Plane trees, Shabat-Zapponi polynomials and Julia sets

A tree, embedded into plane, is a dessin d’enfant and its Belyi function is a polynomial — Shabat polynomial. The Zapponi form of this polynomial is unique, so we can correspond to an embedded tree the Julia set of its Shabat-Zapponi polynomial. In this purely experimental work we study relations between the form of a tree and properties (form, connectedness, Hausdorff dimension) of its Julia set.