Numerical simulations of a growing network: Anistropy depends on the applied stress.

<p>(A) The effect of external stress. Each vein is represented by a black line. The red box is the unit cell with periodic boundary conditions. For visualization, the texture tensor of each areole is shown in the middle of the areole (blue, not to scale), and the averaged texture tensor in the middle of each figure (green, not to scale). The three tissues grew under turgor pressure; in addition, the stress <i>σ</i>_<i>xx</i> along the <i>x</i> direction or <i>σ</i>_<i>yy</i> along the <i>y</i> direction were set equal to the magnitude of turgor pressure <i>P</i>_<i>tur</i>. (B) The distribution of the main orientation (the orientation of the eigenvector associated with the highest eigenvalue) of the texture tensor in the simulation. The distribution is seen to be relatively widely scattered around 90° when no external stress is present (green). When stress is applied, the distribution becomes sharply concentrated around the direction of the external stress (orange and blue). (C) The anisotropy of the texture tensor field averaged over 40 simulations, as a function of the external stress. The stress is measured in units of the turgor pressure, and the anisotropy is measured when the network has doubled its area from the end of the vein creation stage (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004819#sec013" target="_blank">Methods</a>).