob2o59b2obob2obob2o6b2obob2obob2o$41bo
3b6o3bo4bo3b6o3bo57bo3b6o3bo4bo3b6o3bo$41bobo3b2o3bobo4bobo3b2o3bobo57b
obo3b2o3bobo4bobo3b2o3bobo$38bo3bo11b2o2b2o11bo3bo51bo3bo11b2o2b2o11b
o3bo$37bob2o32b2obo49bob2o32b2obo$40bobo12bo2bo12bobo55bobo12bo2bo12b
obo$37b2ob5o10b4o10b5ob2o49b2ob5o10b4o10b5ob2o$40bo2b2o9b6o9b2o2bo55b
o2b2o9b6o9b2o2bo$40b2o2b2o7b8o7b2o2b2o55b2o2b2o7b8o7b2o2b2o$40bobo6b2o
bo8bob2o6bobo55bobo6b2obo8bob2o6bobo$42bo5bobo4bo2bo4bobo5bo59bo5bobo
4bo2bo4bobo5bo$40b3o6bo3bob4obo3bo6b3o55b3o6bo3bob4obo3bo6b3o$39b2o8b
2ob2o2b2o2b2ob2o8b2o53b2o8b2ob2o2b2o2b2ob2o8b2o$50b2o2bo4bo2b2o75b2o2b
o4bo2b2o$41b3o5bo4bo4bo4bo5b3o57b3o5bo4bo4bo4bo5b3o$41b4o24b4o57b4o24b
4o$40bo4bo5bo2bo4bo2bo5bo4bo55bo4bo5bo2bo4bo2bo5bo4bo$38b2o5bo7b2o4b2o
7bo5b2o51b2o5bo7b2o4b2o7bo5b2o$37b3o13b2o4b2o13b3o49b3o13b2o4b2o13b3o
$37bo4b2o7bo2bo4bo2bo7b2o4bo49bo4b2o7bo2bo4bo2bo7b2o4bo$38bo3b2o6bo5b
2o5bo6b2o3bo51bo3b2o6bo5b2o5bo6b2o3bo$38bo3b3o6bo4b2o4bo6b3o3bo51bo3b
3o6bo4b2o4bo6b3o3bo$42bobo11b2o11bobo59bobo11b2o11bobo$43b2o8bo6bo8b2o
61b2o8bo6bo8b2o$53b2o4b2o81b2o4b2o$40bobo28bobo55bobo28bobo$40bo2bo11b
o2bo11bo2bo55bo2bo11bo2bo11bo2bo$39bo3bo4b3obo8bob3o4bo3bo53bo3bo4b3o
bo8bob3o4bo3bo$38bo10bo3bobo2bobo3bo10bo51bo10bo3bobo2bobo3bo10bo$44b
o4bobob3o2b3obobo4bo63bo4bobob3o2b3obobo4bo$38b2o4bo6b3obo2bob3o6bo4b
2o51b2o4bo6b3obo2bob3o6bo4b2o$42bo2bo4b2o10b2o4bo2bo59bo2bo4b2o10b2o4b
o2bo$42bo10bo6bo10bo59bo10bo6bo10bo$41b2o28b2o57b2o28b2o$37bo4b2o26b2o
4bo49bo4b2o26b2o4bo$36b2o38b2o47b2o38b2o$36bo2bo34bo2bo47bo2bo34bo2bo
$38b3o32b3o51b3o32b3o$37bo38bo49bo38bo$41b2o28b2o57b2o28b2o$37bo3bobo
26bobo3bo49bo3bobo26bobo3bo$39b3o2bo24bo2b3o53b3o2bo24bo2b3o$36b2o38b
2o47b2o38b2o$40bo32bo55bo32bo$39bo34bo53bo34bo$39b2ob2o26b2ob2o53b2ob
2o26b2ob2o$42bo28bo59bo28bo2$44b2o22b2o63b2o22b2o$41b3o26b3o57b3o26b3o
$41b2o28b2o57b2o28b2o!

could a rake be possible?

Post by **Sokwe** » January 23rd, 2025, 7:34 pm

Zodduniverse wrote: January 23rd, 2025, 2:08 pm I made a block puffer using a reduced version of the first puffer

could a rake be possible?

Where did that forward-domino-sparking c/5 orthogonal spaceship come from? I don't remember it off-hand, and it doesn't appear to be in the moving objects collection or any post in this thread containing the word "domino". Note that the central component is unnecessary, and it can be made to have only one forward domino spark.

By the way, this particular puffer mechanism is the same as the one found in jslife-moving/velocity-c5o/rake-c5o-p360.rle. Many other c/5 orthogonal rakes can be found in Paul Tooke's c/5 rakes collection.

Also, I moved your post to the spaceship discussion thread.

moebius · Post by **moebius** » January 24th, 2025, 9:34 am

Hi Matthias,

You wrote:

There are of course several ways to measure spaceship height. Your method seems like it may (or may not?) be slightly different than Keith's moving box method, which is of course different from the all-phases definition. I'm especially curious to know if anyone can confirm my old result that there are no period-5 2c/5 ships that fit in the same height-10 bounding box through its entire period.

Tim, were these searches done with knightt? Are they complete in the sense that all 2c/5 ships of "height 47/48" can be constructed from the ships in the above collections? If so, do you think a similar "height 50" search could be completed? I would assume "height 50" means "(up to) height 10 in each phase". Is this correct?

I do max height searches using "knighty", a modified version of "knightt" that puts all phases of a column of cells of a spaceship in a single 64 bit integer. It does fairly reliably find all (in the constructible from sense) spaceships up to the specified height. There is a natural way to order the phases when the movement amount is relatively prime to the period. This leads directly to a conception of height that is probably identical to Keith's moving windows idea.

For example for a height 47 2c/5 spaceship the heights of the phase of the spaceships must fit within the following envelope with phase 0 being what I consider the most advanced phase (also phase 5 is included for illustration and is a 2 cell advanced version of phase 0):

Code: Select all

01234 5
      x
   xx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxx   
x

Envelope for a height 48 2c/5 spaceship:

Code: Select all

01234 5
      x
   xx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxx   
xx

Envelope for a height 49 2c/5 spaceship:

Code: Select all

01234 5
      x
   xx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx  
xx

Envelope for a height 50 2c/5 spaceship:

Code: Select all

01234 5
      x
   xx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx x
xxxxx  
xxx

So for a height 50 spaceship all phases can be height 10, but they have to move in the specified envelope. So running such a search would not exclude certain pathological examples of ways to fit within a single height 10 unmoving envelope.

Have a happy day,

Tim Coe

Edit:

The following might come to mind:

Question: What happens when the movement is not relatively prime to the period?

Answer: knighty doesn't work

Zodduniverse · Post by **Zodduniverse** » January 24th, 2025, 12:35 pm

Sokwe wrote: January 23rd, 2025, 7:34 pm Where did that forward-domino-sparking c/5 orthogonal spaceship come from?

Here's the post where the ship was discovered(?)

May13 wrote: October 15th, 2022, 10:29 pm
May13 wrote: January 31st, 2022, 11:52 pm Returning to my own search, this partial can eat boats and blinkers:
Code: Select all
Completed using ikpx2, JLS and qfind:
Code: Select all

Anivec · Post by **Anivec** » January 24th, 2025, 12:58 pm

Zodduniverse wrote: January 23rd, 2025, 2:08 pm
I made a block puffer using a reduced version of the first puffer

Code: Select all

x = 203, y = 140, rule = B3/S23
38b3o13b3o89b3o13b3o$38bo2bo3b2ob2o3bo2bo89bo2bo3b2ob2o3bo2bo$36b8obo
3bob8o85b8obo3bob8o$35bobobob3obo3bob3obobobo83bobobob3obo3bob3obobob
o$35bo23bo83bo23bo$37bo3bo3b2ob2o3bo3bo87bo3bo3b2ob2o3bo3bo$35b2o4bo11b
o4b2o83b2o4bo11bo4b2o$35bo6bo9bo6bo83bo6bo9bo6bo$41bo11bo95bo11bo2$41b
2o9b2o95b2o9b2o$40bo2bo7bo2bo93bo2bo7bo2bo$39bo2b2o7b2o2bo91bo2b2o7b2o
2bo$40b3o9b3o93b3o9b3o$42bo9bo97bo9bo2$38b5o4bo4b5o89b5o4bo4b5o$38b2o
4b3ob3o4b2o89b2o4b3ob3o4b2o$39bo5bo3bo5bo91bo5bo3bo5bo$39bobo2bo5bo2b
obo91bobo2bo5bo2bobo$44bo5bo101bo5bo$44b2o3b2o101b2o3b2o2$41b3o7b3o95b
3o7b3o$43bo7bo99bo7bo$40bo3bo5bo3bo93bo3bo5bo3bo$40bo4bo3bo4bo93bo4bo
3bo4bo$40bo13bo93bo13bo$40b5o5b5o93b5o5b5o8$64b3o$64bo$10bo7bo46bo118b
o7bo$4b2obobob2o3b2obobob2o153b2obobob2o3b2obobob2o$b3obob3o9b3obob3o
147b3obob3o9b3obob3o$bo3bobo5bobo5bobo3bo147bo3bobo5bobo5bobo3bo$5b2o
6bobo6b2o155b2o6bobo6b2o$2b2o9bobo9b2o149b2o9bobo9b2o$2b2ob2o15b2ob2o
149b2ob2o15b2ob2o$6bo15bo68b3o86bo15bo$93bo$92bo2$154bo$154bo$153b2o3b
2o4b3o$151b4o2bo2bo$156bo2bo$149b2obo2bob3o$10bo5b2o5b2o5bo117b3obo3b
o15bo5b2o5b2o5bo$8bo2b2ob2o2bo3bo2b2ob2o2bo34bo3b3o5b3o3bo31bo3b3o5b3o
3bo10bo6b2o15bo2b2ob2o2bo3bo2b2ob2o2bo$6b3o4bobo3bobo3bobo4b3o29b2ob5o
b2o3b2ob5ob2o25b2ob5ob2o3b2ob5ob2o6bo4bo3bo13b3o4bobo3bobo3bobo4b3o$6b
2o2bo2b3ob2o3b2ob3o2bo2b2o27bob2obo5bobobobo5bob2obo21bob2obo5bobobob
o5bob2obo4bo4bo17b2o2bo2b3ob2o3b2ob3o2bo2b2o$6b3o2b3o4bo3bo4b3o2b3o26b
o3bobo3b5ob5o3bobo3bo19bo3bobo3b5ob5o3bobo3bo3bo3bo18b3o2b3o4bo3bo4b3o
2b3o$7bobo2bo15bo2bobo31b3o5b2o3b2o5b3o27b3o5b2o3b2o5b3o8bo2bo2b2o15b
obo2bo15bo2bobo$8bo23bo29bo2bob3o13b3obo2bo21bo2bob3o13b3obo2bo8bo3bo
6b2o8bo23bo$64bo23bo25bo23bo21b2o3$71b2o5b2o43b2o5b2o$63b4obobobo5bob
obob4o27b4obobobo5bobobob4o$62b3obobob2obo3bob2obobob3o25b3obobob2obo
3bob2obobob3o$4bo5b2o5b2o5bo37bo3bobo13bobo3bo25bo3bobo13bobo3bo37bo5b
2o5b2o5bo$2bo2b2ob2o2bo3bo2b2ob2o2bo36bob3o5b2ob2o5b3obo27bob3o5b2ob2o
5b3obo36bo2b2ob2o2bo3bo2b2ob2o2bo$3o4bobo3bobo3bobo4b3o34b2o21b2o27b2o
21b2o34b3o4bobo3bobo3bobo4b3o$2o2bo2b3ob2o3b2ob3o2bo2b2o34b5o15b5o27b
5o15b5o34b2o2bo2b3ob2o3b2ob3o2bo2b2o$3o2b3o4bo3bo4b3o2b3o37b2o15b2o33b
2o15b2o37b3o2b3o4bo3bo4b3o2b3o$bobo2bo15bo2bobo147bobo2bo15bo2bobo$2b
o23bo43bo7bo45bo7bo43bo23bo$64b2obobob2o3b2obobob2o33b2obobob2o3b2obo
bob2o$61b3obob3o9b3obob3o27b3obob3o9b3obob3o$61bo3bobo5bobo5bobo3bo27b
o3bobo5bobo5bobo3bo$65b2o6bobo6b2o35b2o6bobo6b2o$62b2o9bobo9b2o29b2o9b
obo9b2o$62b2ob2o15b2ob2o29b2ob2o15b2ob2o$66bo15bo37bo15bo5$46b4o14b4o
67b4o14b4o$45b6o12b6o65b6o12b6o$43bo3b2o3bo8bo3b2o3bo61bo3b2o3bo8bo3b
2o3bo$42b2obob2obob2o6b2obob2obob2o59b2obob2obob2o6b2obob2obob2o$41bo
3b6o3bo4bo3b6o3bo57bo3b6o3bo4bo3b6o3bo$41bobo3b2o3bobo4bobo3b2o3bobo57b
obo3b2o3bobo4bobo3b2o3bobo$38bo3bo11b2o2b2o11bo3bo51bo3bo11b2o2b2o11b
o3bo$37bob2o32b2obo49bob2o32b2obo$40bobo12bo2bo12bobo55bobo12bo2bo12b
obo$37b2ob5o10b4o10b5ob2o49b2ob5o10b4o10b5ob2o$40bo2b2o9b6o9b2o2bo55b
o2b2o9b6o9b2o2bo$40b2o2b2o7b8o7b2o2b2o55b2o2b2o7b8o7b2o2b2o$40bobo6b2o
bo8bob2o6bobo55bobo6b2obo8bob2o6bobo$42bo5bobo4bo2bo4bobo5bo59bo5bobo
4bo2bo4bobo5bo$40b3o6bo3bob4obo3bo6b3o55b3o6bo3bob4obo3bo6b3o$39b2o8b
2ob2o2b2o2b2ob2o8b2o53b2o8b2ob2o2b2o2b2ob2o8b2o$50b2o2bo4bo2b2o75b2o2b
o4bo2b2o$41b3o5bo4bo4bo4bo5b3o57b3o5bo4bo4bo4bo5b3o$41b4o24b4o57b4o24b
4o$40bo4bo5bo2bo4bo2bo5bo4bo55bo4bo5bo2bo4bo2bo5bo4bo$38b2o5bo7b2o4b2o
7bo5b2o51b2o5bo7b2o4b2o7bo5b2o$37b3o13b2o4b2o13b3o49b3o13b2o4b2o13b3o
$37bo4b2o7bo2bo4bo2bo7b2o4bo49bo4b2o7bo2bo4bo2bo7b2o4bo$38bo3b2o6bo5b
2o5bo6b2o3bo51bo3b2o6bo5b2o5bo6b2o3bo$38bo3b3o6bo4b2o4bo6b3o3bo51bo3b
3o6bo4b2o4bo6b3o3bo$42bobo11b2o11bobo59bobo11b2o11bobo$43b2o8bo6bo8b2o
61b2o8bo6bo8b2o$53b2o4b2o81b2o4b2o$40bobo28bobo55bobo28bobo$40bo2bo11b
o2bo11bo2bo55bo2bo11bo2bo11bo2bo$39bo3bo4b3obo8bob3o4bo3bo53bo3bo4b3o
bo8bob3o4bo3bo$38bo10bo3bobo2bobo3bo10bo51bo10bo3bobo2bobo3bo10bo$44b
o4bobob3o2b3obobo4bo63bo4bobob3o2b3obobo4bo$38b2o4bo6b3obo2bob3o6bo4b
2o51b2o4bo6b3obo2bob3o6bo4b2o$42bo2bo4b2o10b2o4bo2bo59bo2bo4b2o10b2o4b
o2bo$42bo10bo6bo10bo59bo10bo6bo10bo$41b2o28b2o57b2o28b2o$37bo4b2o26b2o
4bo49bo4b2o26b2o4bo$36b2o38b2o47b2o38b2o$36bo2bo34bo2bo47bo2bo34bo2bo
$38b3o32b3o51b3o32b3o$37bo38bo49bo38bo$41b2o28b2o57b2o28b2o$37bo3bobo
26bobo3bo49bo3bobo26bobo3bo$39b3o2bo24bo2b3o53b3o2bo24bo2b3o$36b2o38b
2o47b2o38b2o$40bo32bo55bo32bo$39bo34bo53bo34bo$39b2ob2o26b2ob2o53b2ob
2o26b2ob2o$42bo28bo59bo28bo2$44b2o22b2o63b2o22b2o$41b3o26b3o57b3o26b3o
$41b2o28b2o57b2o28b2o!

could a rake be possible?

Reduction:

Code: Select all

x = 203, y = 140, rule = B3/S23
38b3o13b3o89b3o13b3o$38bo2bo3b2ob2o3bo2bo89bo2bo3b2ob2o3bo2bo$36b8obo
3bob8o85b8obo3bob8o$35bobobob3obo3bob3obobobo83bobobob3obo3bob3obobob
o$35bo23bo83bo23bo$37bo3bo3b2ob2o3bo3bo87bo3bo3b2ob2o3bo3bo$35b2o4bo11b
o4b2o83b2o4bo11bo4b2o$35bo6bo9bo6bo83bo6bo9bo6bo$41bo11bo95bo11bo2$41b
2o9b2o95b2o9b2o$40bo2bo7bo2bo93bo2bo7bo2bo$39bo2b2o7b2o2bo91bo2b2o7b2o
2bo$40b3o9b3o93b3o9b3o$42bo9bo97bo9bo2$38b5o4bo4b5o89b5o4bo4b5o$38b2o
4b3ob3o4b2o89b2o4b3ob3o4b2o$39bo5bo3bo5bo91bo5bo3bo5bo$39bobo2bo5bo2b
obo91bobo2bo5bo2bobo$44bo5bo101bo5bo$44b2o3b2o101b2o3b2o2$41b3o7b3o95b
3o7b3o$43bo7bo99bo7bo$40bo3bo5bo3bo93bo3bo5bo3bo$40bo4bo3bo4bo93bo4bo
3bo4bo$40bo13bo93bo13bo$40b5o5b5o93b5o5b5o8$64b3o$64bo$10bo7bo46bo118b
o7bo$4b2obobob2o3b2obobob2o153b2obobob2o3b2obobob2o$b3obob3o9b3obob3o
147b3obob3o9b3obob3o$bo3bobo5bobo5bobo3bo147bo3bobo5bobo5bobo3bo$5b2o
6bobo6b2o155b2o6bobo6b2o$2b2o9bobo9b2o149b2o9bobo9b2o$2b2ob2o15b2ob2o
149b2ob2o15b2ob2o$6bo15bo68b3o86bo15bo$93bo$92bo2$154bo$154bo$153b2o3b
2o4b3o$151b4o2bo2bo$156bo2bo$149b2obo2bob3o$10bo5b2o5b2o5bo117b3obo3b
o15bo5b2o5b2o5bo$8bo2b2ob2o2bo3bo2b2ob2o2bo34bo3b3o5b3o3bo31bo3b3o5b3o
3bo10bo6b2o15bo2b2ob2o2bo3bo2b2ob2o2bo$6b3o4bobo3bobo3bobo4b3o29b2ob5o
b2o3b2ob5ob2o25b2ob5ob2o3b2ob5ob2o6bo4bo3bo13b3o4bobo3bobo3bobo4b3o$6b
2o2bo2b3ob2o3b2ob3o2bo2b2o27bob2obo5bobobobo5bob2obo21bob2obo5bobobob
o5bob2obo4bo4bo17b2o2bo2b3ob2o3b2ob3o2bo2b2o$6b3o2b3o4bo3bo4b3o2b3o26b
o3bobo3b5ob5o3bobo3bo19bo3bobo3b5ob5o3bobo3bo3bo3bo18b3o2b3o4bo3bo4b3o
2b3o$7bobo2bo15bo2bobo31b3o5b2o3b2o5b3o27b3o5b2o3b2o5b3o8bo2bo2b2o15b
obo2bo15bo2bobo$8bo23bo29bo2bob3o13b3obo2bo21bo2bob3o13b3obo2bo8bo3bo
6b2o8bo23bo$64bo23bo25bo23bo21b2o3$71b2o5b2o43b2o5b2o$63b4obobobo5bob
obob4o27b4obobobo5bobobob4o$62b3obobob2obo3bob2obobob3o25b3obobob2obo
3bob2obobob3o$4bo5b2o5b2o5bo37bo3bobo13bobo3bo25bo3bobo13bobo3bo37bo5b
2o5b2o5bo$2bo2b2ob2o2bo3bo2b2ob2o2bo36bob3o5b2ob2o5b3obo27bob3o5b2ob2o
5b3obo36bo2b2ob2o2bo3bo2b2ob2o2bo$3o4bobo3bobo3bobo4b3o34b2o21b2o27b2o
21b2o34b3o4bobo3bobo3bobo4b3o$2o2bo2b3ob2o3b2ob3o2bo2b2o34b5o15b5o27b
5o15b5o34b2o2bo2b3ob2o3b2ob3o2bo2b2o$3o2b3o4bo3bo4b3o2b3o37b2o15b2o33b
2o15b2o37b3o2b3o4bo3bo4b3o2b3o$bobo2bo15bo2bobo147bobo2bo15bo2bobo$2b
o23bo43bo7bo45bo7bo43bo23bo$64b2obobob2o3b2obobob2o33b2obobob2o3b2obo
bob2o$61b3obob3o9b3obob3o27b3obob3o9b3obob3o$61bo3bobo5bobo5bobo3bo27b
o3bobo5bobo5bobo3bo$65b2o6bobo6b2o35b2o6bobo6b2o$62b2o9bobo9b2o29b2o9b
obo9b2o$62b2ob2o15b2ob2o29b2ob2o15b2ob2o$66bo15bo37bo15bo5$46b4o103b4o
$45b6o101b6o$43bo3b2o3bo97bo3b2o3bo$42b2obob2obob2o95b2obob2obob2o$41b
o3b6o3bo93bo3b6o3bo$41bobo3b2o3bobo93bobo3b2o3bobo$38bo3bo10bo3bo87bo
3bo10bo3bo$37bob2o14b2obo85bob2o14b2obo$40bobo10bobo91bobo10bobo$37b2o
b5o6b5ob2o85b2ob5o6b5ob2o$40bo2b2o6b2o2bo91bo2b2o6b2o2bo$40b2o2b2o4b2o
2b2o91b2o2b2o4b2o2b2o$40bobo10bobo91bobo10bobo$42bo10bo95bo10bo$40b3o
10b3o91b3o10b3o$39b2o14b2o89b2o14b2o2$41b3o8b3o93b3o8b3o$41b4o6b4o93b
4o6b4o$40bo4bo4bo4bo91bo4bo4bo4bo$38b2o5bo4bo5b2o87b2o5bo4bo5b2o$37b3o
16b3o85b3o16b3o$37bo4b2o8b2o4bo85bo4b2o8b2o4bo$38bo3b2o8b2o3bo87bo3b2o
8b2o3bo$38bo3b3o6b3o3bo87bo3b3o6b3o3bo$42bobo6bobo95bobo6bobo$43b2o6b
2o97b2o6b2o2$40bobo10bobo91bobo10bobo$40bo2bo8bo2bo91bo2bo8bo2bo$39bo
3bo8bo3bo89bo3bo8bo3bo$38bo18bo87bo18bo$44bo6bo99bo6bo$38b2o4bo6bo4b2o
87b2o4bo6bo4b2o$42bo2bo4bo2bo95bo2bo4bo2bo$42bo10bo95bo10bo$41b2o10b2o
93b2o10b2o$37bo4b2o8b2o4bo85bo4b2o8b2o4bo$36b2o20b2o83b2o20b2o$36bo2b
o16bo2bo83bo2bo16bo2bo$38b3o14b3o87b3o14b3o$37bo20bo85bo20bo$41b2o10b
2o93b2o10b2o$37bo3bobo8bobo3bo85bo3bobo8bobo3bo$39b3o2bo6bo2b3o89b3o2b
o6bo2b3o$36b2o20b2o83b2o20b2o$40bo14bo91bo14bo$39bo16bo89bo16bo$39b2o
b2o8b2ob2o89b2ob2o8b2ob2o$42bo10bo95bo10bo2$44b2o4b2o99b2o4b2o$41b3o8b
3o93b3o8b3o$41b2o10b2o93b2o10b2o!

Post by **Sokwe** » February 2nd, 2025, 9:35 am

This is a record-keeping post for when I update the moving objects collection.

The OWSS collection within the moving objects collection is missing the following 5 ships:

Code: Select all

x = 64, y = 28, rule = B3/S23
3o9b3o9b3o9b3o9bo13bo$o2bo8bo2bo8bo2bo8bo2bo7b3o11b3o$o5b3o3bo11bo5b3o
3bo9b2obo4b3o3b2obo$o4bo2bo3bo3bo7bo4bo2bo3bo3bo5b3o4bo2bo3b3o$o7bo3bo
11bo7bo3bo3bo5b3o7bo3b3o$bobo4bo4bobo8bo7bo3bo9b3o7bo3b3o$4bo3bo16bobo
4bo4bobo7b2o7bo4b2o$4bo3bo19bo3bo19bo3bo$8bo23bo23bo$5bobo21bobo21bobo
8$24b3o9b3o9bo13bo$24bo2bo8bo2bo7b3o11b3o$24bo5b3o3bo9b2obo4b3o3b2obo$
24bo4bo2bo3bo3bo5b3o4bo2bo3b3o$24bo7bo3bo3bo5b3o7bo3b3o$24bo7bo3bo9b3o
7bo3b3o$25bobo4bo4bobo7b2o7bo4b2o$28bo3bo19bo3bo$28bo3bo19bo3bo$32bo
23bo$29bobo21bobo!

Here are (I think) all of the OWSSs supported by exactly two standard spaceships up to 34 bits (grouped by OWSS length):

Code: Select all

x = 383, y = 129, rule = B3/S23
31b3o3b3o3b3o9b3o3b3o3b3o15b3o3b3o15b3o3b3o87b3o3b3o$31bo2bobo2bo3bo2b
o8bo2bobo2bo3bo2bo13bo2bo3bo2bo13bo2bo3bo2bo85bo2bo3bo2bo$31bo7bo3bo
11bo7bo3bo11b3o5bo3bo11b3o5bo3bo83b3o5bo3bo$31bo7bo3bo11bo7bo3bo11bo2b
o4bo3bo11bo2bo4bo3bo83bo2bo4bo3bo$32bobo4bo4bobo8bo7bo4bobo8bo7bo4bobo
8bo7bo4bobo80bo7bo4bobo$35bo3bo16bobo4bo15bo7bo15bo7bo87bo7bo$39bo23bo
16bob2o3bo15bo7bo88bobo4bo$36bobo21bobo21bobo17bobobobo96bo$obobo3bo
195bobo2$4bo3bo2$obobo3bo2$4bo3bo2$obobo3bo2$31b3o3b3o15b3o3b3o21b3o
21b3o93b3o$31bo2bobo2bo15bo2bobo2bo20bo2bo20bo2bo92bo2bo$31bo7bo3b3o9b
o7bo3b3o9b3o5bo3b3o9b3o5bo3b3o81b3o5bo3b3o$31bo7bo3bo2bo8bo7bo3bo2bo8b
o2bo4bo3bo2bo8bo2bo4bo3bo2bo80bo2bo4bo3bo2bo$32bobo4bo3bo11bo7bo3bo11b
o7bo3bo11bo7bo3bo83bo7bo3bo$35bo3bo3bo12bobo4bo3bo11bo7bo3bo11bo7bo3bo
83bo7bo3bo$39bo4bobo16bo4bobo9bob2o3bo4bobo8bo7bo4bobo81bobo4bo4bobo$
36bobo21bobo21bobo17bobobobo96bo$204bobo22$31b3o33b3o21b3o9b3o$31bo2bo
32bo2bo20bo2bo8bo2bo$31bo5b3o3b3o9b3o3b3o3bo17b3o3bo11bo5b3o3b3o9b3o3b
3o3b3o15b3o3b3o33b3o3b3o3b3o9b3o3b3o3b3o9b3o3b3o3b3o15b3o3b3o15b3o3b3o
39b3o21b3o$31bo4bo2bo3bo2bo8bo2bobo2bo3bo3bo12bo2bo3bo3bo7bo4bo2bo3bo
2bo8bo2bobo2bo3bo2bo13bo2bo3bo2bo32bo2bobo2bo3bo2bo8bo2bobo2bo3bo2bo8b
o2bobo2bo3bo2bo13bo2bo3bo2bo13bo2bo3bo2bo37bo2bo20bo2bo$31bo7bo3bo11bo
7bo3bo11b3o5bo3bo11bo7bo3bo11bo7bo3bo11b3o5bo3bo35bo7bo3bo11bo7bo3bo
11bo7bo3bo11b3o5bo3bo11b3o5bo3bo35b3o5bo3b3o9b3o5bo3b3o$32bobo4bo3bo
11bo7bo4bobo8bo2bo4bo4bobo8bo7bo3bo11bo7bo3bo11bo2bo4bo3bo35bo7bo3bo
11bo7bo3bo11bo7bo3bo11bo2bo4bo3bo11bo2bo4bo3bo35bo2bo4bo3bo2bo8bo2bo4b
o3bo2bo$35bo3bo4bobo8bo7bo15bo7bo16bobo4bo4bobo8bo7bo4bobo8bo7bo4bobo
33bobo4bo4bobo8bo7bo4bobo8bo7bo4bobo8bo7bo4bobo8bo7bo4bobo32bo7bo3bo
11bo7bo3bo$35bo3bo16bobo4bo15bo7bo19bo3bo15bo7bo15bo7bo43bo3bo16bobo4b
o15bo7bo15bo7bo15bo7bo39bo7bo3bo11bo7bo3bo$39bo23bo15bo7bo23bo16bob2o
3bo15bo7bo43bo3bo19bo3bo16bobo4bo15bo7bo15bo7bo40bobo4bo4bobo8bo7bo4bo
bo$36bobo21bobo17bobobobo21bobo21bobo16bo3b2obo48bo23bo23bo16bob2o3bo
15bo7bo43bo3bo16bobo4bo$obobo3bobobo139bobo49bobo21bobo21bobo21bobo17b
obobobo48bo23bo$348bobo21bobo$4bo7bo2$obobo3bobobo2$4bo7bo2$obobo3bobo
bo18b3o69b3o$31bo2bo68bo2bo$31bo5b3o15b3o3b3o3b3o15b3o3b3o9bo5b3o15b3o
3b3o21b3o63b3o3b3o15b3o3b3o21b3o21b3o$31bo4bo2bo15bo2bobo2bo3bo2bo13bo
2bo3bo2bo8bo4bo2bo15bo2bobo2bo20bo2bo63bo2bobo2bo15bo2bobo2bo20bo2bo
20bo2bo$31bo7bo3b3o9bo7bo3bo11b3o5bo3bo11bo7bo3b3o9bo7bo3b3o9b3o5bo3b
3o57bo7bo3b3o9bo7bo3b3o9b3o5bo3b3o9b3o5bo3b3o$32bobo4bo3bo2bo8bo7bo3bo
3bo7bo2bo4bo3bo3bo7bo7bo3bo2bo8bo7bo3bo2bo8bo2bo4bo3bo2bo56bo7bo3bo2bo
8bo7bo3bo2bo8bo2bo4bo3bo2bo8bo2bo4bo3bo2bo$35bo3bo3bo11bo7bo3bo11bo7bo
3bo12bobo4bo3bo11bo7bo3bo11bo7bo3bo59bo7bo3bo11bo7bo3bo11bo7bo3bo11bo
7bo3bo$35bo3bo3bo12bobo4bo4bobo8bo7bo4bobo12bo3bo3bo11bo7bo3bo11bo7bo
3bo60bobo4bo3bo11bo7bo3bo11bo7bo3bo11bo7bo3bo$39bo4bobo16bo15bo7bo23bo
4bobo9bob2o3bo4bobo8bo7bo4bobo60bo3bo4bobo9bobo4bo4bobo8bo7bo4bobo8bo
7bo4bobo$36bobo21bobo17bobobobo21bobo21bobo16bo3b2obo72bo23bo16bob2o3b
o15bo7bo$152bobo73bobo21bobo21bobo17bobobobo10$55b3o3b3o21b3o$55bo2bob
o2bo20bo2bo$55bo7bo3b3o9b3o5bo3b3o$55bo7bo3bo2bo8bo2bo4bo3bo2bo$55bo7b
o3bo11bo7bo3bo$56bobo4bo3bo3bo7bo7bo3bo3bo$63bo3bo11bo7bo3bo$60bobo5bo
bo9bobobobo5bobo25$obobo3bo3bo2$4bo3bo3bo18b3o3b3o15b3o3b3o21b3o21b3o
93b3o$31bo2bobo2bo15bo2bobo2bo20bo2bo20bo2bo92bo2bo$obobo3bobobo18bo7b
o4bo10bo7bo4bo10b3o5bo4bo10b3o5bo4bo82b3o5bo4bo$31bo7bo3b3o9bo7bo3b3o
9bo2bo4bo3b3o9bo2bo4bo3b3o81bo2bo4bo3b3o$4bo7bo19bobo4bo2b2obo9bo7bo2b
2obo9bo7bo2b2obo9bo7bo2b2obo81bo7bo2b2obo$35bo3bo2b3o11bobo4bo2b3o10bo
7bo2b3o10bo7bo2b3o82bo7bo2b3o$obobo7bo26bo3b2o18bo3b2o11bob2o3bo3b2o
10bo7bo3b2o83bobo4bo3b2o$36bobo21bobo21bobo17bobobobo96bo$204bobo!

here are the total counts for different lengths of OWSSs escorted by exactly two standard spaceships:

Length 7: 20 * (1+19/2) = 210
Length 8: 19 * (1+18/2) = 190
Length 9: 17 * (1+16/2) = 153
Length 10: 16 * (1+15/2) = 136
Length 11: 11 * (1+10/2) = 66
Length 12: 6 * (1+5/2) = 21
Length 13: 2 * (1+1/2) = 3
Length 14: 1 * (1+0/2) = 1
All lengths: 780

Edit: Mark Niemiec's Life page indicates that there are three glide-symmetric LWSS-supported 9WSSs, but after trying seemingly all positions and phase combinations, I could only find these two:

Code: Select all

x = 43, y = 10, rule = B3/S23
7b3o23b3o$6bo2bo22bo2bo$2bo6bo4bo12b3o5bo3b3o$b3o5bo3b3o11bo2bo4bo3bo
2bo$2obo5bo2b2obo11bo7bo3bo$3o6bo2b3o12bo7bo3bo$b2o6bo3b2o13bobo4bo4bo
bo$9bo21bo3bo$5bo3bo25bo$6bobo23bobo!

Am I missing something?

amling · Post by **amling** » February 3rd, 2025, 1:51 pm

I had never run any version of LLSSS min pop stuff for 2c/4 since it was never going to terminate past pop 17, but I realized it doesn't have to be terminate to be useful. Maybe.

I ran e.g. pop 32 (inspired by a news item mentioning something about "the only known pop 32 ship") to 60 GB and sorted through the results.

The worst of the two limiting generations completed w_pos 47 which could find a pattern of height 39W or 19.5 Y rows (staggered envelope). Ultimately my best efforts to strip down and remove disconnected stuff ends with these 201 results (I now realize some of these are duplicates in different generations for complicated reasons):

Code: Select all

#C [[ TRACK 0 -1/2 ]]
x = 19, y = 3621, rule = B3/S23
3o$o2bo$o$o$bobo11$2b3o$bo2bo$4bo$o3bo$4bo$bobo11$2b3o$bo2bo$4bo$o3bo$
o3bo$4bo$bobo11$3o3b3o$o2bobo2bo$o7bo$o7bo$bobobobo11$3o$o2bo$o5b3o$o
4bo2bo$o7bo$bobo4bo$8bo$5bobo11$3o$o2bo$o5b3o$o4bo2bo$o7bo$o7bo$bobobo
bo11$3o3b3o$o2bobo2bo$o7bo$o7bo$o7bo$bobobobo11$3o3b3o$o2bobo2bo$o7bo$
o7bo$o4bobo$o$bobo11$3o3b3o$o2bobo2bo$o7bo$o7bo$o3b2obo$bobo11$3o$o2bo
$o$o3bo2b3o$o3bobo2bo$o8bo$bobo5bo$6bobo11$3o$o2bo$o6b3o$o5bo2bo$bobo
5bo$5bo3bo$5bo3bo$9bo$6bobo11$3o$o2bo3b3o$o5bo2bo$o8bo$bobobo3bo$5bo3b
o$9bo$6bobo11$3o$o2bo$o5b3o$o4bo2bo$o7bo$bobo4bo$4bo3bo$8bo$5bobo11$3o
$o2bo$o5b3o$o4bo2bo$o7bo$o7bo$bobo4bo$8bo$5bobo11$3o$o2bo$o5b3o$o4bo2b
o$o7bo$o7bo$bob2o3bo$5bobo11$3o4b3o$o2bo2bo2bo$o8bo$o4bo3bo$bobobo3bo$
9bo$6bobo11$3o3b3o$o2bobo2bo$o7bo$o7bo$o7bo$o7bo$bobobobo11$3o3b3o$o2b
obo2bo$o7bo$o7bo$o7bo$o3b2obo$bobo11$bo$3o4b3o$ob2o2bo2bo$b3o5bo$b2o2b
o3bo$9bo$6bobo11$bo4b3o$3o2bo2bo$ob2o4bo$b4o3bo$b2o5bo$5bobo11$8b3o$3o
4bo2bo$o2bo6bo$o5bo3bo$o3bo5bo$o3bo2bobo$o$bobo11$6b3o$3o3bo2bo$o2bo2b
o$o5bo$o3bobo$o3bo$o5b3o$bobo11$3o$o2bo$o7b3o$o3bo2bo2bo$o3bo5bo$o5bo
3bo$bobo6bo$7bobo11$3o$o2bo4b3o$o6bo2bo$o3bo5bo$o3bobo3bo$o9bo$bobo3bo
bo11$3o$o2bo$o$o3bo2b3o$o5bo2bo$bobo5bo$5bo3bo$5bo3bo$9bo$6bobo11$3o$o
2bo$o$o5bo$o4b3o$bo3bob2o$6b3o$6b3o$6b2o11$3o5b3o$o2bo3bo2bo$o9bo$o3bo
bo3bo$o5bo3bo$bobo6bo$7bobo11$7b3o$6bo2bo$2bo6bo$b3o5bo$2obo5bo$3o6bo$
3o5bo$b2o11$bo4b3o$3o2bo2bo$ob2o4bo$b4o3bo$b2obo3bo$8bo$5bobo11$3o$o2b
o4bo$o6b3o$o3bob2obo$o3bob3o$o6b2o$bobo11$8b3o$7bo2bo$3o7bo$o2bo2bo3bo
$o5bo3bo$o3bo5bo$o3bo2bobo$o$bobo11$8b3o$3o4bo2bo$o2bo6bo$o5bo3bo$o3bo
bo3bo$o3bo5bo$o6bobo$bobo11$7bo$3o3b3o$o2bo2bob2o$o6b3o$o3bo2b3o$o6b2o
$bobo11$bo$3o4b3o$ob2o2bo2bo$b3o5bo$b3obo3bo$b2o6bo$6bobo11$3o5bo$o2bo
3b3o$o6bob2o$o7b3o$o3bo3b3o$bobo4b2o11$3o5b3o$o2bo3bo2bo$o9bo$o3bobo3b
o$o3bobo3bo$o9bo$bobo3bobo11$3o4bo$o2bo2b3o$o4b2obo$o3b4o$o4b3o$bobo2b
2o11$2bo5b3o$b3o3bo2bo$2obo6bo$3o7bo$3o7bo$b2o3bo3bo$7bobo11$b3o3b3o3b
3o$o2bo3bo2bobo2bo$3bo3bo7bo$3bo3bo7bo$obo5bobobobo11$9bo$2b3o3b3o$bo
2bo2b2obo$4bo2b3o$o3bo2b3o$o3bo3b2o$4bo$bobo11$8b3o$2bo4bo2bo$b3o6bo$
2obo2bo3bo$3o7bo$3o3bo3bo$b2o4bobo11$7bo$3o3b3o$o2bo2bob2o$o6b3o$o3bo
2b3o$o6b2o$o3bo$bobo11$7b3o$bo4bo2bo$3o6bo$ob2obo3bo$b3obo3bo$b3o5bo$b
2o3bobo11$2b3o$bo2bo$4bo$o3bo6b3o$4bo5bo2bo$bobo2b2o5bo$6b2obo3bo$9bo
3bo$13bo$10bobo11$2b3o$bo2bo5bo$4bo4b3o$o3bo3b2obo$o3bo3b3o$4bo3b3o$bo
bo5b2o11$bo$3o4b3o$ob2o2bo2bo$b3o5bo$b3obo3bo$b2o2bo3bo$9bo$6bobo11$3o
$o2bo$o$o3bo4b3o$o3bo4bo2bo$bo3bo3bo$6bo2bo3bo$3bo5bo3bo$5bo3bo$10bobo
11$3o4bo$o2bo2b3o$o4b2obo$o3b4o$o3b4o$o5b2o$bobo11$13b3o$13bo2bo$3o3b
3o4bo$o2bobo2bo4bo$o7bo5bobo$o7bo$bobo4bo$8bo$5bobo11$13b3o$6b3o4bo2bo
$5bo2bo4bo$3o5bo4bo$o2bo4bo5bobo$o7bo$o7bo$bobobobo11$8bo$7b3o$3o4bob
2o$o2bo4b3o$o7b3o$o7b3o$o7b2o$o$bobo11$8b3o$8bo2bo$8bo5b3o$b3o4bo4bo2b
o$o2bo4bo7bo$3bo4bo7bo$3bo5bobobobo$obo11$7b3o$7bo2bo$b3o3bo5b3o$o2bo
3bo4bo2bo$3bo3bo7bo$3bo3bo7bo$obo5bobobobo11$6b3o4b3o$5bo2bo4bo2bo$3o
5bo4bo$o2bo4bo4bo$o7bo5bobo$o7bo$bobobobo11$6b3o3b3o$5bo2bo3bo2bo$3o5b
o3bo$o2bo4bo3bo$o7bo4bobo$o4bobo$o$bobo11$2bo$b3o3b3o$2obo2bo2bo$3o6bo
$3o6bo$3o6bo$b2o6bo$6bobo11$2b3o3b3o3b3o$bo2bo3bo2bobo2bo$4bo3bo7bo$o
3bo3bo7bo$4bo4bobobobo$bobo11$b3o$o2bo$3bo4b3o$3bo4bo2bo$obo5bo5b3o$8b
o4bo2bo$8bo7bo$8bo7bo$9bobobobo11$b3o$o2bo4b3o3b3o$3bo4bo2bobo2bo$3bo
4bo7bo$obo5bo7bo$8bo4bobo$8bo$9bobo11$b3o3b3o$o2bo3bo2bo$3bo3bo5b3o$3b
o3bo4bo2bo$obo4bo7bo$7bo7bo$8bobobobo11$b3o3b3o3b3o$o2bo3bo2bobo2bo$3b
o3bo7bo$3bo3bo7bo$obo5bobo4bo$15bo$12bobo11$b3o3b3o3b3o$o2bo3bo2bobo2b
o$3bo3bo7bo$3bo3bo7bo$obo5bob2o3bo$12bobo11$b3o3b3o3b3o$o2bo3bo2bobo2b
o$3bo3bo7bo$3bo3bo7bo$obo4bo4bobo$7bo$8bobo11$3o$o2bo$o5b3o3b3o$o4bo2b
o3bo2bo$o7bo3bo$bobo4bo3bo$8bo4bobo$5bobo11$3o$o2bo$o5b3o3b3o$o4bo2bo
3bo2bo$o7bo3bo$o7bo3bo$bobobobo5bobo11$3o5bo$o2bo3b3o$o6bob2o$o7b3o$o
7b3o$o7b3o$bobo4b2o11$3o3b3o$o2bobo2bo$o7bo$o7bo4b3o$bobo4bo4bo2bo$8bo
4bo$5bobo5bo$14bobo11$3o3b3o$o2bobo2bo$o7bo3b3o$o7bo3bo2bo$bobo4bo3bo$
8bo3bo$5bobo5bobo11$3o3b3o4b3o$o2bobo2bo4bo2bo$o7bo4bo$o7bo4bo$bobo4bo
5bobo$8bo$5bobo11$3o3b3o3b3o$o2bobo2bo3bo2bo$o7bo3bo$o7bo3bo$bob2o3bo
4bobo$5bobo11$3o3b3o3b3o$o2bobo2bo3bo2bo$o7bo3bo$o7bo3bo$o7bo4bobo$bob
obobo11$b3o$o2bo6b3o$o4bo4bo2bo$3bobo2bo4bo$2o4bobobo$5bobo4b2o$3bo4bo
$4bo5bo$9bo11$b3o4b3o$bo2bo2bo2bo$o3bo5bo$2bobobo3bo$2bo3bo3bo$2b2o6bo
$3b2o2bobo$3b2o$2bo11$3o$o2bo4b3o$o6bo2bo$o9bo$bobo6bo$5b2o2bo$5bo$6bo
$b3o$o2bo$3bo$3bo$obo11$3o$o2bo$o6bo$o5b3o$o5bob2o$o6b3o$bo2bo2b3o$3bo
3b3o$7b2o11$15b3o$14bo2bo$b3o4b3o6bo$o2bo4bo2bo5bo$3bo4bo5bobo$3bo4bo
3bo$obo5bo3bo$8bo$9bobo11$15b3o$b3o4b3o3bo2bo$o2bo4bo2bo5bo$3bo4bo8bo$
3bo4bo3bobobo$obo5bo3bo$8bo$9bobo11$14b3o$3o3b3o5bo2bo$o2bobo2bo5bo$o
7bo5bo3bo$o7bo5bo$bobo4bo6bobo$8bo$5bobo11$14b3o$14bo2bo$7b3o4bo$6bo2b
o4bo$9bo5bobo$3o2bo3bo$o2bobo3bo$o8bo$o5bobo$bobo11$14b3o$13bo2bo$16bo
$b3o3b3o2bo3bo$o2bo3bo2bobo3bo$3bo3bo8bo$3bo3bo5bobo$obo5bobo11$14b3o$
13bo2bo$8b3o5bo$8bo2bo4bo$8bo7bo$b3o4bo4bobo$o2bo4bo3bo$3bo4bo$3bo5bob
o$obo11$14b3o$13bo2bo$8b3o5bo$8bo2bo4bo$2b3o3bo7bo$bo2bo3bo4bobo$4bo3b
o$o3bo4bobo$4bo$bobo11$14b3o$13bo2bo$2b3o3b3o5bo$bo2bo3bo2bo4bo$4bo3bo
7bo$o3bo3bo7bo$4bo4bobobobo$bobo11$13b3o$13bo2bo$13bo$3o3b3o4bo3bo$o2b
obo2bo4bo$o7bo5bobo$o7bo$bobo4bo$8bo$5bobo11$13b3o$13bo2bo$6b3o4bo$5bo
2bo4bo$3o5bo5bobo$o2bo4bo$o7bo$o7bo$o4bobo$o$bobo11$13b3o$13bo2bo$3o3b
3o4bo$o2bobo2bo4bo$o7bo5bobo$o7bo$o7bo$bob2o3bo$5bobo11$13b3o$13bo2bo$
3o3b3o4bo$o2bobo2bo4bo$o7bo5bobo$o7bo$o7bo$o7bo$bobobobo11$13b3o$6b3o
4bo2bo$5bo2bo4bo$3o5bo4bo$o2bo4bo5bobo$o7bo$o7bo$o4bobo$o$bobo11$13b3o
$3o3b3o4bo2bo$o2bobo2bo4bo$o7bo4bo$o7bo5bobo$o7bo$bob2o3bo$5bobo11$13b
3o$12bo2bo$7b3o5bo$7bo2bo4bo$b3o3bo7bo$o2bo3bo7bo$3bo3bo4bobo$3bo3bo$o
bo5bobo11$13b3o$12bo2bo$7b3o5bo$7bo2bo4bo$b3o3bo7bo$o2bo3bo4bobo$3bo3b
o3bo$3bo3bo$obo5bobo11$13b3o$12bo2bo$b3o3b3o5bo$o2bo3bo2bo4bo$3bo3bo7b
o$3bo3bo7bo$obo4bo4bobo$7bo$8bobo11$13b3o$12bo2bo$b3o3b3o5bo$o2bo3bo2b
o4bo$3bo3bo7bo$3bo3bo4bobo$obo4bo3bo$7bo$8bobo11$12b3o$12bo2bo$6b3o3bo
$5bo2bo3bo3bo$3o5bo3bo$o2bo4bo4bobo$o7bo$o7bo$bobobobo11$12b3o$12bo2bo
$6b3o3bo$5bo2bo3bo3bo$3o5bo3bo$o2bo4bo4bobo$o7bo$o4bobo$o$bobo11$12b3o
$12bo2bo$3o3b3o3bo$o2bobo2bo3bo3bo$o7bo3bo$o7bo4bobo$bobo4bo$8bo$5bobo
11$10b3o$10bo2bo$2b3o5bo5b3o$bo2bo5bo4bo2bo$4bo5bo7bo$o3bo5bo7bo$4bo6b
obobobo$bobo11$10b3o$2b3o5bo2bo$bo2bo5bo5b3o$4bo5bo4bo2bo$o3bo5bo7bo$
4bo5bo7bo$bobo7bobobobo11$10b3o3b3o$10bo2bobo2bo$2b3o5bo7bo$bo2bo5bo7b
o$4bo5bo4bobo$o3bo5bo$4bo6bobo$bobo11$10b3o3b3o$2b3o5bo2bobo2bo$bo2bo
5bo7bo$4bo5bo7bo$o3bo5bo4bobo$4bo5bo$bobo7bobo11$9b3o3b3o$9bo2bobo2bo$
2b3o4bo7bo$bo2bo4bo7bo$4bo5bobobobo$o3bo$o3bo$4bo$bobo11$9b3o3b3o$2b3o
4bo2bobo2bo$bo2bo4bo7bo$4bo4bo7bo$o3bo5bobobobo$o3bo$4bo$bobo11$8b3o$
8bo2bo$8bo$b3o4bo3bo2b3o$o2bo4bo3bobo2bo$3bo4bo8bo$3bo5bobo5bo$obo11bo
bo11$8b3o$8bo2bo$8bo5b3o$b3o4bo4bo2bo$o2bo4bo7bo$3bo4bo7bo$3bo5bobo4bo
$obo13bo$13bobo11$8b3o$8bo2bo$8bo5b3o$b3o4bo4bo2bo$o2bo4bo7bo$3bo4bo7b
o$3bo5bob2o3bo$obo10bobo11$8b3o$8bo2bo$2b3o3bo5b3o$bo2bo3bo4bo2bo$4bo
3bo7bo$o3bo3bo7bo$4bo4bobobobo$bobo11$8b3o4b3o$8bo2bo2bo2bo$8bo8bo$b3o
4bo3bo4bo$o2bo4bo3bobobo$3bo4bo$3bo5bobo$obo11$8b3o3b3o$8bo2bobo2bo$8b
o7bo$b3o4bo7bo$o2bo4bo7bo$3bo4bo3b2obo$3bo5bobo$obo11$8b3o3b3o$8bo2bob
o2bo$2b3o3bo7bo$bo2bo3bo7bo$4bo3bo7bo$o3bo4bobobobo$4bo$bobo11$8b3o$7b
o2bo$7bo2bo$7bo3bo$6bo4bo$2bo3bo$b3o6b2o$2obo3b2o$3o$3o$b2o11$7b3o4b3o
$6bo2bo4bo2bo$9bo4bo$3o2bo3bo4bo$o2bobo3bo5bobo$o8bo$o5bobo$bobo11$7b
3o3b3o$6bo2bo3bo2bo$3o6bo3bo$o2bo5bo3bo$o5bobo5bobo$o3bo$o3bo$o$bobo
11$7b3o3b3o$7bo2bobo2bo$b3o3bo7bo$o2bo3bo7bo$3bo3bo7bo$3bo3bo4bobo$obo
4bo$8bobo11$7b3o3b3o$7bo2bobo2bo$b3o3bo7bo$o2bo3bo7bo$3bo3bo4bobo$3bo
3bo3bo$obo4bo$8bobo11$7b3o$7bo2bo$5bo$7bo3bo$4bo3b3o$bo3b2o$3o2b2o$ob
2o$b3o$b3o$b2o11$6b3o$5bo2bo$3o5bo3b3o$o2bo4bo3bo2bo$o7bo3bo$o4bobo4bo
3bo$o11bo$bobo9bobo11$6b3o$5bo2bo$3o5bo3b3o$o2bo4bo3bo2bo$o7bo3bo$o7bo
3bo$bobo4bo4bobo$8bo$5bobo11$6b3o$5bo2bo$3o5bo3b3o$o2bo4bo3bo2bo$o7bo
3bo$o7bo3bo$bob2o3bo4bobo$5bobo11$6b3o$5bo2bo$3o5bo3b3o$o2bo4bo3bo2bo$
o7bo3bo$o7bo3bo$o7bo4bobo$bobobobo11$6b3o$5bo2bo$3o5bo3b3o$o2bo4bo3bo
2bo$o7bo3bo$o7bo3bo$o4bobo5bobo$o$bobo11$6b3o$5bo2bo$3o5bo3b3o$o2bo4bo
3bo2bo$o7bo3bo$o7bo3bo$o3b2obo5bobo$bobo11$6b3o4b3o$5bo2bo4bo2bo$3o5bo
4bo$o2bo4bo4bo$o7bo5bobo$o7bo$o3b2obo$bobo11$6b3o3b3o$5bo2bo3bo2bo$3o
5bo3bo$o2bo4bo3bo3bo$o7bo3bo$o4bobo5bobo$o$bobo11$6b3o3b3o$5bo2bo3bo2b
o$3o5bo3bo$o2bo4bo3bo$o7bo4bobo$o7bo$o3b2obo$bobo11$6b3o3b3o$5bo2bo3bo
2bo$3o5bo3bo$o2bo4bo3bo$o7bo4bobo$o4bobo$o3bo$o$bobo11$2b3o$bo2bo5b3o$
4bo5bo2bo$o3bo5bo5b3o$4bo5bo4bo2bo$bobo6bo7bo$10bo7bo$11bobobobo11$2b
3o$bo2bo$4bo$o3bo4b3o$4bo4bo2bo$bobo5bo5b3o$9bo4bo2bo$9bo7bo$9bo7bo$
10bobobobo11$2b3o$bo2bo$4bo$o3bo4b3o3b3o$o3bo4bo2bobo2bo$4bo4bo7bo$bob
o5bo7bo$10bobobobo11$2b3o$bo2bo$4bo3b3o3b3o$o3bo3bo2bobo2bo$4bo3bo7bo$
bobo4bo7bo$8bo7bo$9bobobobo11$2b3o5b3o$bo2bo5bo2bo$4bo5bo5b3o$o3bo5bo
4bo2bo$4bo5bo7bo$bobo6bo7bo$11bobobobo11$2b3o5b3o3b3o$bo2bo5bo2bobo2bo
$4bo5bo7bo$o3bo5bo7bo$4bo5bo4bobo$bobo6bo$11bobo11$2b3o3b3o$bo2bo3bo2b
o$4bo3bo5b3o$o3bo3bo4bo2bo$4bo3bo7bo$bobo4bo7bo$9bobobobo11$2b3o3b3o3b
3o$bo2bo3bo2bobo2bo$4bo3bo7bo$o3bo3bo7bo$4bo4bob2o3bo$bobo9bobo11$2b3o
3b3o3b3o$bo2bo3bo2bobo2bo$4bo3bo7bo$o3bo3bo7bo$4bo3bo7bo$bobo5bobobobo
11$2b3o3b3o3b3o$bo2bo3bo2bobo2bo$4bo3bo7bo$o3bo3bo7bo$4bo3bo4bobo$bobo
4bo$9bobo11$bo$3o$ob2o3b3o$b3o2bo2bo$b3o5bo$b3obo3bo$b2o2bo3bo$9bo$6bo
bo11$b3o$o2bo$3bo4b3o4b3o$3bo4bo2bo2bo2bo$obo5bo8bo$8bo3bo4bo$8bo3bobo
bo$8bo$9bobo11$b3o$o2bo11b3o$3bo4b3o3bo2bo$3bo4bo2bo5bo$obo5bo8bo$8bo
3bobobo$8bo3bo$8bo$9bobo11$b3o$o2bo4b3o$3bo4bo2bo$3bo4bo$obo5bo3bo2b3o
$8bo3bobo2bo$8bo8bo$9bobo5bo$14bobo11$b3o$o2bo4b3o4b3o$3bo4bo2bo2bo2bo
$3bo4bo8bo$obo5bo3bo4bo$8bo3bobobo$8bo$9bobo11$b3o$o2bo$3bo4b3o$3bo4bo
2bo$obo5bo5b3o$8bo4bo2bo$8bo7bo$8bo7bo$9bob2o3bo$13bobo11$b3o$o2bo4b3o
$3bo4bo2bo$3bo4bo5b3o$obo5bo4bo2bo$8bo7bo$8bo7bo$9bob2o3bo$13bobo11$b
3o$o2bo4b3o3b3o$3bo4bo2bobo2bo$3bo4bo7bo$obo5bo7bo$8bo7bo$8bo7bo$9bobo
bobo11$b3o11b3o$o2bo10bo2bo$3bo4b3o6bo$3bo4bo2bo5bo$obo5bo5bobo$8bo3bo
$8bo3bo$8bo$9bobo11$b3o10b3o$o2bo9bo2bo$3bo4b3o5bo$3bo4bo2bo4bo$obo5bo
7bo$8bo7bo$8bo4bobo$8bo$9bobo11$b3o4b3o$o2bo4bo2bo$3bo4bo5b3o$3bo4bo4b
o2bo$obo5bo7bo$8bo7bo$9bobo4bo$16bo$13bobo11$b3o4b3o3b3o$o2bo4bo2bobo
2bo$3bo4bo7bo$3bo4bo7bo$obo5bo7bo$8bo7bo$9bobobobo11$b3o4b3o3b3o$o2bo
4bo2bobo2bo$3bo4bo7bo$3bo4bo7bo$obo5bo7bo$8bo3b2obo$9bobo11$b3o3b3o$o
2bo3bo2bo3b3o$3bo3bo5bo2bo$3bo3bo8bo$obo5bobobo3bo$12bo3bo$16bo$13bobo
11$b3o3b3o$o2bo3bo2bo$3bo3bo5b3o$3bo3bo4bo2bo$obo4bo7bo$7bo7bo$8bobo4b
o$15bo$12bobo11$b3o3b3o$o2bo3bo2bo$3bo3bo5b3o$3bo3bo4bo2bo$obo4bo7bo$
7bo7bo$7bo7bo$8bobobobo11$b3o3b3o$o2bo3bo2bo$3bo3bo5b3o$3bo3bo4bo2bo$o
bo4bo7bo$7bo7bo$7bo4bobo$7bo$8bobo11$b3o3b3o$o2bo3bo2bo$3bo3bo5b3o$3bo
3bo4bo2bo$obo4bo7bo$7bo7bo$7bo3b2obo$8bobo11$b3o3b3o3b3o$o2bo3bo2bobo
2bo$3bo3bo7bo$3bo3bo7bo$obo4bo7bo$8bob2o3bo$12bobo11$b3o3b3o3b3o$o2bo
3bo2bobo2bo$3bo3bo7bo$3bo3bo7bo$obo4bo7bo$7bo7bo$8bobobobo11$b3o3b3o3b
3o$o2bo3bo2bobo2bo$3bo3bo7bo$3bo3bo7bo$obo4bo4bobo$7bo3bo$7bo$8bobo11$
3o$o2bo$o6b3o$o5bo2bo$bobo5bo$5bo3bo4b3o$5bo3bo4bo2bo$9bo4bo$6bobo5bo$
15bobo11$3o$o2bo10b3o$o6b3o4bo2bo$o5bo2bo4bo$bobo5bo4bo$5bo3bo5bobo$5b
o3bo$9bo$6bobo11$3o$o2bo3b3o$o5bo2bo$o8bo$bobobo3bo4b3o$5bo3bo4bo2bo$
9bo4bo$6bobo5bo$15bobo11$3o$o2bo$o5b3o$o4bo2bo$o7bo$o7bo4b3o$bobo4bo4b
o2bo$8bo4bo$5bobo5bo$14bobo11$3o$o2bo$o5b3o4b3o$o4bo2bo4bo2bo$o7bo4bo$
bobo4bo4bo$4bo3bo5bobo$8bo$5bobo11$3o$o2bo$o5b3o4b3o$o4bo2bo4bo2bo$o7b
o4bo$o7bo4bo$bobo4bo5bobo$8bo$5bobo11$3o$o2bo$o5b3o3b3o$o4bo2bo3bo2bo$
o7bo3bo$bobo4bo3bo3bo$8bo3bo$5bobo5bobo11$3o$o2bo9b3o$o5b3o4bo2bo$o4bo
2bo4bo$o7bo4bo$bobo4bo5bobo$4bo3bo$8bo$5bobo11$3o$o2bo9b3o$o5b3o4bo2bo
$o4bo2bo4bo$o7bo4bo$o7bo5bobo$bobo4bo$8bo$5bobo11$3o$o2bo$o5b3o3b3o$o
4bo2bo3bo2bo$o7bo3bo$o7bo3bo$bob2o3bo4bobo$5bobo11$3o11b3o$o2bo3b3o4bo
2bo$o5bo2bo4bo$o8bo4bo$bobobo3bo5bobo$5bo3bo$9bo$6bobo11$3o10b3o$o2bo
9bo2bo$o5b3o4bo$o4bo2bo4bo$o7bo5bobo$bobo4bo$4bo3bo$8bo$5bobo11$3o9b3o
$o2bo8bo2bo$o5b3o3bo$o4bo2bo3bo3bo$o7bo3bo$bobo4bo4bobo$8bo$5bobo11$3o
$o2bo4bo$o6b3o$o3bo2bob2o$o7b3o$o7b3o$bob2o3b3o$8b2o11$3o4b3o4b3o$o2bo
2bo2bo4bo2bo$o8bo4bo$o4bo3bo4bo$bobobo3bo5bobo$9bo$6bobo11$3o4b3o3b3o$
o2bo2bo2bo3bo2bo$o8bo3bo$o3bo4bo3bo$o3bobobo5bobo$o$bobo11$3o3b3o$o2bo
bo2bo$o7bo$o7bo4b3o$o7bo4bo2bo$o7bo4bo$bobobobo5bo$14bobo11$3o3b3o$o2b
obo2bo$o7bo3b3o$o7bo3bo2bo$bobo4bo3bo$8bo3bo3bo$5bobo4bo$13bobo11$3o3b
3o$o2bobo2bo$o7bo3b3o$o7bo3bo2bo$o7bo3bo$bob2o3bo3bo$5bobo5bobo11$3o3b
3o$o2bobo2bo$o7bo3b3o$o7bo3bo2bo$o7bo3bo$o7bo3bo$bobobobo5bobo11$3o3b
3o4b3o$o2bobo2bo4bo2bo$o7bo4bo$o7bo4bo3bo$bobobobo5bo3bo$13bo$14bobo
11$3o3b3o3b3o$o2bobo2bo3bo2bo$o7bo3bo$o7bo3bo3bo$o4bobo4bo$o12bobo$bob
o11$3o3b3o3b3o$o2bobo2bo3bo2bo$o7bo3bo$o7bo3bo$o7bo4bobo$bobo4bo$8bo$
5bobo11$3o3b3o3b3o$o2bobo2bo3bo2bo$o7bo3bo$o7bo3bo$o7bo4bobo$bob2o3bo$
5bobo11$8b3o3b3o$2bo5bo2bobo2bo$b3o4bo7bo$2obo4bo7bo$3o5bo4bobo$b2o5bo
$9bobo11$8b3o$3o4bo2bo$o2bo6bo$o9bo$o6bobo$bo2b2o$5bo$4bo$7b3o$7bo2bo$
7bo$7bo3bo$7bo$8bobo11$6b3o$5bo2bo5bo$3o5bo4b3o$o2bo4bo4bob2o$o7bo5b3o
$o7bo5b2o$bobobobo11$6b3o4bo$5bo2bo3b3o$3o5bo3bob2o$o2bo4bo4b3o$o7bo4b
2o$o7bo$bobobobo11$2bo$b3o4b3o$2obo4bo2bo$3o5bo5b3o$b2o5bo4bo2bo$8bo7b
o$9bobo4bo$16bo$13bobo11$2bo$b3o4b3o3b3o$2obo4bo2bobo2bo$3o5bo7bo$b2o
5bo7bo$8bo7bo$9bobobobo11$2bo$b3o4b3o3b3o$2obo4bo2bobo2bo$3o5bo7bo$b2o
5bo7bo$8bo3b2obo$9bobo11$2bo4b3o$b3o3bo2bo$2obo3bo5b3o$3o4bo4bo2bo$b2o
4bo7bo$8bobo4bo$15bo$12bobo11$2bo4b3o3b3o$b3o3bo2bobo2bo$2obo3bo7bo$3o
4bo7bo$b2o4bo7bo$8bobobobo11$2bo4b3o3b3o$b3o3bo2bobo2bo$2obo3bo7bo$3o
4bo7bo$b2o4bo4bobo$7bo$8bobo11$2bo4b3o3b3o$b3o3bo2bobo2bo$2obo3bo7bo$
3o4bo7bo$b2o4bo3b2obo$8bobo11$2b3o6b3o$bo2bo5bo2bo$4bo8bo$o3bo4bo3bo$o
3bo2bobo3bo$4bobobo4bo$bobo8bo$6b2ob2o11$bo$3o4b3o3b3o$ob2o2bo2bo3bo2b
o$b3o5bo3bo$b2o2bo3bo3bo$9bo4bobo$6bobo11$bo4b3o3b3o$3o2bo2bo3bo2bo$ob
2o4bo3bo$b4o3bo3bo$b2o5bo4bobo$5bobo11$3o$o2bo10bo$o5b3o4b3o$o4bo2bo4b
ob2o$o7bo5b3o$bobo4bo5b2o$8bo$5bobo11$3o$o2bo$o5b3o4bo$o4bo2bo3b3o$o7b
o3bob2o$bobo4bo4b3o$8bo4b2o$5bobo11$3o$o2bo$o$o$bobo$5b3o2b3o$5bobobo
2bo$5bo2b2o3bo$6bobo2bobo$6bo3b2ob2o11$3o9b3o$o2bo7bo2bo$o13bo$o13bo$b
obo2b3o2bobo$5bo3bo$5bo3bo$5b5o$5bo3bo11$3o$o2bo5bo$o7b3o$o3bo2b2obo$o
5bo$bobo2bob2obo$5bo5bo$5b2ob2o$5b3o11$3o$o2bo5b3o$o7bo2bo$o3bo6bo$o3b
o2bo3bo$o4bo5bo$bo3b2obobo$5bo$5bo$5bo$5bo$2bobo11$3o$o2bo$o7b3o$o3bo
2bo2bo$o9bo$bobo6bo$5b2o2bo$5bo$6bo$b3o$o2bo$3bo$3bo$obo!

Unfortunately the only computer-adjudicable (by me) definition of connectedness is probably too lax, counting e.g. LWSS-on-LWSS as connected due to the overpopulation birth suppression they are connected(ish) by. As a result these results are drowning in various nominally connected *WSS flotillae. I skimmed them anyway by eye, but it's very hard to make sense of quickly. I see a lot of things that are known but e.g. this pop 32 weirdo I could not find in jslife-moving:

Code: Select all

#C [[ TRACK 0 -1/2 ]]
x = 12, y = 12, rule = B3/S23
3o$o2bo5b3o$o7bo2bo$o3bo6bo$o3bo2bo3bo$o4bo5bo$bo3b2obobo$5bo$5bo$5bo$
5bo$2bobo!

Unfortunately I'm sort of out of ideas about how to make anything more useful of this.

EDIT: The news item was "This leaves LWSS pulling Unnamed tagalong 23P4H2V0 as the only currently known spaceship up to 32 cells without a known glider synthesis." and I notice that this pop 32 ship doesn't (yet) have a synthesis on catalogue which seems to contradict that so maybe it is new?

MathAndCode · Post by **MathAndCode** » February 3rd, 2025, 11:35 pm

amling wrote: February 3rd, 2025, 1:51 pmUnfortunately the only computer-adjudicable (by me) definition of connectedness is probably too lax, counting e.g. LWSS-on-LWSS as connected due to the overpopulation birth suppression they are connected(ish) by. As a result these results are drowning in various nominally connected *WSS flotillae. I skimmed them anyway by eye, but it's very hard to make sense of quickly. I see a lot of things that are known but e.g. this pop 32 weirdo I could not find in jslife-moving:
Code: Select all
#C [[ TRACK 0 -1/2 ]]
x = 12, y = 12, rule = B3/S23
3o$o2bo5b3o$o7bo2bo$o3bo6bo$o3bo2bo3bo$o4bo5bo$bo3b2obobo$5bo$5bo$5bo$
5bo$2bobo!
Unfortunately I'm sort of out of ideas about how to make anything more useful of this.

It can be viewed as the shortest member of a family, analogously to the LWSS, MWSS, and HWSS.

Code: Select all

x = 72, y = 14, rule = B3/S23
3o27b3o27b3o$o2bo5b3o18bo2bo5b3o18bo2bo5b3o$o7bo2bo18bo7bo2bo18bo7bo2b
o$o3bo6bo18bo3bo6bo18bo3bo6bo$o3bo2bo3bo18bo3bo2bo3bo18bo3bo2bo3bo$o4b
o5bo18bo4bo5bo18bo4bo5bo$bo3b2obobo20bo3b2obobo20bo3b2obobo$5bo29bo29b
o$5bo29bo29bo$5bo29bo29bo$5bo25bo3bo25bo3bo$2bobo30bo25bo3bo$32bobo30b
o$62bobo!

The back part can also be connected to certain things analogously to XWSSes. For example, here is a doubly amling Canada Grey.

Code: Select all

x = 47, y = 35, rule = B3/S23
13b3o$13bo2bo5b3o$13bo7bo2bo$13bo3bo6bo$13bo3bo2bo3bo$13bo4bo5bo$14bo
3b2obobo$18bo$18bo$18bo3b3o$14bo3bo3bo2bo$14bo3bo3bo$18bo3bo$18bo3bo2$
16b3o3b3o$17bo5bo$17b7o$16bo7bo10b3o$15b11o9bo2bo5b3o$14bo11bo8bo7bo2b
o$13b15o7bo3bo6bo$12bo15bo6bo3bo2bo3bo$11b19o5bo4bo5bo$10bo19bo5bo3b2o
bobo$3o6b23o8bo$o2bo4bo23bo7bo$o6b27o6bo$o3bobo11bobobo11bobo3bo$o5b7o
bo11bob7o5bo$o4b2o3bobobo11bobobo3b2o4bo$bo3bo29bo3bo$5bo29bo$3b3o29b
3o$4b2o29b2o!

There is a third way to connect it, but this is more trivial.

Code: Select all

x = 58, y = 39, rule = B3/S23
24b3o$24bo2bo5b3o$24bo7bo2bo$24bo3bo6bo$24bo3bo2bo3bo$24bo4bo5bo$25bo
3b2obobo$29bo$29bo$29bo3b3o$29bo3bo2bo$29bo3bo$29bo3bo$29bo3bo2$27b3o
3b3o$28bo5bo$28b7o$27bo7bo10b3o$26b11o9bo2bo5b3o$25bo11bo8bo7bo2bo$24b
15o7bo3bo6bo$23bo15bo6bo3bo2bo3bo$22b19o5bo4bo5bo$21bo19bo5bo3b2obobo
$11b3o6b23o8bo$2b3o6bo2bo4bo23bo4bo2bo$bo2bo6bo6b27o6bo$4bo6bo3bobo11b
obobo11bobo3bo$o3bo6bo5b7obo11bob7o5bo$4bo2b3obo4b2o3bobobo11bobobo3b
2o4bo$bobo6bobo3bo29bo3bo$10bo5bo29bo$10bo3b3o29b3o$10bo4b2o29b2o$10b
o$10bo$10bo$9bo!

Here is a triply amling hammerhead.

Code: Select all

x = 36, y = 31, rule = B3/S23
21b3o$21bo2bo5b3o$21bo7bo2bo$21bo3bo6bo$21bo3bo2bo3bo$21bo4bo5bo$2b3o
17bo3b2obobo$bo2bo6b3o12bo$4bo6bo2bo11bo$o3bo6bo14bo$o3bo6bo3bo6bo3bo
$4bob3o2bo3bo6bo3bo$bobobo6bo3bo4bo3bo$5bo11bo2bo$5bo12b2o$5bo9bobo2b
obo$5bo3bo5bo6bo$5bo10b2o2b2o$6bobo5b2o6b2o9bo$13b3obo2bob3o7b3o$12b2o
2bo4bo2b2o6bob2o$12bobo8bobo7b3o$13b3o6b3o8b3o$13b3o6b3o4b2o2b3o$13b2o
8b2o2bob2o2b2o$28b3o$29b2o$28b3o$28b3o$28b3o$29b2o!

confocaloid · Post by **confocaloid** » February 3rd, 2025, 11:48 pm

^^ More connections:

Code: Select all

x = 137, y = 137, rule = B3/S23
102b5o$101bo4bo$106bo$101bo3bo$103bo$101bo$95b8o$94bo8b2o$89bo16bo$
107bo$89bo6b2o3bo5bo$90b6o6b6o$94bo$96bo$94bo3bo$99bo$94bo4bo$95b5o14$
53b5o$52bo4bo73b6o$57bo72bo5bo$52bo3bo68bo10bo$54bo80bo$52bo72bo6b2o$
47b7o72b6o$46bo7b2o74bo$57bo74bo$46bo11bo29b5o9b5o23bo3bo$48bo3bo5bo
28bo4bo8bo4bo28bo$46bo6b6o33bo13bo23bo4bo$41b7o39bo3bo9bo3bo25b5o$40bo
7b2o39bo13bo$51bo35bo13bo$40bo11bo28b8o6b8o$42bo3bo5bo22b2o3bo8b2o3bo
8b2o$40bo6b6o20bo32bo$35b7o65bo$34bo7b2o29bo8b2o3bo8b2o3bo5bo$45bo28b
8o6b8o6b6o$34bo11bo33bo13bo$36bo3bo5bo35bo13bo$34bo6b6o33bo3bo9bo3bo$
15b5o9b7o49bo13bo$14bo4bo8bo7b2o42bo4bo8bo4bo$19bo19bo41b5o9b5o$14bo3b
o9bo11bo$16bo13bo3bo5bo$14bo13bo6b6o$8b8o6b8o$2b2o3bo8b2o3bo8b2o99b6o$
o32bo92bo3bo5bo$34bo89bo11bo$o8b2o3bo8b2o3bo5bo100bo$b8o6b8o6b6o89bo7b
2o$7bo13bo103b7o$9bo13bo106bo$7bo3bo9bo3bo106bo$12bo13bo103bo3bo$7bo4b
o8bo4bo108bo$8b5o9b5o103bo4bo$131b5o7$95b6o$90bo3bo5bo$88bo11bo$99bo$
88bo7b2o$89b7o$94bo6b6o$96bo3bo5bo$94bo11bo$105bo$94bo7b2o$95b7o$100bo
30b6o$102bo22b2o3bo5bo$100bo3bo18bo12bo$105bo29bo$100bo4bo17bo8b2o$
101b5o18b8o$130bo$132bo$130bo3bo$135bo$130bo4bo$131b5o4$83b6o$78bo3bo
5bo$76bo11bo$87bo$76bo7b2o$77b7o$82bo6b6o$84bo3bo5bo$82bo11bo$93bo$82b
o7b2o$83b7o$88bo6b6o$90bo3bo5bo$88bo11bo$99bo$88bo7b2o$89b7o$94bo6b6o$
96bo3bo5bo$94bo11bo$105bo$94bo7b2o$95b7o$100bo$102bo$100bo3bo$105bo$
100bo4bo$101b5o!

Timelord Missionary · February 5th, 2025, 9:46 pm

Hey all, is there a suitable sparking ship or puffer that this could be made into a glide-symmetric spaceship with speed 2c/5 and reduced speed 8c/20?

Code: Select all

x = 14, y = 8, rule = B3/S23
6b2o$6bob2o$7b2obo$8b3o$4b2o2b2o$2o2b4o4b2o$3o2b3o3b3o$b2o8b2o!

Oh, and by the way, 66P10H4V0 doesn't work, even without the bulky 44P5H2V0 over it.

EDIT: gliders work, though they leave easily-deletable blocks.

Code: Select all

x = 10, y = 8, rule = B3/S23
2b2o$2bob2o$3b2obo$4b3o$2o2b2o$4o4b2o$b3o3b2o$9bo!

Post by **Sokwe** » February 5th, 2025, 10:03 pm

Timelord Missionary wrote: February 5th, 2025, 9:46 pm is there a suitable sparking ship or puffer that this could be made into a glide-symmetric spaceship with speed 2c/5 and reduced speed 8c/20?
Code: Select all
x = 14, y = 8, rule = B3/S23
6b2o$6bob2o$7b2obo$8b3o$4b2o2b2o$2o2b4o4b2o$3o2b3o3b3o$b2o8b2o!

It looks potentially possible, although I think it would need a custom p5 2c/5 ship to get it to work. LLSSS might be well-suited for this, but I'm not skilled enough at setting up such a search. Maybe Amling could give some pointers.

Also, the left-hand spark is one cell too far away. It should instead look like this:

Code: Select all

x = 13, y = 9, rule = B3/S23
$5b2o$5bob2o$6b2obo$7b3o$3b2o2b2o$2ob4o4b2o$3ob3o3b3o$b2o7b2o!

amling · Post by **amling** » February 6th, 2025, 9:17 am

Sokwe wrote: February 5th, 2025, 10:03 pm
Timelord Missionary wrote: February 5th, 2025, 9:46 pm is there a suitable sparking ship or puffer that this could be made into a glide-symmetric spaceship with speed 2c/5 and reduced speed 8c/20?
Code: Select all
x = 14, y = 8, rule = B3/S23
6b2o$6bob2o$7b2obo$8b3o$4b2o2b2o$2o2b4o4b2o$3o2b3o3b3o$b2o8b2o!
It looks potentially possible, although I think it would need a custom p5 2c/5 ship to get it to work.

I am skeptical of this being possible. It's a rather demanding "spark" to begin with and then it has to survive both of those interactions, especially the crazy one on the left side there where the spark would-be predecessor is already touching.

You can try to search at 8c/20 with a perturbation-finding style constraint, something like:

Code: Select all

|        LLLuuuuuuuuuuRRR |        LLLuuuuuuuuuuRRR |        LLLuuuuuuuuuuRRR |       LLLuuuuuuuuuuRRR  |       LLLuuuuuuuuuuRRR  |      LLLuuuuuuuuuuRRR   |      LLLuuuuuuuuuuRRR   |      LLLuuuuuuuuuuRRR   |     LLLuuuuuuuuuuRRR    |     LLLuuuuuuuuuuRRR    |    LLLuuuuuuuuuuRRR     |    LLLuuuuuuuuuuRRR     |    LLLuuuuuuuuuuRRR     |   LLLuuuuuuuuuuRRR      |   LLLuuuuuuuuuuRRR      |  LLLuuuuuuuuuuRRR       |  LLLuuuuuuuuuuRRR       |  LLLuuuuuuuuuuRRR       | LLLuuuuuuuuuuRRR        | LLLuuuuuuuuuuRRR        |
|        .....**......... |        ....*.*......... |        ....*.**........ |       ....**..*.......  |       ....*****.......  |      .....*....*.....   |      ....**...**.....   |      ....**.....*....   |     .....**.........    |     ....***.........    |    .....**.........     |    ....*.*.........     |    ....*.*.........     |   ....**.*........      |   ....*...........      |  .....**..*......       |  .....****.......       |  ....*...........       | .....**.........        | ....*...........        |
|        ....**.......... |        ....*........... |        ...**........... |       ....**.**.......  |       ...*...**.......  |      ....*....*......   |      ....*.*..**.....   |      ....*.....*.....   |     ....**..........    |     ....*...........    |    ....**..........     |    ....*...........     |    ...**...........     |   ....**.**.......      |   ...*...**.......      |  ....*....*......       |  ....*.*..**.....       |  ....*.....*.....       | ....**..........        | ....*...........        |
|        .....**......... |        ....*.*......... |        ....*.*......... |       ....**.*........  |       ....*...........  |      .....**..*......   |      .....****.......   |      ....*...........   |     .....**.........    |     ....*...........    |    .....**.........     |    ....*.*.........     |    ....*.**........     |   ....**..*.......      |   ....*****.......      |  .....*....*.....       |  ....**...**.....       |  ....**.....*....       | .....**.........        | ....***.........        |
|        ......*......... |        .....**......... |        .....**......... |       ......**........  |       .....***........  |      ......**........   |      .....*.**.......   |      .....*..........   |     ......WWWWWW....    |     .....*WWWWWW....    |    ......*WWWWWW...     |    .....**WWWWWW...     |    .....**WWWWWW...     |   ................      |   .....**.*.......      |  .....*...*......       |  ........***.....       |  ................       | ................        | ................        |
|        ................ |        ................ |        ................ |       ................  |       ................  |      .......*........   |      ......**........   |      ......WWWW......   |     ......WWWWWW....    |     ......WWWWWW....    |    .......WWWWWW...     |    .......WWWWWW...     |    ......*WWWWWW...     |   ......***.......      |   .......*........      |  ........**......       |  ........**......       |  ......WWWW.*....       | ......WWWWWW....        | ......WWWWWW....        |
|        4444444444444444 |        4444444444444444 |        4444444444444444 |       4444444444444444  |       4444444444444444  |      4444444444444444   |      4444444444444444   |      444444WWWW444444   |     444444WWWWWW4444    |     444444WWWWWW4444    |    4444444WWWWWW444     |    4444444WWWWWW444     |    4444444WWWWWW444     |   4444444444444444      |   4444444W44444444      |  4444444444444444       |  4444444444444444       |  444444WWWW444444       | 444444WWWWWW4444        | 444444WWWWWW4444        |
|        4444444444444444 |        4444444444444444 |        4444444444444444 |       4444444444444444  |       4444444444444444  |      4444444444444444   |      4444444444444444   |      444444WWWW444444   |     444444WWWWWW4444    |     444444WWWWWW4444    |    4444444WWWWWW444     |    4444444WWWWWW444     |    4444444WWWWWW444     |   4444444444444444      |   4444444444444444      |  4444444444444444       |  4444444444444444       |  444444WWWW444444       | 444444WWWWWW4444        | 444444WWWWWW4444        |
|        4444444444444444 |        4444444444444444 |        4444444444444444 |       4444444444444444  |       4444444444444444  |      4444444444444444   |      4444444444444444   |      4444444444444444   |     444444WWWWWW4444    |     444444WWWWWW4444    |    4444444WWWWWW444     |    4444444WWWWWW444     |    4444444WWWWWW444     |   4444444444444444      |   4444444444444444      |  4444444444444444       |  4444444444444444       |  4444444444444444       | 4444444444444444        | 4444444444444444        |
|        4444444444444444 |        4444444444444444 |        4444444444444444 |       4444444444444444  |       4444444444444444  |      4444444444444444   |      4444444444444444   |      4444444444444444   |     4444444444444444    |     4444444444444444    |    4444444444444444     |    4444444444444444     |    4444444444444444     |   4444444444444444      |   4444444444444444      |  4444444444444444       |  4444444444444444       |  4444444444444444       | 4444444444444444        | 4444444444444444        |
|        4444444444444444 |        4444444444444444 |        4444444444444444 |       4444444444444444  |       4444444444444444  |      4444444444444444   |      4444444444444444   |      4444444444444444   |     4444444444444444    |     4444444444444444    |    4444444444444444     |    4444444444444444     |    4444444444444444     |   4444444444444444      |   4444444444444444      |  4444444444444444       |  4444444444444444       |  4444444444444444       | 4444444444444444        | 4444444444444444        |
|        4444444444444444 |        4444444444444444 |        4444444444444444 |       4444444444444444  |       4444444444444444  |      4444444444444444   |      4444444444444444   |      4444444444444444   |     4444444444444444    |     4444444444444444    |    4444444444444444     |    4444444444444444     |    4444444444444444     |   4444444444444444      |   4444444444444444      |  4444444444444444       |  4444444444444444       |  4444444444444444       | 4444444444444444        | 4444444444444444        |
|        4444444444444444 |        4444444444444444 |        4444444444444444 |       4444444444444444  |       4444444444444444  |      4444444444444444   |      4444444444444444   |      4444444444444444   |     4444444444444444    |     4444444444444444    |    4444444444444444     |    4444444444444444     |    4444444444444444     |   4444444444444444      |   4444444444444444      |  4444444444444444       |  4444444444444444       |  4444444444444444       | 4444444444444444        | 4444444444444444        |

There are a lot of knobs to fiddle in terms of where there are 4's or W's, how many mid_steps, do you try to include some sort of PD steps in closures, etc. I played with it for maybe 45m here and couldn't produce a search anything even resembling viable but my pessimism about the possibility is probably not helping me do my best work.

ConwayLife.com

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