Special Models for Animation - Computer Animation: Algorithms and Techniques - page 380

axiom: ( A ,0)

( A ,3) => ( S ,0) [ ( B ,0)] ( S ,0)
( B ,2)

=> ( S ,0)

FIGURE 12.20
Simple timed L-system.

difference between its terminal age and its local age. Each symbol appearing in a string has a local
age less than its terminal age. The geometric interpretation of each symbol is potentially based on
the local age of that symbol. Thus, the appearance of buds and stems can be modeled according to their
local age.
In the simple example of Figure 12.20 , the symbol A can be thought of as a plant seed; S can be
thought of as an internode stem segment; and B can be thought of as a bud that turns into the stem
of a branch. After three units of time the seed becomes a stem segment, a lateral bud, and another stem
segment. After two more time units, the bud develops into a branching stem segment.

Interacting with the environment
The environment can influence plant growth in many ways. There are local influences such as physical
obstacles, including other plants and parts of the plant itself. There are global influences such as amount
of sunlight, length of day, gravity, and wind. But even these global influences are felt locally. The wind
can be blocked from part of the plant, as can the sun. And even gravity can have more of an effect on an
unsupported limb than on a supported part of a vine. The nutrients and moisture in the soil affect
growth. These are transported throughout the plant, more or less effectively depending on local damage
to the plant structure.
Mech and Prusinkiewicz [ 11 ] describe a framework for the modeling and animation of plants that
bidirectionally interacts with the environment. They describe open L-systems , in which communication
terms of the form ? E ( x 1 , x 2 ,

, x m ) are used to transmit information as well as request information
from the environment. In turtle graphic interpretation of an L-system string, the string is scanned left to
right. As communication terms are encountered, information is transmitted between the environment
and the plant model. The exact form of the communication is defined in an auxiliary specification file
so that only relevant information is transmitted. Information about the environment relevant to the plant
model includes distribution of nutrients, direction of sunlight, and length of day. The state of the plant
model can be influenced as a result of this information and can be used to change the rate of elongation
as well as to control the creation of new offshoots. Information from the plant useful to the environ-
mental model includes use of nutrients and shade formation, which, in turn, can influence other plant
models in the environment.

...

12.2.4 Summary
L-systems, in all the variations, are an interesting and powerful modeling tool. Originally intended only
as a static modeling tool, L-systems can be used to model the time-varying behavior of plantlike growth
and motion. See Figure 12.21 (Color Plate 13) for an example from a video that used L-systems to
animate plantlike creatures. Because of the iterative nature of string development, the topological