On Wednesday, March 27, 2002, at 04:56 PM, [EMAIL PROTECTED] wrote: > On 27 Mar 2002 at 22:43, Eugene Leitl wrote: > >> On Wed, 27 Mar 2002 [EMAIL PROTECTED] wrote: >> >>> I don't recall ever having read of this type of structure before, >>> but it seems so obvious that I'm sure it's been discussed before. >>> So is there a name for it? Does anyone use it? has it been >>> shown to be utterly worthless? >> >> You don't mean something like this: >> http://www.perfdynamics.com/Papers/Gnews.html do you? >> > > Yeah, I think what I was describing was more or less what > they call a hypercube, or maybe just a cube. > I'm not one of those people that > can actually envision multidimensional structures, so I only > know "this is a 4-cube" if I see the coordinates.
No need to "visualize" 4D spaces, 5D spaces, and so on. Think in terms of how many nearest neighbors a point is, a la my last post: -- in a 1-dimensional space/topology, 2 nearest neighbors (left, right) -- in a 2-dimensional space/topology, 4 nearest neighbors (left, right, above, below) -- in a 3-dimensional space/topology, 6 nearest neighbors (6 faces of a cube) -- in a 4-dimensional space/topology, 8 nearest neighbors -- in an n-dimensional space/topology, 2n nearest neighbors (all using the definition of distance in terms of unit vectors, not diagonals) Actual machine hypercubes are just made in the obvious way: by connecting vertices/nodes the way a physical hypercube would be connected. In fact, since wires are small [though not infinitely small, and certainly not of zero propagation delay], it's possible to connect every node to every other node. --Tim May "That the said Constitution shall never be construed to authorize Congress to infringe the just liberty of the press or the rights of conscience; or to prevent the people of the United States who are peaceable citizens from keeping their own arms." --Samuel Adams
