ConwayLife.com

Well, the data transmission rate of the LST is so horrible that it only really makes sense if you want to transmit halfway across the universe. Each sequence of 10 pulses carries one bit and it has an insane cooldown time, so a line of c/2 spaceships would have a much better bitrate, at the expense of signal latency.

Phantom Hoover wrote:Well, the data transmission rate of the LST is so horrible that it only really makes sense if you want to transmit halfway across the universe.

Depends how big the universe is.

Depends if it's a torus, if it is, then you would have to go FOREVER!

Extrementhusiast wrote:Depends if it's a torus, if it is, then you would have to go FOREVER!

If the universe is a torus then "halfway across the universe" is half of the path you need to cross before you end up where you started, so you wouldn't be going forever.

However since the universe in Life is supposed to be infinite, in the general case you indeed would be going forever even if it's just "halfway" across the universe...

In this context "the universe" means the area wherein stuff is happening.

Phantom Hoover wrote:In this context "the universe" means the area wherein stuff is happening.

You're no fun. >:-|

Splitbumping this from the "Two Forbidden Directions" thread into the more general one.

Nathaniel wrote:Anywho, it's always great to have new ways to look at problems like this. Any chance of applying it to rules other than B3 rules? If I recall correctly, there is a 3c/4 diagonal spaceship known in a B0 rule, and I'm not aware of any non-trivial speed limits in rules like that.

3c/4 is quite obviously the diagonal spaceship speed limit in B0 rules.

B0/D8 rules are equivalent with alternating between two A0 rules. B2 rules allow reaching a diagonal speed of c/2 for information transmission into vacuum. B1 rules allow reaching a speed of c/1. B1 rules do not support spaceships though, so the fastest possible spaceship would be one that alternates between a number of B1 stages and at least one A1 stage. With two rules alternated, the fastest option is B1 ~ B2, which comes out at precisely 3c/4.

Also note e.g. the following speed limits:
• B1 ~ B3 rules: c/1 orthogonally, c/2 diagonally. Note that the former is faster than you'd expect from the plain B3 spaceship speed limit of c/2. This is because B1 also allows widening the bow of the ship, and hence the relevant speed limit is the maximum general orthogonal growth rate, which is c/1. The same does not apply to the diagonal case as B1 stages always maintain intact the diagonal width of the bow. (In fact, maximally fast B1 ~ B3 diagonal spaceships necessarily cannot contain any B3 contribution to the engine, as this can only possibly contract the bow.)
• B2 ~ B3 rules: c/2 orthogonally, c/2 diagonally. The same bow-width argument as for B1 ~ B3 diagonal applies for the orthogonal case here. Diagonally the situation is the inverse: B2 is capable of widening the bow, hence we can plug in the general diagonal B3 growth rate.
• B1 ~ B1 ~ B2 rules: 5c/6 diagonally (and c/1 orthogonally).

Engines for the B1 ~ B3 orthogonal and B2 ~ B3 diagonal cases are simple to sketch: You may notice that a survival condition between 2 and 4 is necessary for both phases of a B2 ~ B3 c/2 diagonal ship, though. I cannot see immediately what the speed limit would be without this — exceeding c/3 might still be possible (say, 3c/8), since c/2 orthogonally requires "ignoring" B3 contributions.

• B2 ~ B3 rules: c/2 orthogonally, c/2 diagonally. The same bow-width argument as for B1 ~ B3 diagonal applies for the orthogonal case here. Diagonally the situation is the inverse: B2 is capable of widening the bow, hence we can plug in the general diagonal B3 growth rate.

You sure about that?

Pteriforever wrote:

• B2 ~ B3 rules: c/2 orthogonally, c/2 diagonally. The same bow-width argument as for B1 ~ B3 diagonal applies for the orthogonal case here. Diagonally the situation is the inverse: B2 is capable of widening the bow, hence we can plug in the general diagonal B3 growth rate.

You sure about that?

Hm, you're right, I went wrong there somewhere.
This approach seems to come with some survival condition requirements, though, in order to facilitate a B3 stage used to regrow the bow.

A similar case (for again 5c/8 diagonal) seems possible for B1 ~ B3 too, then. Actually, this might even allow using two B3 growth stages per a B3 non-growth stage, for 4c/6 speed.