dvgrn

Yes, there's a fairly simple proof, specific to the B3/S23 Life rule, not true for all similar CA rules. Unfortunately this comment box is too small to contain it... and the proof only applies to structures traveling through empty space. If you're allowed to have pre-existing live cells ahead of the glider, there are known "wires" that transmit information diagonally at 2c/3, easily fast enough to get ahead of a glider and stop it.

In B3/S23 Life, there just happened to be small c/4 diagonal, c/2 orthogonal, and c/7 orthogonal spaceships. The c/7 "loafer" ( http://conwaylife.com/wiki/Loafer ) was only found a few years ago, and was a huge surprise. Seems to be more or less the luck of the draw which velocity vectors happen to have smaller spaceships. There probably _is_ a knightship somewhat smaller than Sir Robin, but it's harder to find because it's a little wider, so it's still hiding somewhere in a much larger search space.

Not a simple explanation, I don't think. The size of the smallest spaceship with a given speed and direction is an emergent consequence of iterative rules, so explaining "why" for a Life spaceship is like trying to explain the Seahorse Valley in the Mandelbrot set. In both cases, the iteration rule is simple, but the consequences are complex -- no pun intended.

It's easy to stop one of these knightships -- an eater has been built already -- and just as easy to make a knightship detector. However, a gun to make new "Sir Robin"s is not likely to appear any time soon: there are construction problems that are thousands of times easier, that are not anywhere near being solved yet.

People have been looking for one of these for decades. Guess Moore's Law (and SAT solvers) have finally caught up to this problem!

People have been trying to write good games based on Conway's Life for decades, but it seems as if most game mechanisms end up having too steep a learning curve -- mostly because the system is too sensitive, so one bit out of place tends to cause huge, unpredictable, uncontrollable effects.

Seems to me Life has a lot of potential as abstract art, though. I'm almost curious enough about what they're doing in Second Life these days, to sign up and go have a look:

http://www.conwaylife.com/forums/viewtopic.php?f=7&t=2068#p2...