Ebook: The Algorithmic Beauty of Plants

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 growth processes 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.

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This book is the first comprehensive volume on the computer simulation of plant development. It contains a full account of the algorithms used to model plant shapes and developmental processes, Lindenmayer systems in particular. With nearly 50 color plates, the spectacular results of the modelling are vividly illustrated. "This marvelous book will occupy an important place in the scientific literature." #Professor Heinz-Otto Peitgen# "The Algorithmic Beauty of Plants will perform a valuable service by popularizing this enlightening and bewitching form of mathematics." #Steven Levy# " ... the garden here is full of delights and an excellent introduction to L-systems, ..." #Alvy Ray Smith, IEEE Computer Graphics and its Applications#

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This book is the first comprehensive volume on the computer simulation of plant development. It contains a full account of the algorithms used to model plant shapes and developmental processes, Lindenmayer systems in particular. With nearly 50 color plates, the spectacular results of the modelling are vividly illustrated. "This marvelous book will occupy an important place in the scientific literature." #Professor Heinz-Otto Peitgen# "The Algorithmic Beauty of Plants will perform a valuable service by popularizing this enlightening and bewitching form of mathematics." #Steven Levy# " ... the garden here is full of delights and an excellent introduction to L-systems, ..." #Alvy Ray Smith, IEEE Computer Graphics and its Applications#
Content:
Front Matter....Pages i-xii
Graphical modeling using L-systems....Pages 1-50
Modeling of trees....Pages 51-62
Developmental models of herbaceous plants....Pages 63-97
Phyllotaxis....Pages 99-118
Models of plant organs....Pages 119-131
Animation of plant development....Pages 133-144
Modeling of cellular layers....Pages 145-174
Fractal properties of plants....Pages 175-189
Epilogue....Pages 190-191
Back Matter....Pages 193-228

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This book is the first comprehensive volume on the computer simulation of plant development. It contains a full account of the algorithms used to model plant shapes and developmental processes, Lindenmayer systems in particular. With nearly 50 color plates, the spectacular results of the modelling are vividly illustrated. "This marvelous book will occupy an important place in the scientific literature." #Professor Heinz-Otto Peitgen# "The Algorithmic Beauty of Plants will perform a valuable service by popularizing this enlightening and bewitching form of mathematics." #Steven Levy# " ... the garden here is full of delights and an excellent introduction to L-systems, ..." #Alvy Ray Smith, IEEE Computer Graphics and its Applications#
Content:
Front Matter....Pages i-xii
Graphical modeling using L-systems....Pages 1-50
Modeling of trees....Pages 51-62
Developmental models of herbaceous plants....Pages 63-97
Phyllotaxis....Pages 99-118
Models of plant organs....Pages 119-131
Animation of plant development....Pages 133-144
Modeling of cellular layers....Pages 145-174
Fractal properties of plants....Pages 175-189
Epilogue....Pages 190-191
Back Matter....Pages 193-228
....