  Numerical experiments by Werness, Lee and the third author suggested that
dessin d'enfants associated to large trivalent trees approximate the developed
deltoid introduced by Lee, Lyubich, Makarov and Mukherjee. In this paper, we
confirm this conjecture. As a side product of our techniques, we give a new
proof of a theorem of Bishop which says that ``true trees are dense.'' We also
exhibit a sequence of trees whose conformally natural shapes converge to the
cauliflower, the Julia set of $z\mapsto z^2+1/4$.
