Why must a knightship have a period of 6 or more?

For general discussion about Conway's Game of Life.
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Alegend
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Joined: October 5th, 2009, 3:20 pm

Why must a knightship have a period of 6 or more?

Post by Alegend » October 10th, 2009, 12:16 pm

Can somebody tell me how this was calculated, please?

HartmutHolzwart
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Location: Germany

Re: Why must a knightship have a period of 6 or more?

Post by HartmutHolzwart » October 11th, 2009, 5:47 am

There is an easy classical proof that a diagonal frontier in empty space can just move with velocity at most c/2 (adding horizontal and vertical components of the velocity vector.

Try to proof on your own, spoiler will follow later.

Alegend
Posts: 31
Joined: October 5th, 2009, 3:20 pm

Re: Why must a knightship have a period of 6 or more?

Post by Alegend » October 11th, 2009, 9:42 am

1x1 movement can only be done at c/2, or lower, so that means, that a knightship, with 2x1 movement can only be done at period 6, or higher.

And a camelship, with it's 3x1 movement can only be done at period 8, or higher, right?

HartmutHolzwart
Posts: 842
Joined: June 27th, 2009, 10:58 am
Location: Germany

Re: Why must a knightship have a period of 6 or more?

Post by HartmutHolzwart » October 11th, 2009, 11:26 am

Correct. It's bit hard to describe the proof, although it's easy

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