  We employ N--body/$3D$ gas dynamic simulations of the formation of galaxy
clusters to determine whether cluster X--ray morphologies can be used as
cosmological constraints. Confirming the analytic expectations of Richstone,
Loeb, \& Turner, we demonstrate that cluster evolution is sensitive to the
cosmological model in which the clusters form. We further show that
evolutionary differences are echoed in the gross morphological features of the
cluster X--ray emission.
  We examine current--epoch X--ray images of models originating from the same
initial density fields evolved in three different cosmologies: (i) an unbiased,
low density universe with $\Omega_o \se 0.2$; (ii) an unbiased universe
dominated by vacuum energy with $\Omega_o \se 0.2$ and $\lambda_o \se 0.8$ and
(iii) a biased Einstein--deSitter model ($\Omega \se 1$, $\sigma_8=0.59$).
Using measures of X--ray morphology such as the axial ratio and centroid
shifting, we demonstrate that clusters evolved in the two low $\Omega_o$ models
are much more regular, spherically symmetric, and centrally condensed than
clusters evolved in the Einstein--deSitter model. This morphology--cosmology
connection, along with the availability of a large body of cluster X--ray
observations, makes cluster X--ray morphology both a powerful and a practical
cosmological discriminant.
