Symmetry in Plants

Abstract

This book is dedicated to the brothers L. Bravais and A. Bravais a botanist and a crystallographer respectively who put the study of phyllotaxis on the right track, and also to all those who hold the torch today. FOREWORD MULTIDISCIPLINARITY: A KEY TO PHYLLOTAXISROGER V. JEAN and DENIS BARABE The Subject of the BookDaisies are well-known to lovers who, since time immemorial, have liked to play a game by taking away its petals one after the other. More significant for science are the spiral patterns made by the florets in the head (capitulum) of the daisy, or the patterns made by the scales of pine cones. These were observed by naturalists, and a new field of research was born in the XlXth century under the name "phyllotaxis" (the arrangements of leaves on stems). Daisies and sunflowers are the emblems of phyllotaxis: all the problems of phyllotaxis seem to be summarized therein. The presence of particular numbers (e.g. Fibonacci numbers, an angle of 137.5°, the golden number r = (-^5 + l)/2 « 1.618), and forms (e.g. logarithmic spirals) in their capituli, and in shoot apices, demands an explanation, and has served as a spur to the human intellect.Phyllotaxis is devoted to the description, characterization and generation of the patterns made by similar elements (e.g. scales, florets) on plants and inside their buds, and to the study of regularities and irregularities in the growth processes leading to their formation. It is in phyllotaxis that symmetry in plants is most striking and puzzling.The collective book Symmetry in Plants aims at a better understanding of the phenomenon of phyllotaxis. It deals with biological, mathematical, descriptive, causal and systemic phyllotaxis. It aims at reflecting the widest possible range of ideas and researches closely related to phyllotaxis, so as to represent the pulse of those who are devoting their time and reflection to a science in the making.The book has three parts of equal importance. They deal with data collecting and pattern recognition (Part I), with pattern generation (Part II), and with the problem of origins of phyllotactic patterns (Part III). The chapters have been distributed in these three categories, and then put in alphabetical order of authors' names. The Authors and the ReadersThe presence of four prologues -by a mathematician, a botanist, a crystallographer and a molecular geneticist, show the necessity of a great variety of expertise to deal adequately with phyllotaxis. Phyllotaxis is at the intersection of many different lines of research. Symmetry in Plants is of interest to pure and applied mathematicians, engineers, physicists, crystallographers, chemists, and biologists (especially botanists), to name a few.The book offers a dialogue between data collectors and model builders. Data and modelling are two essential ingredients, of equal importance, in our quest for understanding in phyllotaxis. There is a spiralling movement going from one to the other. From available data, models are built, deductions are made and compared to data, hypotheses ar...

Functional approach to high-throughput plant growth analysis

“…The results shown in Figure 7a reveals that our leaf orientation based method is better (with shorter distance to actual plant center) than the center of mass approach (p-value 0.18 with a two-tailed t-test with unequal variance [34]). The p-value is insignificant because of the symmetry of plants [22]. Nevertheless, our approach provides practically more precise plant centers.…”

Shape Limit in Triangular Spiral Tilings

“…Phyllotaxis [1] is an interdisciplinary subject related to physics, biology, and mathematics [2,3], where the golden section τ = (1 + √ 5)/2, the Fibonacci numbers, and continued fraction expansions play important roles [4,5]. In [6], a quasi-crystalline structure is observed in a circular defect line in the parastichy transition of spiral phyllotaxis.…”

Application of Two Mathematical Models to the Araceae, a Family of Plants with Enigmatic Phyllotaxis

“…This underlines too the rewarding advantage of multidisciplinary exchanges (e.g. the collective book by Jean and Barabe , 1998a), here between theoretical and empirical biology.…”