  We construct elliptic operators with scalar coefficients on the complements
$(\mathbb{R}^2 \setminus S)^+$ of some Koch-type snowflakes $S$, whose
Hausdorff dimensions cover the full range $(1, \ln{(4)}/\ln{(3)})$, such that
the operator's elliptic measures are equal to the Hausdorff measure on the
boundary. This provides another example of the phenomenon that, though purely
unrectifiable boundaries of domains are often characterised by the harmonic
measure being singular with respect to the Hausdorff measure on the boundary,
for some purely unrectifiable boundaries one can construct an elliptic operator
whose elliptic measure behaves in a drastically different way. Plus, in
$\mathbb{R}^2$, this operator can be chosen in a way that its coefficient is
scalar, as opposed to a $2 \times 2$ matrix-valued one.
