Watersheds are Schramm-Loewner Evolution curves
  We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter $\kappa$. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE$_\kappa$, with $\kappa=1.734\pm0.005$, being the only known physical example of an SLE with $\kappa<2$. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic Conformal Field Theory (CFT) with central charge $c\approx-7/2$. 
E. Daryaei, N. A. M. Araujo, K. J. Schrenk, S. Rouhani, H. J. Herrmann
cond-mat.stat-mech