The architecture of nature can be seen at play in a tree: no two are alike. The Pythagoras' tree behaves just as a "tree" in that the root plus the same movement repeated over and over again grows from a seed, to a plant, to a tree. In human life, this movement is termed cell division. With triples, this movement is a geometrical and mathematical propagation explained by the central square theory. This movement explains how triples split into other triples via branches. It is a chain in space and time, where all branches grow from a specific triple, and vice versa. Examples applied at different locations in the tree have shown the same thing--the basic movement is the law that governs the birth and growth of the Pythagoras' tree. All branches come in pairs, and grow steadily along the tree. And finally, it was found that the geometric composition of the tree is heterogeneous. That is, the Pythagoras' tree is not only a tree made of triples/triangles, but also of squares. This led to the discovery of the tree of squares. These two trees are numerical images or interpretations of the same geometrical Pythagoras' tree that grows not only with triangles, but also with their central squares.