In this paper we study the equilibrium mechanics problem that originates in a binary tree with infinite levels subjected to loads on its topmost branches. The application of the laws of mechanics to find the equilibrium configuration shows that the functional forms of the vertical and horizontal displacements of its end nodes converge to a Takagi curve and a linear combination of inverses of $\beta$-Cantor functions respectively as the number of levels tend to infinity. As a consequence, the shape of the canopy results from the combination of these two emerging fractals that were not present in the unloaded tree. Besides, our study also shows that the analytical expressions of the emerging fractals depend on the mechanical properties of the binary tree, indicating that the binary tree is a link between these two emerging fractals. In addition, we prove that the fractal dimensions of Takagi and $\beta$-Cantor are related in this model.

在本文中，我们研究了平衡力学问题，该问题起源于具有无限层级的二叉树，其最顶端的树枝承受载荷。应用力学定律寻找平衡构型表明，其末端节点的垂直和水平位移的函数形式收敛到一条高木曲线和逆的线性组合。$\beta$-康托函数分别作为级别数趋于无穷大。因此，树冠的形状是由卸载的树中不存在的这两个新兴分形的组合产生的。此外，我们的研究还表明，新兴分形的解析表达式取决于二叉树的力学性质，表明二叉树是这两个新兴分形之间的纽带。此外，我们证明了 Takagi 的分形维数和$\beta$-康托尔在这个模型中是相关的。