.jpg "fig:"){width="0cm"} ![Top left: random potential $V(\vec{x})$. The 0D square domain is divided in 00 $\times$ 00 small squares. In each square, the potential $V$ is assigned an independent random value uniformly distributed between 0 and $V_{max}$ (here 0000). Top right: 0D view of the landscape of $u$, obtained by solving $L u = 0$, where $L = - \Delta + V(\vec{x})$. Bottom: 0D color representation of the map of $u$, together with the streamlines. The thicker lines correspond to the deepest valleys and the moderately thick lines to the more shallow ones. This landscape draws an intricate network of interconnected valleys. One can conjecture that in the limit of a Brownian potential, this network becomes scale invariant and exhibit fractal properties.[]{data-label="fig:random_u"}](random_u