  Using a complex parametrisation of $su(2)$, we show a change of coordinates
that maps the maximally symmetric rolling $(2,3,5)$-distribution to the flat
Cartan distribution. This establishes the local equivalence between the
maximally symmetric rolling model and the flat Cartan or Hilbert-Cartan
distribution. For the maximally symmetric rolling distribution, we write down
the vector fields that bracket-generate to give the split real form of the Lie
algebra of $\frak{g}_2$, with two of the vector fields in the
bracket-generating set given by the span of the rolling distribution.
