  The (chordal) Loewner differential equation encodes certain curves in the
half-plane (aka traces) by continuous real-valued driving functions. Not all
curves are traces; the latter can be defined via a geometric condition called
the local growth property. In this paper we give two other equivalent
conditions that characterise traces: 1. A continuous curve is a trace if and
only if mapping out any initial segment preserves its continuity (which can be
seen as an analogue of the domain Markov property of SLE). 2. The (not
necessarily simple) traces are exactly the uniform limits of simple traces.
Moreover, using methods by Lind, Marshall, Rohde (2010), we infer that uniform
convergence of traces imply uniform convergence of their driving functions.
