Introduction to the Modeling of Plants and Flowers Using String Rewriting Anne M. Burns, Long Island University Introduction In 1984, Alvy Ray Smith (Smith, 1994) presented a method of modeling plants and flowers using parallel graph grammars, called L-grammars or L-systems, after lAndenmayer (Lindenmayer, 1968). This technique is based on the definition of a grammar consisting of a set of productions, or string rewriting rules. For a brief introduction to this topic, see for example (Foley, 1990). Through the use of examples and exercises this software presents an introduction and sampling of topics from string rewriting and related topics, based on this modeling of plants and flowers using L-Systems. My intent is to show that mathenaatics, science and art are interrelated subjects, and to stimulate a greater interest in ntathematics in young people by showing some applications to nontraditional areas through the use of computer graphics. The possible audience for this software includes the following: • * . , , Students ill computer graphics courses Instructors and students in college math I, a survey ntath course i"or liberal arts students or art students Biology students who might be interested in the concept of a ntathematical model for plant growth htstructors and students in computer science who are interested in interesting applications of certain data structures Gifted high school students who should be introduced to areas of research in mathematics, computer science and biology, of which they are lnOSt likely not aware H a r d w a r e requirenlents The program requires all IBM PC or compatible with 640 Kb RAM, a VGA card and DOS 3.3 or higher. The program is contained on one 3 1/2 inch high density diskette and performs better if copied to a hard disk, but a hard disk is not necessary. Description of the program There is no programming involved and the program is very easy to use. It runs fl'om a lnenn, and is started by typing the word "menu." The menu allows rite user to select an introduction to the program or one of 13 units. The introduction gives an overview of the proglam and contains a list of references for further study. Each of the 13 units begins with an explanation of its purpose and directions for using the unit. Some of the explanations contain terms that may be unfamiliar to the student, such as expected value, stack, linked list, etc. These terms have not been put there to scare the student, but are intended as suggestions to programnters. It is important to realize that knowledge of these terms is not necessary to the learning of the material; the paragraphs containing these ternts can be skipped over. The first four units are examples. The first unit contains four pictures which have been composed using string rewriting. The second unit illustrates the basic structure of each of the ntost common inflorescences, which is the general arrangement and disposition of the flowers on an axis. It then incorporates each inflorescence into a plant (most of the plants are hypothetical) which has been created using string rewriting, ht the third unit one particular inflorescence is singled out and the student can experiment with how it looks in the various stages of its development. The fourth unit shows how a computer graphics picture is "painted." h takes about seven minutes to run. The next five units are the actual lessons introducing the mathematics of string rewriting as it applies to the geometry of plants. In Lessons 2 through 5, it is suggested that the user print out the explanatory pages of those traits by holding down the Shift and PrintScreen keys while the page is displayed on the screen. (In Lesson 1 some of the explanations are done in graphics mode and cannot be printed out except on a graphics printer.) Also a pencil and paper are almost mandatory for those units, in these units the student can invent his or her own string rewriting systems and then visualize plants that con'espond to thent. Lesson 1 explains how strings of characters can be used to represent plants. This lesson defines a few basic terms used to describe tile parts of a plant and how they can be made to correspond to symbols in a string. It then provides exercises so the student can test his or her understanding. Lesson 2 explains how the string is generated from a single symbol using productions. The student may then define his or her own productions and visualize the results. These two units can be used by programmers or artists for the testing of productions. Lesson 3 is a brief introduction to paranaetric string rewriting and how it can be used to illustrate various stages in the growth of a flower. In lesson 4 after a very brief introduction to stochastic L-systems, the student can experinlent with the effects of assigning different probabilities to productions. Finally, Lesson 5 is another brief introduction, this time to a different approach, node rewriting. Again, after an explanation, the student can experiment with the assignment of probabilities and visualize the effects. The rest of the units are related topics that might be of interest in creating scenes. Unit 10 concerns phyllotaxis as it applies to the disk flowers on a sunflower. Units 11 and 12 both use an algorithm I call the midpoint method but with different results. After an explanation of how the midpoint method works, in 1 l the sin(lent can e x p e r i i n e n t with a variety of p a r a m e t e r s to create designs, some of which are reminiscent of Persian rugs, while in 12 the same prograln is used with a different assignment of colors and parameters to create the effect of clouds. The last unit allows the student to experiment with creating a VGA palette; it explains how to assign to the 16 color registers any one of 262,144 possible colors. The palette created may be saved to a file and retrieved at a later elate.

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