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We show that when observing the range of a chordal SLE$_\kappa$ curve for$\kappa \in (4,8)$, it is not possible to recover the order in which the pointshave been visited. We also derive related results about conformal loopensembles (CLE): (i) The loops in a CLE$_\kappa$ for $\kappa \in (4,8)$ are notdetermined by the CLE$_\kappa$ gasket. (ii) The continuum percolationinterfaces defined in the fractal carpets of conformal loop ensemblesCLE$_{\kappa}$ for $\kappa \in (8/3, 4)$ (we defined these percolationinterfaces in previous work, and showed there that they are SLE$_{16/\kappa}$curves) are not determined by the CLE$_{\kappa}$ carpet that they are definedin.

Non-simple SLE curves are not determined by their range