  This work shows that fractals can be obtained from Mechanical Laws without
being forced by any algorithm, closing the gap between the Platonic world of
Mathematics and Nature. Fractal tree crown directly emerges when applying
elasticity theory to branching stresses in a binary tree. Vertical
displacements of nodes are given by the Takagi curve, while the horizontal ones
are given by a linear combination of inverses of $\beta$-Cantor functions. In
addition, both fractal dimensions are related, which suggests a deeper
connection between the Takagi Curve and the $\beta$-Cantor function.
