  In many fields, the spatial clustering of sampled data points has many
consequences. Therefore, several indices have been proposed to assess the level
of clustering affecting datasets (e.g. the Morisita index, Ripley's K-function
and R\'enyi's generalized entropy). The classical Morisita index measures how
many times it is more likely to select two measurement points from the same
quadrats (the data set is covered by a regular grid of changing size) than it
would be in the case of a random distribution generated from a Poisson process.
The multipoint version (k-Morisita) takes into account k points with k greater
than or equal to 2. The present research deals with a new development of the
k-Morisita index for (1) monitoring network characterization and for (2) the
detection of patterns in monitored phenomena. From a theoretical perspective, a
connection between the k-Morisita index and multifractality has also been found
and highlighted on a mathematical multifractal set.
