  The principles underlying plant development are extended to allow a more
molecular mechanism to elaborate the schema by which ground cells differentiate
into vascular cells. Biophysical considerations dictate that linear dynamics
are not sufficent to capture facilitated auxin transport (e.g., through PIN).
We group these transport facilitators into a non-linear model under the
assumption that they attempt to minimize certain {\em differences} of auxin
concentration. This Constant Gradient Hypothesis greatly increases the
descriptive power of our model to include complex dynamical behaviour.
Specifically, we show how the early pattern of PIN1 expression appears in the
embryo, how the leaf primordium emerges, how convergence points arise on the
leaf margin, how the first loop is formed, and how the intricate pattern of PIN
shifts during the early establishment of vein patterns in incipient leaves of
Arabidopsis. Given our results, we submit that the model provides evidence that
many of the salient structural characteristics that have been described at
various stages of plant development can arise from the uniform application of a
small number of abstract principles.
