Phyllotaxis Models
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| Author | : Jean-Paul Walch |
| Publisher | : John Wiley & Sons |
| Total Pages | : 228 |
| Release | : 2023-07-13 |
| Genre | : Science |
| ISBN | : 1394228120 |
The equations of phyllotaxis were discovered by Douady and Couder: these describe the inhibition "force" generated by an incipient primordium, preventing the initiation of other primordia in its vicinity: the method that was lacking was to take into account the distance of primordia to the meristem apex over the course of its development. With these parameters, our model integrates both biochemical "forces" (inhibition due to auxin) and mechanical forces (contact pressure). This powerful tool allows us to revisit many important notions of plant biology. For example, we model auxin concentrations at the plant apex, as well as the development of vegetative and reproductive meristems. We also explain why the whorls of monocots are trimerous and those of plants with quincuncial perianths are pentamerous. We design a geometric method for reconstructing inflorescences from their building blocks, i.e. floral meristems. We also show that phyllotaxic spirals are only the application of a general property of symmetry, the advantages of which have been exploited by natural selection.
| Author | : Boris Rozin |
| Publisher | : BrownWalker Press |
| Total Pages | : 186 |
| Release | : 2020-08-01 |
| Genre | : Science |
| ISBN | : 1627347488 |
This book is devoted to anyone who is in search of beauty in mathematics, and mathematics in the beauty around us. Attempting to combine mathematical rigor and magnificence of the visual perception, the author is presenting the mathematical study of phyllotaxis, the most beautiful phenomenon of the living nature. The distinctive feature of this book is an animation feature that explains the work of mathematical models and the transformation of 3D space. The analysis of the phyllotactic pattern as a system of discrete objects together with the mathematical tools of generalized sequences made it possible to find a universal algorithm for calculating the divergence angle. In addition, it is serving as a new proof of the fundamental theorem of phyllotaxis and analytically confirming well-known formulas obtained intuitively earlier as well as casting some doubts on a few stereotypes existing in mathematical phyllotaxis. The presentation of phyllotaxis morphogenesis as a recursive process allowed the author to formulate the hydraulic model of phyllotaxis morphogenesis and propose a method for its experimental verification. With the help of artificial intelligence, the author offered methodology for the digital measurement of phyllotaxis allowing a transition to a qualitatively new level in the study of plant morphogenesis. Due to the successful combination of mathematical constructions and their visual presentation, the materials of this study are comprehensible to readers with high school advanced mathematical levels.
| Author | : Denis Barabe |
| Publisher | : World Scientific |
| Total Pages | : 298 |
| Release | : 2020-04-22 |
| Genre | : Science |
| ISBN | : 9811211027 |
The book provides a current review of the field of phyllotaxis from a variety of perspectives, that is, morphological, developmental, biochemical, molecular genetics, biophysical, and evolutionary.This unique book covers phyllotactic processes from the level of genes involved in the establishment of patterns to modeling the emergence of those patterns in space and time. The models in question (deterministic or stochastic) touch on various fields, including geometry, biochemistry, and biophysics.Not only providing a recent review but also current critique and analysis of the discipline, the book will appeal to a variety of individuals involved in developmental modeling as well as pattern initiation and formation. The text is highly illustrated with excellent pictures representing recent developments in the field.A biological context or perspective to models and ideas is explored in the book. Terminology specific to the discipline is defined and updated as well.
| Author | : Jean-Paul Walch |
| Publisher | : John Wiley & Sons |
| Total Pages | : 260 |
| Release | : 2024-07-24 |
| Genre | : Science |
| ISBN | : 1394306342 |
Symmetry and the causes of shifts in different types of symmetries in flowers follow specific patterns that are ruled by developmental and genetic factors. Using a unified system of phyllotaxic equations, we have modeled the molecular mechanisms and pressure forces that act in inflorescence and floral meristems, giving flowers their organ arrangement. In this book, we state general physical principles, whereby the symmetry of the perianth is derived from the symmetry of certain TCP gene expression. Thus, we define the interplay between the expression of CYC2-like genes and the phyllotactic mechanisms. This new evo-devo approach is applied to major groups of angiosperms with predominantly actinomorphic flowers (in which rare zygomorphy is positional) and groups with mainly bilaterally symmetrical flowers (in which zygomorphy is constitutional). It has thus allowed us to revisit the contributions of the great floral morphologists of the 20th and early 21st centuries.
| Author | : Roger V. Jean |
| Publisher | : Cambridge University Press |
| Total Pages | : 404 |
| Release | : 2009-03-19 |
| Genre | : Mathematics |
| ISBN | : 9780521104692 |
In this book, the many facets of phyllotaxis are dealt with in an integrated manner. The author describes a unified concept of phyllotaxis, and presents a mathematical model of plant growth based on experimental, anatomical, cellular, physiological, and paleontological observations. The model not only provides a framework for formal analyses of botanical data, but also emphasizes the relevance of phyllotaxis to other structures, such as crystals, and proteins.
| Author | : Xavier J.R. Avula |
| Publisher | : Elsevier |
| Total Pages | : 1023 |
| Release | : 2014-05-09 |
| Genre | : Mathematics |
| ISBN | : 1483190595 |
Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.
| Author | : Roger V. Jean |
| Publisher | : World Scientific |
| Total Pages | : 900 |
| Release | : 1998 |
| Genre | : Science |
| ISBN | : 9789810226213 |
The book deals with biological, mathematical, descriptive, causal and systemic phyllotaxis. It aims at reflecting the widest possible range of ideas and research closely related to phyllotaxis and contains 30 well illustrated chapters.The book has three parts of equal importance. The first two parts concern data collecting, pattern recognition and pattern generation to which students of phyllotaxis are well accustomed. The third part is devoted to the problem of origins of phyllotactic patterns, giving the field of phyllotaxis the universality it requires to be fully understood.Phyllotaxis-like patterns are found in places where genes are not necessarily present. Part III concerns general comparative morphology, homologies with phyllotactic patterns, and recent trends on evolution that can help to understand phyllotaxis.The distinguished researchers who accepted to participate in the production of this book, strongly contributed to the field of phyllotaxis in the past and have devoted a lot of their time to the fascinating subject coming up with most valuable findings, or are newcomers with original ideas that may be very relevant for the future of the field. The book summarizes and updates their contributions, and promotes new avenues in the treatment of phyllotaxis.This book on mathematical and biological phyllotaxis is the first collective book ever. A landmark in the history of phyllotaxis.
| Author | : Michael T. McManus |
| Publisher | : CRC Press |
| Total Pages | : 328 |
| Release | : 2002 |
| Genre | : Nature |
| ISBN | : 9780849397929 |
This book presents an overview of the role of meristematic tissues in plant growth and development, with an emphasis on advances of the last decade. It examines meristematic tissues as a defined, independent tissue type in plants and gives consideration to their origin, maintenance, and function. The editors pay particular attention to the molecular mechanisms underlying meristem formation and maintenance. This volume is a tremendously valuable resource for plant geneticists, developmental biologists, and molecular biologists.
| Author | : Istv n Hargittai |
| Publisher | : World Scientific |
| Total Pages | : 594 |
| Release | : 1992 |
| Genre | : Science |
| ISBN | : 9789810206000 |
Fivefold symmetry is common in flowers, fruits, molecules, logos, and buildings, but it is a forbidden symmetry in the world of crystals. A few years ago, the so-called quasicrystals were discovered displaying fivefold symmetry, and it caused a minirevolution in crystallography. There has been increased awareness of fivefold symmetry in all domains of human interest ever since. The present book brings together authors and ideas on a common theme from mathematics, the sciences, design, and anthropology to history, literature, and the arts. Its 29 chapters are an offering by scientists and humanists from 13 countries to a broad readership of professionals and laypersons about fivefold symmetry and the areas that are being bridged by this unique concept.
| Author | : Przemyslaw Prusinkiewicz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 235 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 1461384761 |
Now available in an affordable softcover edition, this classic in Springer's acclaimed Virtual Laboratory series is the first comprehensive account of the computer simulation of plant development. 150 illustrations, one third of them in colour, vividly demonstrate the spectacular results of the algorithms used to model plant shapes and developmental processes. The latest in computer-generated images allow us to look at plants growing, self-replicating, responding to external factors and even mutating, without becoming entangled in the underlying mathematical formulae involved. The authors place particular emphasis on Lindenmayer systems - a notion conceived by one of the authors, Aristid Lindenmayer, and internationally recognised for its exceptional elegance in modelling biological phenomena. Nonetheless, the two authors take great care to present a survey of alternative methods for plant modelling.
