Double Helix of Phyllotaxis

Analysis of the Geometric Model of Plant Morphogenesis

by Boris Rozin


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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.


See related article by author, Progress in Biophysics and Molecular Biology. (Volume 182, September 2023, Pages 8-14.)

See review in Plant Science Bulletin by Richard Lis, (Spring 2022, Vol. 68, No. 1, pg 88.)

See review in International Society of Plant Morphologists by Karl J. Niklas, 71(1&2) page 67, 2021.

See full review in Systematic Botanye by Khalil Al Said (46 (4), p. 1141, 2021.

A new theoretical model of phyllotactic patterns is presented in this book, based on the geometry of two oppositely twisted spirals or helices. Many of the models previously proposed to explain observations of phyllotactic patterns are thus explained mathematically. The book is abundantly illustrated with computer graphics and supplemented by hyperlinks to many more images and video animations avaiable online, showing the way phyllotactic patterns vary with growth and change in the geometry of the plant axis.
See full review in Botanical Taxonomy and Geobotany by Simon Joseph Mayo (16 August 2021)

See full review in the Journal of the Botanical Research Institute of Texas by Rick L. Hammer, 15(2) page 582, 2021

See review in the University of Chicago Press Journal The Quarterly Review of Biology by Johan Gielis, Volume 96, Number 2, June 2021

About the Author

Boris Rozin was born in Kiev, Ukraine. In 1981, he graduated from the math and physics High School #145 in Kiev and could not enter the top universities in Moscow and Kiev due to governmental anti-Semitism in the USSR. In 1989, he graduated with an Honors degree from the National Vinnitsa Technical University in Ukraine with a masterís degree in Computer Science and Engineering. Immediately after graduation, he started working as a full-time assistant professor at the Department of Applied Mathematics and Computer Science of the National Vinnitsa Technical University. He taught: Applied Theory of Digital Devices, mathematical Modeling, Discrete Mathematics and Graph Theory. Along with teaching, he studied in the PhD program, but due to anti-Semitism, the university administration put obstacles in the way of getting the degree.YouTube channel Double Helix of Phyllotaxis