2003/03/01 by Johan Gielis · 1 voice · 3 citations
Agricultural and Biological Sciences · Engineering · Mathematics · #Leaf Properties and Growth Measurement #Morphological variations and asymmetry #Tree Root and Stability Studies
paper · doi:10.3732/ajb.90.3.333
openalex publication_date 2003/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23
To study forms in plants and other living organisms, several mathematical tools are available, most of which are general tools that do not take into account valuable biological information. In this report I present a new geometrical approach for modeling and understanding various abstract, natural, and man-made shapes. Starting from the concept of the circle, I show that a large variety of shapes can be described by a single and simple geometrical equation, the Superformula. Modification of the parameters permits the generation of various natural polygons. For example, applying the equation to logarithmic or trigonometric functions modifies the metrics of these functions and all associated graphs. As a unifying framework, all these shapes are proven to be circles in their internal metrics, and the Superformula provides the precise mathematical relation between Euclidean measurements and the internal non-Euclidean metrics of shapes. Looking beyond Euclidean circles and Pythagorean measures reveals a novel and powerful way to study natural forms and phenomena.