ABSTRACT
The development of spontaneous stationary vegetative patterns in an arid isotropic homogeneous environment is investigated by means of hexagonal and rhombic planform nonlinear stability analyses applied to the appropriate governing equation for this phenomenon. In particular, that process can be represented by a fourth-order partial differential spatial-temporal logistic evolution equation for the total plant biomass per unit area divided by the carrying capacity of its territory and defined on an unbounded flat domain. Those patterns that consist of parallel stripes, labyrinth-like mazes, rhombic arrays of rectangular patches, and hexagonal distributions of spots or gaps are generated by the balance between the effects of short-range facilitation and long-range competition. Then those theoretical predictions are compared with both relevant observational evidence and existing numerical simulations from some nonlinear vegetative pattern formation studies.
