Let $X$ be a spatial blue noise point process in the plane where points are at least distance $d$ apart for $d > 0$.
For a closed region in the plane $B$, let $N(B)$ count the number of points in $B$.
What is the distribution of $N(B)$?
My guess is that $N(B)$ could be a truncation of a Poisson distribution, from my intuition that blue noise is like white noise but with a minimum distance between points. See Baddeley, Spatial point processes and their applications for white noise, as in a spatial Poisson process.
Remark: This question is my attempt to resolve an earlier question from a different direction.
References
Baddeley, Adrian, Spatial point processes and their applications, Weil, Wolfgang (ed.), Stochastic geometry. Lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September 13–18, 2004. With additional contributions by D. Hug, V. Capasso, E. Villa. Berlin: Springer (ISBN 3-540-38174-0/pbk). Lecture Notes in Mathematics 1892, 1-75 (2007). ZBL1127.62086.