  We introduce a new type of aperiodic hexagonal monotile; a prototile that
admits infinitely many tilings of the plane, but any such tiling lacks any
translational symmetry. Adding a copy of our monotile to a patch of tiles must
satisfy two rules that apply only to adjacent tiles. The first is inspired by
the Socolar--Taylor monotile, but can be realised by shape alone. The second is
a local growth rule; a direct isometry of our monotile can be added to any
patch of tiles provided that a tree on the monotile connects continuously with
a tree on one of its neighbouring tiles. This condition forces tilings to grow
along dendrites, which ultimately results in nonperiodic tilings. Our local
growth rule initiates a new method to produce tilings of the plane.

Metric Geometry;Combinatorics;Dynamical Systems