Clockspring model of sprouting and blossoming (Q1072471)

The new ''clockspring'' mathematics of \textit{C. Illert} [General theory of life energy. J. Inferential and Deductive Biology 1 (1985)] is shown to apply to plant geometries and, in particular, to the dynamic processes of sprouting and flowering. Indeed, \textit{Y. Kawaguchi}'s [A morphological study of the form of nature. Computer Graphics 16, 223-232 (1982)] already successful model of branching corals and trees is found to be a simple first order version of Illert's generalised second order ''clockspring'' mathematics. The paper does not address the difficult variational mathematics of Illert's optimization problem but, instead, by concentrating upon the descriptive aspect, it has been possible to provide an alternative first- principles derivation of Illert's integral equation using simpler discrete analysis of a kind which will make this area of modelling more accessible to the very applied scientists who will benefit most from its existence and use. These new examples of Illert's mathematics further demonstrate its breadth of application in theoretical morphology. And its success in so many areas - Conchology, Embryology and Botany - should be contrasted with the dwindling returns of conventional models based upon traditional elasticity theory and continuum mechanics.