Weird Challenges

[Rhombic]

What is the highest possible value of P such that a non-totalistic rule exists with spaceships of period P and period P+1?
Current record: 42

What about a totalistic rule with the same characteristic?

And if, instead of period, it is for spaceships of speed c/P and c/(P+1)?

[Saka]

What's the highest period c/2 ship known?

[dvgrn]

What's the highest period c/2 ship known?

There isn't really an upper limit unless you limit the size somehow. Here's a p248 spaceship, for example:

Code: Select all

x = 46, y = 107, rule = B3/S23
13b3o$12bo3bo$7b3obo5bob3o$6bo2bobo5bobo2bo$5bo3bobob3obobo3bo$5bo7bob
o7bo$7bo13bo$4bobo5b2ob2o5bobo$3b2obob2o9b2obob2o$2bobobob2o9b2obobobo
$b2obo2bobo9bobo2bob2o$o3bob2ob3ob3ob3ob2obo3bo$4bo8b3o8bo$2o3bob3ob2o
bob2ob3obo3b2o2$3b2o19b2o$3bo2b2o13b2o2bo$5bobo13bobo$2b2obo17bob2o$5b
ob2o11b2obo$5bo17bo$9b3o5b3o$7bo3bo5bo3bo$2b3o4bobo5bobo4b3o$2bo2bo17b
o2bo$2bo23bo$2bo3bo15bo3bo$2bo3bo15bo3bo$2bo8bo5bo8bo$3bobo3bobo5bobo
3bobo$10b2o5b2o2$24b3o11b3o$23bo3bo9bo3bo$13bobo6b2o4bo7bo4b2o$11bobob
obo3bobob2ob2o5b2ob2obobo$12b2ob2o3b2obo4bob2ob2obo4bob2o$19bo4bo3bo2b
obo2bo3bo4bo$31bobo$19b2o7b2obobob2o7b2o$31bobo$25b3o9b3o$25bo3bo9bo$
25bobo4b3o$31bo2bo4b2o$34bo$30bo3bo$30bo3bo$25bo8bo$25bobo3bobo$25b2o
4$23bo$23bobo$23b2o3$7bo$6b3o12bo$6bob2o11bobo$7b3o11b2o$7b2o$25b3o$
24bo2bo$19bo7bo$19bobobo3bo$19b2o2bo3bo$5bo21bo$4b3o17bobo$4bob2o$5b3o
$5b3o$5b2o3$23bo$22b3o$21b2obo$21b3o$22b2o17$24bo$23b3o$bo21bob2o$3o
21b3o$ob2o20b3o$b3o20b3o$b3o20b2o$b3o$b2o!

Advance the leading block puffer in that conglomeration, including the two HWSSes, by 2N ticks, and you'll get a p248+8N c/2 ship.

I seem to recall there are also period-multiplying attachments for high-period rakes, so the size only goes up linearly as the period goes up exponentially. But offhand I'm only finding examples for c/3. Can someone else dig up a c/2 example?

EDIT: Oh, right -- see Part 6 of David Bell's Spaceships series for several different c/2 period-multiplying methods. Here's one where a linear increase in length produces a factor-of-two increase in period:

Code: Select all

x = 505, y = 98, rule = B3/S23
330b4o$329b6o$328b2ob4o48b2o$329b2o51b2ob4o$383b6o$318b2o64b4o$317b4o$
113b2o201b2ob2o50b2o$111bo4bo200b2o5b2ob3o40b2ob2o8bo$110bo212bo5b2o
40b4o3bo4bobo$110bo5bo47b6o152b2o7bo40b2o3bo5bo2bo$110b6o48bo5bo152bo
5b2o11bo33bo2bo6bo$164bo152b2o5b2ob3o10bobo29b2o3bo5bo2bo10bo$99bo2bo
62bo4bo116b4o25b2ob2o20b2o28b4o3bo4bobo12bo$98bo68b2o117b6o25b4o49b2ob
2o8bo12b3o$98bo3bo49b4o129b2ob4o26b2o51b2o13b2o$98b4o50bo3bo129b2o41b
6o49bo4bo$104b3o2b2o41bo7bo168bo5bo24bo22bo$104b3o2b2o9bo32bo2bo2b7o
109b2o52bo28bobo22bo5bo25bo$104b3o2b2o10b2o35b2ob3o2bo107b4o52bo4bo23b
2o22b6o27bo$70b2o26b4o18b2o31bo2bo2b7o9bobo95b2ob2o54b2o80b3o$68bo4bo
24bo3bo49bo7bo15b2o96b2o5b2ob3o$67bo30bo53bo3bo19bo103bo5b2o$67bo5bo
25bo2bo9b4o36b4o123b2o7bo$67b6o38b6o21bo141bo5b2o11bo133bo44b2o$110b2o
b4o22b2o24b2o107b2o5b2ob3o10bobo72b2o60bo41bo4bo$56bo2bo51b2o25b2o24b
2ob4o22bobo77b2ob2o20b2o72bobo57b3o40bo$55bo109b6o23b2o78b4o94bo102bo
5bo$55bo3bo106b4o24bo80b2o198b6o$55b4o227b6o$61b3o2b2o218bo5bo24bo74b
2o57bo$61b3o2b2o9bo208bo28bobo75b2o57bo$61b3o2b2o10b2o131bobo73bo4bo
23b2o74bo57b3o$55b4o18b2o110b3o20b2o75b2o192b2o$55bo3bo131bo20bo$55bo
134bo223bo22bo$56bo2bo9b4o101bo36bo123bo76bobo20b2o$68b6o21bo79b2o33bo
122bobo24b2o51b2o21b2o$67b2ob4o22b2o76b2o34b3o121b2o24bobo94b2o$68b2o
25b2o263bo95b2o$147b2o125bo47bo135bo$146b2o125bobo45bobo$148bo124bobo
45bobo29bob3o$113bo160bo47bo28bo2b2ob2o$114b2o236bobobo94b2o$23b2o88b
2o38b3o294b2o$22b2ob4o126bo296bo$23b6o125bo317b2o$24b4o14bo23bo23bo23b
o95bo12bo114b2o132b2o29b2o$41bobo21bobo21bobo21bobo15bo79b2o9bo116b2o$
4o37bobo21bobo21bobo21bobo16b2o76b2o10b3o113bo106b2o$o3bo10bo26bo23bo
23bo23bo16b2o2b3o306b2o33b4o$o7b2o4bobo120bo308bo31b6o12b4o$bo2bo2b4o
3bo2b2o117bo87b5o248b2ob4o11b6o$6b2o3bo5b2obo203bo4bo90b2o156b2o14b2ob
4o$bo2bo2b4o3bo2bo3bo12bo189bo65b2o29b2o172b2o$o7b2o4bobo3bo13bo190bo
3bo59b2ob4o24bo118b2o$o3bo10bo4b3o12b2o80b3o107bo62b6o142b2o$4o28b3obo
82bo142b2o14bo2bo9b4o145bo$31b5o82bo106b3o32bo4bo11bo$31b2obo190bo33bo
17bo3bo7bo12b2o$13b5o208bo32bo5bo11b4o4bo3b3o11b2o$13bo4bo240b6o18b2o
5b2o10bo130b2o$13bo57b6o22b3o181b3o6bo139b2o$14bo3bo52bo5bo23bo181b2o
5b2o142bo$16bo54bo28bo118b3o55b4o4bo3b3o126bo2bo$23b5o44bo4bo141bo57bo
3bo7bo127bo$23bo4bo30b2o13b2o144bo56bo139bo3bo$23bo34b2ob2o215bo2bo
135b4o6b2o$24bo3bo30b4o3bo14b3o342b2o$26bo33b2o3bobo2b2o11bo205b6o133b
o$64bo3b2o2bo9bo130b3o73bo5bo$60b2o3bobo2b2o141bo75bo115b2o$59b4o3bo
147bo75bo4bo108b2ob2o11b2o$58b2ob2o136b2o91b2o111b4o3bo5b2o2bo$59b2o
137b2ob2o203b2o3bobo2b2ob3o$199b4o207bo3b2o6bo3bo$72b4o124b2o5b3o196b
2o3bobo2b5obob2o$71b6o130bo197b4o3bo6b2obob2o$70b2ob4o131bo195b2ob2o$
71b2o113b4o215b2o$186bo3bo10bo214b2o$186bo7b2o4bobo211bo4bo$187bo2bo2b
4o3bo2b2o208bo$192b2o3bo2bo2bob2o4bo3bo197bo5bo$187bo2bo2b4o4b2obo6bo
3bo197b6o$186bo7b2o4bo12bo$186bo3bo10bo221b4o$186b4o233bo3bo$423bo$
215bo208bo2bo$195b2o19bo$194b2ob4o14bo$195b6o$196b4o6b2o$205b4o$204b2o
b2o$205b2o!

[calcyman]

What is the highest possible value of P such that a non-totalistic rule exists with spaceships of period P and period P+1?
Current record: 42

29461-generation diehard in a 96-by-16 box:

Code: Select all

x = 96, y = 16, rule = B2in3-cky4ciqrtz5ey6ac/S1c2aek3-acky4t6i7e8
ob2o2bo4b2obo65bob2o2bo5b2o$b4o2b2o2bo2bo65bob3ob6o2bo$obob2ob2ob3o67b
ob2o2b3o3b2obo$b2obobobobobo2bo65b7o2bo3b2o$bobo2bobo4b3o64bo4b2ob3o3b
2o$2bobo3bob5o71bo3bo2bo$bob2obo5bobo65b7ob3obobo$o4bo4b5o66b4o2bo2bo
2bo$bo4b6obobo65bob5o2bob4o$bo3bobob3o2bo65bo5b2obo4b2o$3ob4o2bobo67bo
2bobob2ob2obo$2bob2ob3o2bo2bo64b4o4b3o4bo$b2o2bobobo4b2o64bo6b2obobob
2o$3o4b2ob3obo68bobo2b3ob4o$b2ob3o6b2o66b5ob2o3bo2bo$bobobob2o2b5o64b
3ob3ob2obob2o!

[Saka]

What about highest known period for an ELEMENTARY c/2 ship in any non-totalistic/totalistic CA?