Fillotassi: il più nell'uno

Isola, Stefano

La Matematica nella società e nella cultura, Série 1, Tome 7 (2014) no. 2, pp. 215-246.

Riassunto (VO)

L’osservazione attenta di certe forme botaniche, come le corolle di alcuni fiori, il broccolo romano, le pigne o la corteccia di un ananas, rende progressivamente apparente la presenza di strutture ordinate nella disposizione dei loro elementi, siano essi infiorescenze, semi, petali, scaglie, o altro, cosicché, ad esempio, ciascun elemento appare all’intersezione di due famiglie di spirali diversamente inclinate che si avvolgono in sensi opposti, e per di più formate da un numero di spirali che appartiene quasi invariabilmente alla successione di Fibonacci o sue semplici varianti. I tentativi di modellizzazione matematica di questo fenomeno hanno una storia lunga e interessante, e l’analisi dettagliata di uno di essi, il modello cilindrico di van Iterson, fornisce uno spunto esemplare per alcune valutazioni di natura epistemologica sulla modellizzazione scientifica in biologia. In particolare mette in luce il fatto che una forma debba essere riguardata innanzitutto come il risultato della dinamica di crescita della pianta, e dunque della sua storia singolare.

Abstract

The careful observation of certain botanic forms such as the corolla of some flowers, the Romanesque cauliflower, the pine cones or the cortex of the pineapple, progressively makes apparent the presence of ordered structures in the arrangement of their elements, whether they are inflorescences, seeds, petals, scales, or any other, so that, for instance, each element appears at the intersection of two families of differently inclined spirals which twist in opposite directions, and moreover are formed by a number of spirals that belongs almost invariably to the Fibonacci sequence or its simple variants. Attempts to mathematical modeling of this phenomenon have a long and interesting history, and the detailed analysis of one of them, the cylindrical model of van Iterson, provides an exemplary cue for some feedback of epistemological nature on scientific modeling in biology. In particular, it highlights the fact that a form should be regarded primarily as the result of the dynamics of growth of the plant, and therefore of its singular history.

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