dbell wrote: ↑May 27th, 2023, 4:21 am

that c/4 spaceships are known for all periods of the form 388 + 4N based on glider loops?

It's currently 120 + 4N. It should be possible to construct glider loop based rakes (and hence ships) down to period 92 as I suggested

here, but nobody has yet tried to complete the construction.

Technically to make

*glider loop based* rakes at periods 92 + 4N we would need fanouts that work at these periods (and a HWSS synthesis that works at p92). In the link above I only show fanouts for periods 92, 108, 112, and 116 (the only "unsolved" periods above 80). Fanouts for periods 96 and 100 work essentially like the fanout for period 92. A p104 fanout is also easy to make:

Code: Select all

```
x = 514, y = 68, rule = B3/S23
499bo$497bo2bo$318b2o162bobo12bo3b5obo$318b2o162bo3bo7bobo4b5o$482bo2b
2o5b2o2b2o3bob7o$433bo22b2o26bobo3bo4bo11bobo2b2o$313b2o117b2o5bo11bo
4bo23bo6bo8bob2o11bo$310b2ob2o115bo2bobo2bobo9bob2o2b3o16b2ob2obobob2o
b3obob5o$313bo20bo71bo2b2o14bo2b2o6b3obo8bo8bo16bo2bo7bob2o5b2o$308b2o
13b2o5bobo2b2o63b2o3bo3b2o5b3o6b2obo5bo2bo8b4o4bo2b3o13bobobobo4bo2bo$
305bo2b3ob2o4b2o3bo2b7o66bo4b2o6bob7o4bo2bo2bo11b2ob3obo3b2o2b2o10bo2b
obobob2o$303b2o3bob3obo2b2obobob5o67b2ob2o3b2o2bo2b3o2b5o7bo2bo3b3o4bo
2bo5bob3o3bo3bo3b2o3bo9bo$305bo2b2o3b4o5b7obo64b3obo8bo6bo5bo7b2o7b5o
2b2obo5b2o6bobobobo2bob2o2bo4bo$307bo2bo4bo2bo77b5o2b3o2bo2bob2o6bo2b
2o13b4obo16b2o3b2obobobobo5bobo$291b4o13b2o4b2obo82bobo7bo4bo5bo2b3o
18bo21bo2b2ob2o3b2o$288b2obo3b2ob2o14bo3bobo80b2obobo19bo18bo21bo2b2ob
2o3b2o$285bo9b4obo102bo35b4obo16b2o3b2obobobobo5bobo$281b2o2b2obob2o2b
o3bo106bo23b2o7b5o2b2obo5b2o6bobobobo2bob2o2bo4bo$280bo2bo5bo3bo5bo
105bo22bo2bo3b3o4bo2bo5bob3o3bo3bo3b2o3bo9bo$273b4obo10b2ob2o5bo125bo
2bo2bo11b2ob3obo3b2o2b2o10bo2bobobob2o$273bo2b4obo8bobo6b2o124b2obo5bo
2bo8b4o4bo2b3o13bobobobo4bo$284bob2o2bo8b2o124bo2b2o6b3obo8bo8bo16bo2b
o$273b3o8bo4bo140bo2bobo2bobo9bob2o2b3o16b2ob2obobo$284bob2o2bo8b2o
131b2o5bo11bo4bo23bo$273bo2b4obo8bobo6b2o132bo22b2o$273b4obo10b2ob2o5b
o$280bo2bo5bo3bo5bo$281b2o2b2obob2o2bo3bo$285bo9b4obo$288b2obo3b2ob2o$
291b4o6$2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o$obo
23bobo23bobo23bobo23bobo23bobo23bobo23bobo23bobo23bobo23bobo23bobo$b2o
24b2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o24b2o2$289bo$264bobo
20bo$262b2o3b2o17bo5bo42b5obo$262bobo10bo2b2o5bo7bo40bob4o$264bo10bo2b
3obo2bob5obo4bo33bo5b6o$261bo8b2o3bo4bobobo2bo4b3obobo16b2o13bo3b2o5bo
bo2b2o$261b2o3bo3bob3o9b3o9bobo13b3o15bo4bo9bo$267bo3b4o33bobob4o14bob
o2bo2bo$264b2ob2o3bo11b3o9bobo9bo3bob2o19b2o3b2o$265bob2o11bobobo2bo4b
3obobo9bobobob2o22bo$264b2obo9b4obo2bob5obo4bo12bob3o19b2obo$267bo9b3o
5bo7bo20b3o18bob2o$263bo2bo7b2o2bo7bo5bo19bo2bo18bo5b2o$263bo2b2o5bo3b
2o8bo24b3o19b3obob2o$264b2o10b3o10bo44bobobob2obo4bo$272bo2bo36b3o17bo
2b2obob3o6bo$273b2o37bo2bo14b2o4b3obo3b4obo4bo$262b3o8bobobo36b3o15bo
5b2o3b2o3b3obobo$265bobo5bo3bo33bob3o27bo8bobo$261bo2bobo6bo34bobobob
2o$260bo3bo9bo2bo30bo3bob2o$261bo46bobob4o$262b2o11b3o34b3o$263b3o9bo
39b2o$263b3o$272b4o$271b3o2bo$272b2o!
```

Since there is already rakes for periods 96, 100, and 104, I see no need to construct a glider-loop based example. This is simply to show that it can be done.

dbell wrote: ↑May 27th, 2023, 4:21 am

that c/5 spaceships are known for all periods of the form 165 + 5N based on glider loops?

Paul Tooke's

c/5 orthogonal rakes collection has glider loop based rakes of periods 60, 65, 70, 75, and 80. I always assumed all higher periods could be achieved using the same basic principles, but I never attempted to prove it for myself.