Light scattered from dynamic random media has numerous applications in medicine, biology, engineering, physics and numerous other fields. Short term and long term variations and correlations in the scattered intensity (“speckle”) provide information about the crossing of scattering paths as a result of the local structure and dynamics within the medium. Poincaré descriptors are statistical tools used to study variations or self-similarity in neighboring values of a quantity. Herein, we modify this definition to examine correlations not only between neighboring (temporally and spatially) values of dynamic speckle patterns, but also between values with larger spatial and temporal distances between them. The effects of incoherently summed, that is, time-averaged speckle patterns will be examined, as will be the separate cases of incoherently summed correlated and un-correlated speckle patterns. The unique case of elongated speckle will also be presented. The ratio of short-term to long-term differences in the pattern, a term referred to as the ‘ellipticity’ of the data, yields information on the dominance of long-term variations in the scattered intensity compared to the short-term variations. We will show that Poincaré descriptors are useful in quantifying the width of the coherence areas in all 3 dimensions in the scattered intensity patterns and also for quantifying motions in speckle patterns from which information about the dynamics of the medium can be inferred.