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I am currently running into this problem: I have a 2D square, and 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 they tend to gather together in some spot area inside the square.

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

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

Any idea would be appreciated. Thanks

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There is something called the discrepancy of a set of points in, say, the unit square. The smaller it is, the more uniformly distributed the point set. It is discussed in detail in the book, Kuipers and Niederreiter, Uniform Distribution of Sequences. You may also be able to find information about it by a judicious websearch.

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