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Jeff Donlan

The answer is: Yes.

John F. Ptak

Okay. Can we expand on this a little, Dr. D? AS I said, the question to me is way more interesting than the start of my answer...

Darien Large

My understanding is that the two-dimensional Game of Life (Conway/Guy) has been demonstrated to support a) self-reproducing patterns and b) Turing-complete computation. This may not be the existence proof you seek, but it's provocative to me at least. My hesitation extending the result from Life to general two-dimensional "worlds" has to do with questions of conservation laws, which on the level at which the Game of Life was designed, do not really exist. Of course, the conservation laws of our own universe are a lot more complicated than "matter can be neither created nor destroyed", so perhaps it's a question of scale.

David Bimler

Dewdney, in "The Planiverse", spent a while looking into the details of how multicellular communication might work in a 2D universe.

http://en.wikipedia.org/wiki/The_Planiverse

There's still the problem that planetary orbits don't exist in 2D (assuming that forces like gravity follow an inverse law rather than an inverse-square law).

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