[math-fun] graviton-like cellular automaton
Gravitons are presumed to change the shape of spacetime, and if there are enough of them, perhaps even its topology. Does anyone on the list know of any cellular automata that, say, change the neighborhood based on the density or topology of clumps of "on" cells, or similar? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
My favorite (completely unsupported by data) speculation on space-time is as a 4-D crystal (the past) with dislocations (the particles) and a phase boundary (the present). Dislocations cannot be individually repaired, but only by pair creation or annihilation, just like particles. The idea is that there is a meta-time in which crystallization happens at the phase boundary. Net growth of the crystal corresponds to observable time. The advancement in meta-time allows for alternative futures to be investigated by growth and retraction of the phase boundary -- note the very close relationship between stat mech and Wigner rotation in QFT. Regular lattices with defects have curvature, so "gravitation" happens automatically in this speculation. I'd like to see an enumeration of the types of defects that can occur in a regular 4-D lattice. Of course, Kaluza-Klein models might make higher dimensional lattices a possibility here as well. On Jun 30, 2010, at 1:00 PM, Mike Stay wrote:
Gravitons are presumed to change the shape of spacetime, and if there are enough of them, perhaps even its topology. Does anyone on the list know of any cellular automata that, say, change the neighborhood based on the density or topology of clumps of "on" cells, or similar? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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For what it's worth, I took the liberty of putting your question on MathOverflow and got a little bit of a discussion going: http://mathoverflow.net/questions/30096/graviton-like-cellular-automaton Paul On Wed, Jun 30, 2010 at 12:00 PM, Mike Stay <metaweta@gmail.com> wrote:
Gravitons are presumed to change the shape of spacetime, and if there are enough of them, perhaps even its topology. Does anyone on the list know of any cellular automata that, say, change the neighborhood based on the density or topology of clumps of "on" cells, or similar? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike <http://www.cs.auckland.ac.nz/%7Emike> http://reperiendi.wordpress.com
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For a cellular automata that simulates some sort of gravity effect, you could use a coupled cellular automata to simulate, on the first layer, (each step) first the Conway's Game of Life rules on the cells, then a varied Larger than-life rule. The second board,containing the gravity values gotten by the number of live neighbors in the Von Neumann neighborhood for each cell of the top layer, would simply be a changing reference table for deciding which Larger-than life rule to choose. Specifically, a larger-than-life rule would be similar to a normal rule on a Moore neighborhood, except that it is performed on a grid of size 2r+1, where r is the radius. For example, you could have a rule that says that the rule will be on a board of radius 2 (5x5), and that the cell in the center will turn on only if there is exactly one live cell. In the gravity-like cellular automaton though, the larger-than-life rule is performed on a neighborhood of radius <corresponding value in board 2 -1> , and is that all the cells that are not on the edges or the corners turn on, and everything else is left alone. For example, if after the Conway step there is one cell on board 1 and a cell of state 3 on board 2, the result would be http://bit.ly/aLuUn5 . What I think it would do is find places where the cells cluster, mass them together, and then explode. However, I haven't yet written a program to simulate this, so I can't really predict it's behavior after more than 1 or 2 steps. --Neil Bickford On Fri, Jul 2, 2010 at 9:22 AM, Paul Reiners <paul.reiners@gmail.com> wrote:
For what it's worth, I took the liberty of putting your question on MathOverflow and got a little bit of a discussion going:
http://mathoverflow.net/questions/30096/graviton-like-cellular-automaton
Paul
On Wed, Jun 30, 2010 at 12:00 PM, Mike Stay <metaweta@gmail.com> wrote:
Gravitons are presumed to change the shape of spacetime, and if there are enough of them, perhaps even its topology. Does anyone on the list know of any cellular automata that, say, change the neighborhood based on the density or topology of clumps of "on" cells, or similar? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike<http://www.cs.auckland.ac.nz/%7Emike><; http://www.cs.auckland.ac.nz/%7Emike> http://reperiendi.wordpress.com
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participants (4)
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Mike Stay -
Neil Bickford -
Paul Reiners -
Tom Knight