Phase classification of the SLE trace
= Phase classification of the SLE trace
{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.