title: Fern leaves and cauliflower curds are not fractals.
abstract: The popular demonstration of drawing a mature fern leaf as expressed by Barnsley's fractal method is mathematically and visually very attractive but anatomically and developmentally misleading, and thus has limited, if any, biological significance. The same is true for the fractal demonstration of the external features of cauliflower curds. Actual fern leaves and cauliflower curds have a very small number of anatomically variable and non-iterating bifurcations, which superficially look self-similar, but do not allow for scaling down of their structure as real fractals do. Moreover, fern leaves and cauliflower curds develop from the inside out through a process totally different from fractal drawing procedures. The above cases demonstrate a general problem of using mathematical tools to investigate or illustrate biological phenomena in an irrelevant manner. A realistic set of mathematical equations to describe fern leaf or cauliflower curd development is needed.
authors.affiliation: Department of Biology & Environment, Faculty of Natural Sciences, University of Haifa, Oranim, Tivon, Israel. levyadun@research.haifa.ac.il
authors.forename: Simcha
authors.initials: S
authors.lastname: Lev-Yadun
mesh_terms: D001937:Brassica / Q000033:anatomy & histology*; D029624:Ferns / Q000033:anatomy & histology*; D017709:Fractals; D056626:Inflorescence / Q000033:anatomy & histology*; D018519:Meristem / Q000033:anatomy & histology*; D018515:Plant Leaves / Q000033:anatomy & histology*