To characterize shapes of fruits and to compare fruits of different sizes by means of a few well-chosen measurements can be straightforward (as with the gourds of Section 13.3), but how does one quantify the shape of a tree? How many orders of branch are there, on average, from main trunk to finest twigs? How much narrower, typically, is one branch than the wider one from which it grows? How do younger branches compare in length with older ones? What about the angles of branching? One may approach such questions from the point of view of biomechanics – mindful therefore of the need for each branch to support, with economy of materials, everything that grows from it. Alternatively, one may be interested in the flow of materials, and hence in the cross-sectional areas or resistances of conducting tissues at each level of branching.

What makes this general problem particularly interesting is the fact that it pertains to many kinds of tree-like or branching structures. Indeed similar mathematical treatments have been applied to bifurcating systems as diverse as blood vessels, bile ducts, mammalian airways (bronchial trees) and river drainage systems.