A mosaic process is formed by centering independent and identically distributed random shapes at the points of a Poisson process in $k$-dimensional space. Clusters of overlapping shapes are called clumps. This paper provides approximations to the distribution of the number of clumps of a specified order within a large region. The approximations cover two different situations--"moderate-intensity" mosaics, in which the covered proportion of the region is neither very large nor very small; and "sparse" mosaics, in which the covered proportion is quite small. Both these mosaic types can be used to model observed phenomena, such as counts of bacterial colonies in a petri dish or dust particles on a membrane filter.
"Clump Counts in a Mosaic." Ann. Probab. 14 (2) 424 - 458, April, 1986. https://doi.org/10.1214/aop/1176992525