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Phyllotaxis, the study of the patterns exhibited by leaves and other organs of plants, raises some of the deepest questions of plant morphogenesis. What principles of biological organisation produce these dynamical geometric systems? The constant occurrence of the Fibonacci sequence in such systems is a phenomenon that has fascinated botanists and mathematicians for centuries. In this book, first published in 1994, the many facets of phyllotaxis are dealt with in an integrated manner for the first time. The author describes a unified concept of phyllotaxis based on experimental, anatomical, cellular, physiological and paleontological observations. The book provides a framework for formal analyses of botanical data and emphasises the relevance of the phyllotactic paradigm in the study of other structures, such as crystals and proteins. It is of interest to cystallographers and physicists as well as to botanists and mathematicians.

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...

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