Art and science illuminate the same subtle proportions in tree branches

Do artists and scientists see the same thing in the shape of trees? When I saw Mondrian’s 1911 “Gray Tree,” I immediately recognized something about trees that I had struggled to describe. The scale invariance in branch diameter dictates how much smaller a limb should be as it branches and how much investment a tree makes in a few thick branches versus many thin ones. Indeed, wherever our team looked at trees in great artwork, such as Klimt’s “Tree of Life” or Matsumura Goshun’s “Cherry Blossoms,” we also found precise scale invariance in the diameter of branches. When Mondrian removes the scale invariance in “Blooming Apple Tree,” viewers just as easily see fish, scales, dancers, water or simply nonrepresentational shapes, whereas the tree in “Gray Tree” is unmistakable.