Conformal loop ensembles:

The conformal loop ensembles CLE(kappa), indexed by a parameter kappa between 8/3 and 8, are random collections of countably many disjoint loops in a planar domain. When kappa is less then or equal to 4, the loops are almost surely simple and disjoint. For larger kappa, the loops may intersect themselves and one another. An instance of CLE(8/3) is almost surely empty (i.e., no macroscopic loops) . An instance of CLE(8) is almost surely a single space filling loop. There is a natural coupling between a CLE on a planar domain and the Gaussian free field on that domain (which I don't describe here). The boundaries between black and white clusters in the figures below are discrete approximations to the conformal loop ensembles constructed from the discrete Gaussian free field.