Beauty is a characteristic of objects that provides a perceptual experience of pleasure. In nature, aesthetic appreciation thereof has given rise to the mathematical search for good series (e.g. the Fibonacci series) and proportions (e.g. the Golden proportion) as important elements of beauty. In 1928 the mathematician George David Birkhoff introduced a formula for aesthetic measurement of an object. Birkhoff equation defines the aesthetic value as the amount of order divided by the complexity of the product. These two features can be measured easily in poetry, music, painting, architecture, etc. In the fine arts, it is the artist who manipulates both these features, but how does nature manage order and complexity in living organisms or their parts? Here we show how Birkhoff equation, applied to the mammalian vascular system of eight representative animals, results in new insights into the organization of the animal vascular system. We found that order and complexity are highly correlated in the mammalian vascular system (_R^2^_=0.9511). Accordingly, in nature both features are not independently managed in the manner of artists. We found significant differences among the Birkhoff aesthetic values in the mammalian arterial system, whereas no such differences exist in the venous system. We anticipate our approach to be useful in the study of morphogenesis and evolution of tree-like structures, employing the Birkhoff aesthetic value as a simple tool for conducting such studies
