Prusinkiewicz, Lindenmayer - The algorithmic beauty of plants.pdf - fraktale, chaos deterministyczny - dt71

Aristid Lindenmayer 1925–1989

Przemyslaw Prusinkiewicz

Aristid Lindenmayer

The Algorithmic Beauty

of Plants

With

James S. Hanan

F. David Fracchia

Deborah Fowler

MartinJ.M.deBoer

Lynn Mercer

With 150 Illustrations, 48 in Color

This edition of The Alogirthmic Beauty of Plants is the electronic version

of the book that was published by Springer-Verlag, New York, in 1990 and

reprinted in 1996. The electronic version has been produced using the orig-

inal L A T E X ﬁles and digital illustrations.

2004 Przemyslaw Prusinkiewicz

Front cover design: The roses in the foreground ( Roses by D. R. Fowler,

J. Hanan and P. Prusinkiewicz [1990]) were modeled using L-systems. Dis-

tributed ray-tracing with one extended light source was used to simulate

depth of ﬁeld. The roses were placed on a background image (photgraphy

by G. Rossbach), which was scanned digitally and post-processed.

Preface

The beauty of plants has attracted the attention of mathematicians for Mathematics

and beauty

centuries. Conspicuous geometric features such as the bilateral sym-

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

form

By emphasizing the relationship between growth and form, this book

follows a long tradition in biology. D’Arcy Thompson [143] traces its

origins to the late seventeenth century, and comments:

Organic form itself is found, mathematically speaking, to be

a function of time.... We might call the form of an organism

an event in space-time , and not merely a conﬁguration in

space .

This concept is echoed by Halle, Oldeman and Tomlinson [58]:

The idea of the form implicitly contains also the history of

such a form.

Prusinkiewicz, Lindenmayer - The algorithmic beauty of plants.pdf

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