Da Vinci wrote in his notebook that “all the branches of a tree at every stage of its height when put together are equal in thickness to the trunk.” In other words, if a tree’s branches were folded upward and squeezed together, the tree would look like one big trunk with the same thickness from top to bottom. To investigate why this rule may exist, physicist Christophe Eloy, from the University of Provence in France, designed trees with intricate branching patterns on a computer. “I designed the lightest tree structure to resist wind while still maintaining the strength of the trunk,” said Eloy.
Trees are fractal in nature, meaning that patterns created by the large structures, such as the main branches, repeat themselves in smaller structures, such as smaller branches. Eloy started with a fractal tree skeleton, in which smaller copies of the main branches are repeatedly added together to create the virtual tree. Each new branch takes after its “mother” branch, mimicking the fractal nature of real trees. At this stage, the model tree served merely as a framework for later determining the most effective branch thickness. Once the skeleton was completed, Eloy put it to the test in a virtual wind tunnel. After applying various wind forces needed to break the branches, Eloy determined the diameters for each branch that limited the chance of snapping. Accounting for every part from the smallest twig to the trunk, the simulation seemed to produce Leonardo's rule.