The Mathematics Of Form And Pattern Applied To Plant Phyllotaxis
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The Mathematics Of Form And Pattern Applied To Plant Phyllotaxis
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Author : James Charles Strickland
language : en
Publisher:
Release Date : 1997
The Mathematics Of Form And Pattern Applied To Plant Phyllotaxis written by James Charles Strickland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Phyllotaxis categories.
Double Helix Of Phyllotaxis
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Author : Boris Rozin
language : en
Publisher: BrownWalker Press
Release Date : 2020-08-01
Double Helix Of Phyllotaxis written by Boris Rozin and has been published by BrownWalker Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-01 with Science categories.
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.
Phyllotactic Patterns A Multidisciplinary Approach
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Author : Denis Barabe
language : en
Publisher: World Scientific
Release Date : 2020-04-22
Phyllotactic Patterns A Multidisciplinary Approach written by Denis Barabe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Science categories.
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.
Do Plants Know Math
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Author : Stéphane Douady
language : en
Publisher: Princeton University Press
Release Date : 2024-09-10
Do Plants Know Math written by Stéphane Douady and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-10 with Mathematics categories.
A breathtakingly illustrated look at botanical spirals and the scientists who puzzled over them Charles Darwin was driven to distraction by plant spirals, growing so exasperated that he once begged a friend to explain the mystery “if you wish to save me from a miserable death.” The legendary naturalist was hardly alone in feeling tormented by these patterns. Plant spirals captured the gaze of Leonardo da Vinci and became Alan Turing’s final obsession. This book tells the stories of the physicists, mathematicians, and biologists who found themselves magnetically drawn to Fibonacci spirals in plants, seeking an answer to why these beautiful and seductive patterns occur in botanical forms as diverse as pine cones, cabbages, and sunflowers. Do Plants Know Math? takes you down through the centuries to explore how great minds have been captivated and mystified by Fibonacci patterns in nature. It presents a powerful new geometrical solution, little known outside of scientific circles, that sheds light on why regular and irregular spiral patterns occur. Along the way, the book discusses related plant geometries such as fractals and the fascinating way that leaves are folded inside of buds. Your neurons will crackle as you begin to see the connections. This book will inspire you to look at botanical patterns—and the natural world itself—with new eyes. Featuring hundreds of gorgeous color images, Do Plants Know Math? includes a dozen creative hands-on activities and even spiral-plant recipes, encouraging readers to explore and celebrate these beguiling patterns for themselves.
The Algorithmic Beauty Of Plants
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Author : Przemyslaw Prusinkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Algorithmic Beauty Of Plants written by Przemyslaw Prusinkiewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
The beauty of plants has attracted the attention of mathematicians for Mathematics centuries. Conspicuous geometric features such as the bilateral sym and beauty metry of leaves, the rotational symmetry of flowers, and the helical arrangements of scales in pine cones have been studied most exten sively. This focus is reflected in a quotation from Weyl [159, page 3], "Beauty is bound up with symmetry. " This book explores two other factors that organize plant structures and therefore contribute to their beauty. The first is the elegance and relative simplicity of developmental algorithms, that is, the rules which describe plant development in time. The second is self-similarity, char acterized by Mandelbrot [95, page 34] as follows: When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar. This corresponds with the biological phenomenon described by Herman, Lindenmayer and Rozenberg [61]: In many growthprocesses of living organisms, especially of plants, regularly repeated appearances of certain multicel lular structures are readily noticeable. . . . In the case of a compound leaf, for instance, some of the lobes (or leaflets), which are parts of a leaf at an advanced stage, have the same shape as the whole leaf has at an earlier stage. Thus, self-similarity in plants is a result of developmental processes. Growth and By emphasizing the relationship between growth and form, this book form follows a long tradition in biology.
Mathematical Approach To Pattern And Form In Plant Growth
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Author : Roger V. Jean
language : en
Publisher: Wiley-Interscience
Release Date : 1984
Mathematical Approach To Pattern And Form In Plant Growth written by Roger V. Jean and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Science categories.
Applied Mathematical Ecology
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Author : Simon A. Levin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied Mathematical Ecology written by Simon A. Levin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The Second Autumn Course on Mathematical Ecology was held at the Intern ational Centre for Theoretical Physics in Trieste, Italy in November and December of 1986. During the four year period that had elapsed since the First Autumn Course on Mathematical Ecology, sufficient progress had been made in applied mathemat ical ecology to merit tilting the balance maintained between theoretical aspects and applications in the 1982 Course toward applications. The course format, while similar to that of the first Autumn Course on Mathematical Ecology, consequently focused upon applications of mathematical ecology. Current areas of application are almost as diverse as the spectrum covered by ecology. The topiys of this book reflect this diversity and were chosen because of perceived interest and utility to developing countries. Topical lectures began with foundational material mostly derived from Math ematical Ecology: An Introduction (a compilation of the lectures of the 1982 course published by Springer-Verlag in this series, Volume 17) and, when possible, progressed to the frontiers of research. In addition to the course lectures, workshops were arranged for small groups to supplement and enhance the learning experience. Other perspectives were provided through presentations by course participants and speakers at the associated Research Conference. Many of the research papers are in a companion volume, Mathematical Ecology: Proceedings Trieste 1986, published by World Scientific Press in 1988. This book is structured primarily by application area. Part II provides an introduction to mathematical and statistical applications in resource management.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 2005
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Dissertations, Academic categories.
Essays On Form In Plants
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Author : C. W. Wardlaw
language : en
Publisher: Manchester University Press
Release Date : 1968
Essays On Form In Plants written by C. W. Wardlaw and has been published by Manchester University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Botany categories.
Mathematical Models In Biology
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Author : Leah Edelstein-Keshet
language : en
Publisher: SIAM
Release Date : 1988-01-01
Mathematical Models In Biology written by Leah Edelstein-Keshet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.