  It is well-known that in two dimensions Turing systems produce spots, stripes
and labyrinthine patterns, and in three dimensions lamellar and spherical
structures or their combinations are observed. We study transitions between
these states in both two and three dimensions by first analytically deriving a
control parameter and a scaling function for the number of clusters. Then, we
apply large scale computer simulations to study the effect of nonlinearities on
clustering, the appearance of topological defects and morphological changes in
Turing structures. In the two-dimensional real space spotty structures we find
some evidence of twin domain formation, of the kind seen in crystalline
materials. With the help of reciprocal space analysis we find indication of
other more general forms of order accommodation, i.e., eutactic local
structures. Also a mechanism for the observed ``connectivity transition'' is
proposed.
