## Phyllotaxis: A Systemic Study in Plant MorphogenesisPhyllotaxis, 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. |

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### Contents

Prologue | 1 |

Part I Pattern recognition | 9 |

a key to the puzzles | 123 |

Part III Origins of phyllotactic patterns | 207 |

Part IV Complements | 273 |

333 | |

372 | |

376 | |

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### Common terms and phrases

Adler’s algorithm allometry alternating whorls angle of intersection anomalous axis bijugate biological capitulum cells Chapter Church consecutive considered conspicuous pair conspicuous parastichy pair contact parastichy pair contact pressure continued fraction corresponding cylindrical lattice decussation deﬁned deﬁnition distichy divergence angle double nodes entropy Equation Erickson example Fibonacci angle Fibonacci numbers Fibonacci sequence ﬁeld ﬁgure ﬁrst ﬁve ﬂoret ﬂowers Fujita function genetic spiral given gives gnomonic golden ratio growth integer interpretative model interval L-systems logarithmic spiral Lucas sequence main sequence mathematical morphogenesis multijugate noble numbers normal phyllotaxis numbers observed obtained opposed parastichy pair organs orthogonal orthostichies parameters Pattern Determination Table phyl phyllo phyllotactic fraction phyllotactic patterns plants plastochrone ratio points primordia primordium problem Proposition representation rhythm Section shoot apex shows spiral patterns spiral systems stem structure sunﬂower symmetry theory tichy tion transitions trimery visible and opposed visible opposed pairs visible opposed parastichy Voronoi polygon whorls