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.