I have a 2D square, and I have a set of points inside it, say, 1000 points. I need a way to see if the distribution of points inside the square are spread out (or more or less uniformly distributed) or are they tending to gather together in some spot inside the square.

I need a mathematical/statistical (not programming) way to determine this. I googled, found something like goodness of fit, Kolmogorov, etc., and just wonder if there are other approaches to achieve this. Need this for class paper.

Inputs: a 2D square, and 1000 points. Output: yes/no (yes = evenly spread out, no = gathering together in some spots).