Information Technology Reference
In-Depth Information
The strings generated by L-systems are
translated
into forms, according to the
turtle interpretation
, where symbols are associated to
segments
, and other
control
symbols are used, say
. In this case, a symbol
F
stands for a segment hav-
ing a given initial length and angle
+
,−,
[
,
]
0
. The turtle encoding of strings is obtained
by translating symbols into movements of a point (the turtle) that can draw while
it moves. When an L-rewriting is applied, the segment of given length
l
, associated
to the symbol
F
, is replaced by a poly-segment of sub-segments of length
l
α
k
.The
fractal dimension of a rule is given by log
k
n
where
n
is the number of sub-segments
of the poly-segment replacing the original segment. This means that, at each rewrit-
ing of the rule, the segment associated to symbol
F
is resized by the factor 1
/
/
k
.
The symbols
+
and
−
stand for a positive or negative deviations of some prefixed
angle
. Brackets represent mechanisms of internal rewriting. In fact, when an open
bracket appears, a form is generated which encodes the string between the open and
closed brackets. After that, the turtle goes back to the same position and angle it had
before the open bracket. In other words, we can assume that during its movement
the turtle can move and draw or can only move (movement without drawing could
be denoted by putting a special symbol
F
). With these assumptions, a string within
brackets encodes the generation of a curve such that, after its generation, the turtle
moves back along this curve with the inverse movement it performed in its genera-
tion, but without drawing (all its symbols
F
become
F
). In Figs. 2.41, 2.43, and 2.44
forms generated by L systems are expressed by means of the turtle interpretation.
δ
Fig. 2.41
Example of forms generated by L systems
