A multiple scaled fractal tree

In a study of two species of oak tree, the distribution and arrangement of branch lengths are found to be governed by a simple algorithm. The algorithm which has its footing in a type of fractal self-similarity observed in other physiological structures (West et al., 1986. J. appl. Physiol. 60, 189-197; Goldberger & West, 1987. Yale J. biol. Med. 60, 421-435), reproduces the observed power-law behaviour of mean branch length with order. Furthermore, the high degree of intra-order variability is accounted for as a natural consequence of the superposition of a multiplicity of scales in the structure. The conclusions of this study point to a genetic rather than environmental origin for the design. © 1990 Academic Press Limited.