It's a more complicated problem than just using uniform distribution over two dimensions separately. If your "evenliness" is the distance between two closest particles, then there are exactly two ways to achieve that: equilateral triangles and squares (well, three if you count hexagons). The only random thing there is the position of one seed and the "direction" in which that will go.

Refer to the image:

That will give you a very regular, grid-like look, though. You could try applying random, minuscule changes to particles distributed that way, and see how that would work.