muzik wrote:I'm assuming that searches for diagonal ships are even harder? How long would searches for c/8, 9, 10 and 11 diagonal take?

Seems like diagonal ships are bigger on average than "equivalent" orthogonal ones -- the glider being the lonely B3/S23 counterxample that proves the rule. So yes, they take exponentially-proportionally longer to find on average.

I'd like to refuse to answer your c/8 through c/11 diagonal questions, on the grounds that it should be clear from previous messages that I really have no idea either!

But sometimes it's hard for me to stop typing, so I've made up an answer below.

If you want to figure these answers out yourself based on my previous crackpot rule-of-thumb estimates, you just need to know how long

Sokwe's search took that found the c/7 diagonal ship -- assuming (on no particularly good grounds) that the higher-period ships are about the same size as the lobster.

Let's say it took a week of searching. Then

- the c/8 ship might take a thousand weeks,
- the c/9 ship might take a million weeks,
- the c/10 ship might take a billion weeks,
- and the c/11 ship might take a trillion weeks.

We could conceivably somehow convince a million people to distribute the million-week search and get done in a reasonable amount of time, but above that we're getting above the spare-computing-power capacity of the Earth today.

-- That's all assuming that my expansion factor of a thousand is correct, which of course it isn't. That would be only ten cells with completely unknown states that WinLifeSearch-or-equivalent has to test in all possible combinations, for each added phase of the spaceship.

If WinLifeSearch actually has to check twenty unknown cells for each added phase (which might be more likely for a lobster-sized spaceship, but I'm not at all sure so please don't quote me on it) then the expansion factor would be more like a million than a thousand.

You can recalculate the above based on that expansion factor... but at some point the ridiculously large numbers stop mattering. The key idea is what's important: higher period searches are

hard, and they get harder very quickly as the period increases.

Clever new algorithms, or continued Moore's Law hardware improvements, might shift the point at which searches become really hard. Currently it seems to be around c/7, except that we can define very limited small search spaces for higher periods and hope to find something like a

copperhead or a

loafer in them. And every now and then that will keep happening, because there are a lot of strange and wonderful Life patterns out there.

But even when (if?) algorithms or computer hardware become a thousand or a million times better than they are now, that might only shift the easy/hard frontier from c/7 to c/8.