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DracoLacertae

conway's game of life and light speed

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I'm sure most of you are familiar with Conway's Game of Life : http://en.wikipedia.org/wiki/Conway's_Game_of_Life

There is a particular structure in this that has always bothered by quite a bit: the 'Fast Forward Force Field,' which is described here: http://en.wikipedia.org/wiki/Conway's_Game_of_Life


I've seen it in action in a Life simulator and I am completely baffled by it. Why? It seems to violate 'the laws'. Check this out:

A. In the game of life, when computing the next generation of each cell, ONLY the 8 neighboring cells are considered.

B. Based on 'a', you can see information travels 1 cell per generation, no faster

C. It's easy to see 'horizontal' or 'vertically' traveling information has a speed limit of 1 cell per generation, so call this speed 1 unit per clock (Commonly called 'C' in the game of life)

D. If you're really paying attention you can realize that information traveling diagonally is traveling sqrt(2) (about 1.4) distance units per generation. It's still one cell per generation, but the distance is a little greater

E. Information can only travel vertically, horizontally or diagonally, so the fastest any information ought to be able to travel in Life is sqrt(2) units per generation.

My question is, how the hell can the Fast Forward Force Field even work? If I input a stream of gliders at a certain spacing representing bits on/off, the output has the same spacing (and thus the same information), but has traveled faster than it should of. What gives? The 'FFFF' propagated gliders at 11 spaces per 6 clocks or 1.8 C !

I always thought this implied that if you build a giant game-of-life machine where information between cells really did travel at the speed of light, such as having each cell connected to its neighbors by several meters (even miles) of optical fiber, the information at the end of the machine would beat the light that's carrying the signals running the machine, and that's just plain wrong!

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