  We study a continuum model of dislocation transport in order to investigate
the formation of heterogeneous dislocation patterns. We propose a physical
mechanism which relates the formation of heterogeneous patterns to the dynamics
of a driven system which tries to minimize an internal energy functional while
subject to dynamic constraints and state dependent friction. This leads us to a
novel interpretation which resolves the old 'energetic vs. dynamic' controversy
regarding the physical origin of dislocation patterns. We demonstrate the
robustness of the developed patterning scenario by considering the simplest
possible case (plane strain, single slip) yet implementing the dynamics of the
dislocation density evolution in two very different manners, namely (i) a
hydrodynamic formulation which considers transport equations that are
continuous in space and time while assuming a linear stress dependency of
dislocation motion, and (ii) a stochastic cellular automaton implementation
which assumes spatially and temporally discrete transport of discrete 'packets'
of dislocation density which move according to an extremal dynamics. Despite
the huge differences between both kinds of models, we find that the emergent
patterns are mutually consistent and in agreement with the prediction of a
linear stability analysis of the continuum model. We also show how different
types of initial conditions lead to different intermediate evolution scenarios
which, however, do not affect the properties of the fully developed patterns.
