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With the rules described in previous sections, modeling of plants becomes possible. A variety of commercial software and shareware are currently available for performing simulations using L-systems. For example, lsys is a plant generation program developed from The Algorithmic Beauty of Plants [Prusinkiewicz and Lindenmayer, 1990]. The code lsys was written by Jonathan Leech in c++ language and runs on UNIX systems. It is a freeware and is available by anonymous ftp from ftp. es . une . edu. The source code can be found in pub/users/ j on/lsys . tar. gz. It is a software package designed for manipulating production L-systems. In addition to specifying the systems and applying production rules, it interprets the results graphically, producing Postscript output. A database containing the positions and widths of all branches generated by L-systems can be obtained by this tool. This software is capable of simulating various examples presented in The Algorithmic Beauty of Plants. In the following examples, we will demonstrate how to model plants by using this tool. lsys accepts a grammar describing OL-systems augmented by brackets, stochastically applied productions, context-sensitivity, and parameters. All these features may be freely combined. Legal input is broken down into several classes: comments, assertions, definitions, the initial string, and productions. Syntactic structures common to all classes of input are described first, then each class. Unless escaped with or as otherwise specified, newline terminates all classes of input. Blank lines and comments are allowed. Example 1: Generating tree-like structure. The input file is as follows.

START :

/ / / / / /

* * * * *

A gene for breast cancer was found in 1994, followed by the discovery of the gene for Parkinson s disease, giving the Human Genome Project yet another boost in both public pro le and government funding Despite the notable successes, progress on sequencing the genome was less than spectacular Even the consortium s initial plan to sequence the complete human genome by the year 2005 seemed overly optimistic Perceptions changed when Craig Venter and his private United States rm, Celera Genomic, buoyed by the prospect of pro ting from patenting millions of gene se quences, entered the race in the late 1990s Venter s rst major success, the rapid sequencing of the H In uenza virus with the aid of proprietary computer methods, took most of the research community by surprise.

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contraction ratio for the trunk * / contraction ratio for the branches * / branching angle from the trunk * / branching angle for lateral axes * / divergence angle * / width decrease rate * /

Figure 12 The time sheet class de nes the properties and methods for each object from the class The objects created from the time sheet class have values for the properties and can execute the methods

A(1,1O)

P1 : A(l, w) : * ----+ !(w)F(l)[&(ao)B(1 * T2, w * wr)]/(d)A(l * Tt, W * wr ) P2 : B(l,w) : * ----+ !(w)F(I)[-(a2)$C(l * T2,W * wr)]C(1 * T1,W * w r ) P3 : C(l, w) : * ----+ !(w)F(I)[+(a2)ffiB(1 * T2, W * wr)]B(1 * Tl, W * wr)

In the definition section, maxgen specifies the maximum number of growth stage, rl for the contraction ratio of straight daughter branch, r2 for the contraction ratio of lateral daughter branch, W r for the width decrease rate, ao for the branching angle for branches arising from the trunk, a2 for the branching angle for branches not directly attached to the trunk, and the divergence angle d specifies the angle between two successive branch planes for branches corning off the trunk. A(1,10) is the axiom (initial string) which specifies a starting trunk with one unit of length and ten units of width. According to production PI, the apex of the main A produces an extension (internode F) of the trunk giving off a straight branch, and a lateral branch (apex B) in each derivation step. The application of rule PI decreases the length and width of the daughter segments by the factors r2 and W r , respectively. The subsequent development of lateral branches are described by rules P2 and P3. In each step, the straight apex, either B or C, issues a lateral apex of the next order at angle a2 or -a2 with respect to the mother axis. Two productions are employed to create lateral branches alternately to the left and right of the mother branch. Figure 13.2.1 shows the plant after 10 growth stages.

In Example 1, the parameters such as branching angles, divergence angles, and so on, are all fixed. All the plants generated using this input will be identical. In order to achieve randomization, we can apply random number generators in the growth process as shown below.

1

/ * contraction ratio for the trunk .* /

/ / / / /

* * *

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