  We explore the morphological and dynamical evolution of galaxy clusters in
simulations using scalar and vector-valued Minkowski valuations and the concept
of fundamental plane relations. In this context, three questions are of
fundamental interest: 1. How does the average cluster morphology depend on the
cosmological background model? 2. Is it possible to discriminate between
different cosmological models using cluster substructure in a statistically
significant way? 3. How is the dynamical state of a cluster, especially its
distance from a virial equilibrium, correlated to its visual substructure? To
answer these questions, we quantify cluster substructure using a set of
morphological order parameters constructed on the basis of the Minkowski
valuations (MVs). The dynamical state of a cluster is described using global
cluster parameters: in certain spaces of such parameters fundamental band-like
structures are forming indicating the emergence of a virial equilibrium. We
find that the average distances from these fundamental structures are
correlated to the average amount of cluster substructure for our cluster
samples during the time evolution. Furthermore, significant differences show up
between the high- and the low-Omega models. We pay special attention to the
redshift evolution of morphological characteristics and find large differences
between the cosmological models even for higher redshifts.
