Prusinkiewicz Przemyslaw, Lindenmayer Aristid. The Algorithmic Beauty of Plants

Springer, 2004. — 228 p.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.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 original LATEX files and digital illustrations.Front cover design: The roses in the foreground (Roses by D. R. Fowler, J. Hanan and P. Prusinkiewicz [1990]) were modeled using L-systems. Distributed 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.Graphical modeling using L-systems
Modeling of trees
Developmental models of herbaceous plants
Phyllotaxis
Models of plant organs
Animation of plant development
Modeling of cellular layers
Fractal properties of plants
Epilogue
Appendix A Software environment for plant modeling
Appendix B About the figures
Appendix C Turtle interpretation of symbols