  Dense flow visualization is a popular visualization paradigm. Traditionally,
the various models and methods in this area use a continuous formulation,
resting upon the solid foundation of functional analysis. In this work, we
examine a discrete formulation of dense flow visualization. From probability
theory, we derive a similarity matrix that measures the similarity between
different points in the flow domain, leading to the discovery of a whole new
class of visualization models. Using this matrix, we propose a novel
visualization approach consisting of the computation of spectral embeddings,
i.e., characteristic domain maps, defined by particle mixture probabilities.
These embeddings are scalar fields that give insight into the mixing processes
of the flow on different scales. The approach of spectral embeddings is already
well studied in image segmentation, and we see that spectral embeddings are
connected to Fourier expansions and frequencies. We showcase the utility of our
method using different 2D and 3D flows.
