The Algorithmic Beauty of Plants

This book explores mathematical models of developmental processes and structures of plants, and illustrates them using state-of-the-art computer-generated images. Plant models which grow, interact with the environment, produce flowers and fruits, and finally die, have an immense intuitive appeal of "bringing life into the computer". In front of a graphics monitor it is easy to forget the underlying mathematical formulae and simply look at plants growing, self-replicating, responding to external factors, even mutating. Without compromising the mathematical rigor of presentation the authors have tried to preserve this area in their research. The following areas receive particular attention: methods for the modelling and rendering of plants which are suitable for realistic image synthesis; the scientific potential of computer graphics in the visualization of biological structures and processes; the relationship between control mechanisms employed by living plants and the resulting complex developmental sequences and structures; and the relationship between developmental processes, self-similarity and fractals.
The formalism of L-systems are adopted as the primary mathematical vehicle used to express developmental processes. The notion of L-systems was conceived in 1968 by Aristid Lindenmayer as a formal model of plant development. Its elegance was promptly recognized by mathematicians, who soon developed a comprehensive theory of L-systems. However, only recently has computer graphics revealed the full potential of L-systems applied to plant modeling. Although the focus is on the results of joint research led by the authors, a survey of alternative methods for plant modelling is also included.