I have a set of N uniformly distributed points in a square whose dimensions are known. I need to find the expected number of clusters we are going to form.
We will form clusters based on a region growing algorithm, that is: starting from a point A we will look for another point B whose distance to the first one is lower than d. If there's any point that satisfies this condition, the cluster will keep growing now looking for a point C whose distance either to A or B is lower than d. Now, if it satisfies the conditions we will do the same thing for A, B and C, and so on.
We will consider a cluster is formed if we have at least 3 points joined using this criteria.
I found this post that gives the probability that the distance between 2 points is lower than d, but I don't know how to adapt it to my case: Probability that uniformly random points in a rectangle have Euclidean distance less than a given threshold
