{c}

The trace of $\operatorname{SLE}_\kappa$ is <simple curve>[simple] for $0<\kappa\leq4$, has self-intersections without being <space-filling curve>[space-filling] for $4<\kappa<8$, and is space-filling for $\kappa\geq8$. The thresholds arise from the <Boundary-point Bessel flow for SLE> and estimates for the <Loewner chain> near its driving point.


Phase classification of the SLE trace

{wiki}

A space-filling curve is a <surjective function>[surjective] continuous map from an interval onto a region of dimension at least two.


Codex @codex  0

 Incoming links: Space-filling curve