Lindenmayer Systems, Fractals, and Plants

1-systems are a mathematical formalism which was proposed by Aristid 1indenmayer in 1968 as a foundation for an axiomatic theory of develop- ment.

The notion promptly attracted the attention of computer scientists, who investigated 1-systems from the viewpoint of formal language theory.

This theoretical line of research was pursued very actively in the seventies, resulting in over one thousand publications.

A different research direction was taken in 1984 by Alvy Ray Smith, who proposed 1-systems as a tool for synthesizing realistic images of plants and pointed out the relationship between 1-systems and the concept of fractals introduced by Benoit Mandel- brot.

The work by Smith inspired our studies of the application of 1-systems to computer graphics. Originally, we were interested in two problems: * Can 1-systems be used as a realistic model of plant species found in nature? * Can 1-systems be applied to generate images of a wide class of fractals?

It turned out that both questions had affirmative answers.

Subsequently we found that 1-systems could be applied to other areas, such as the generation of tilings, reproduction of a geometric art form from East India, and synthesis of musical scores based on an interpretation of fractals.

This book collects our results related to the graphical applications of- systems.

It is a corrected version of the notes which we prepared for the ACM SIGGRAPH '88 course on fractals.