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

An aperiodic monotile that forces nonperiodicity through dendrites