Special Models for Animation - Computer Animation: Algorithms and Techniques - page 377

FAF

F[FBF]F

F[F[FFF]F]F

FIGURE 12.15
Sequence of strings produced by bracketed L-system.

Not only does this representation admit database amplification [ 19 ] , but the expansion of the start
symbol into a terminal string parallels the topological growth process of the plants. In some sense, the
sequence of strings that progress to the final string of all turtle graphic symbols represents the growth of
the plant at discrete events in its evolution (see Figure 12.15 ). This addresses one of the animation
issues with respect to plants—that of animating the development of the branching structure. However,
the gradual appearance and subsequent elongation of elements must also be addressed if a growing
structure is to be animated in a reasonable manner.

Stochastic L-systems
The previous section introduced nondeterminism into the concept of L-systems, but the method used to
select the possible applicable productions for a given symbol was not addressed. Stochastic L-systems
assign a user-specified probability to each production so that the probabilities assigned to productions
with the same left-hand side sum to one. These probabilities indicate how likely it is that the production
will be applied to the symbol on a symbol-by-symbol basis.
Consider the productions of Figure 12.13 being assigned the probabilities shown in Figure 12.16 .
These probabilities will control how likely a production will be to form a branch at each possible
branching point. In this example, left branches are very likely to form, while right branches are some-
what unlikely. However, any arbitrarily complex branching structure has a non-zero probability of
occurring. Using such stochastic (nondeterministic) L-systems, one can set up an L-system that pro-
duces a wide variety of branching structures that still exhibit some family-like similarity [ 16 ] .

S 1.0 ⇒ FAF

A 0.8 ⇒ [ FBF]
A 0.2 ⇒ F
B 0.4 ⇒

[ FBF]

B 0.6 ⇒ F

FIGURE 12.16
Stochastic L-system.