 Trace of a Loewner chain

When the indicated limit exists continuously and the hulls are generated by its past, it defines the trace of the Loewner chain. The hull $K_t$ includes the curve up to time $t$ and any regions it disconnects from infinity. Therefore swallowing a point by $K_t$ is different from visiting that point by the Loewner trace. For SLE, the continuous trace is part of its basic existence theory.