> You are right, this is not a very good measurement.  None the less with
> some change it is suited for comparing distributions.  From all
> distributions with N points the one with the largest minimum distance
> between two points could be considered as the best.

Without having tried I would suspect this to favor grids.

> A different measurement would be calculating the sum of the inverse
> distances of every point to all other points.  All this sums together
> should be low for a good distribution.

Another aspect are boundary effects. Take, for simplicity, a
one-dimensional
example: 4 points in the unit interval. In the optimum one point will be
at 0
and another at one. Because of symmetry the other two will be at x and
1-x.
The function you want to minimze then is 4/x+4/(1-x)+2/(1-2x). The
optimum
due to common sense is x=1/3 while this does not minimize the function:
Its derivative at 1/3 is 9, while it would be 0 at the minimum.

This does not matter though, if the distribution is calculated on a
boundary-less space, such as a torus, and then mapped to the space we
are interested in.

> The problem is that this would not detect anisotropy.

What is anisotropy?

  Mark

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