Describing long-range patterns in leaf vasculature by metaphoric fields

Some patterns in dicotyledonous leaf vasculature depict rather precise, long-range structural features. This work identifies and quantifies these previously unrecognized features in terms of an empirically derived mathematical formalism that generates wave-like spatial patterns referred to as metaphoric fields. These patterns were used to specify regularities in the long-range structure of dicot leaf vasculature, and were found to account significantly for the predominant features of all 27 dicot species studied. The conserved features of these metaphoric fields are discussed in terms of existing models for leaf pattern formation based on efflux-protein mediated auxin transport in a developing cellular field. This work highlights the complex, regular, long-range structures existing in leaf vascular patterns, and provides a means for specifying and identifying the inherent global features of vascular patterns which must be accounted for in functional developmental models.