L-System Language Syntax
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The L-System language is used to produce L-System Fractals. The L-System language supported by the Fractal Science Kit fractal generator is adopted from the Fractint syntax described in the Fractint L-System Documentation and the Fractint L-Systems Tutorial by William McWorter. There are many example L-System files available on the Internet (see below).
The following is a brief description of the syntax. Please see the above references for detailed information.
An L-System program has the following syntax:
<TITLE> {
<INSTRUCTIONS>
}
<TITLE> is the name of the L-System and <INSTRUCTIONS> are L-System statements.
The different L-System statements are given by:
Angle={COUNT} : set angle used by '+' and '-' below to
360/{COUNT}
Angle {COUNT} : set angle used by '+' and '-' below to 360/{COUNT}
Axiom={COMMANDS} : set starting set of commands to {COMMANDS}
Axiom {COMMANDS} : set starting set of commands to {COMMANDS}
{COUNT}+ : turn left {COUNT} times. if {COUNT} is omitted, use 1
{COUNT}- : turn right {COUNT} times. if {COUNT} is omitted, use 1
| : turn 180 degrees or
the largest possible turn < 180 degrees
f : draw a line using the
current direction/length
g : move forward instead
of drawing
\{ANGLE} : turn left {ANGLE} degrees
/{ANGLE} : turn right {ANGLE} degrees
d : draw a line using the
current direction/length
m : move forward instead
of drawing
[ : save state (position,
angle, size, etc.)
] : restore state
! : reverse the meaning of
'+' and '-' and '\' and '/'
@{SCALE} : multiply the current line length by {SCALE}
@q{SCALE} : multiply the line length by the square root of {SCALE}
@I{SCALE} : multiply the line length by the reciprocal of {SCALE}
c{INDEX} : set color map index to {INDEX}
<{COUNT} : increment color map index by {COUNT}
>{COUNT} : decrement color map index by {COUNT}
{LETTER}={COMMANDS} : associate {COMMANDS} with character {LETTER}
Please note the following:
-
Character case is ignored so F is the same as f.
-
In any given L-System program you should use either the relative commands (+, -, f, g) or the absolute commands (\, /, d, m), but not both. The | command applies only to angle associated with the relative commands.
-
Spaces may be used between commands but not between commands and their arguments.
-
All text to the right of a semi-colon (;) character is ignored and can be used to comment code.
-
Do not use { or } characters within comments as this will confuse the compiler.
Example:
Hilbert { ; The Science of Fractal Images, page 278
angle 4
axiom X
X=-YF+XFX+FY-
Y=+XF-YFY-FX+
}
The above L-System program generates the Hilbert Curve.
For additional details on L-System fractals see the following:
Eric W. Weisstein. "Lindenmayer System."
From MathWorld--A Wolfram Web Resource.
"L-System."
From Wikipedia, the free encyclopedia.
Fractint L-System Documentation.
Fractint L-System Tutorial by William McWorter.
Fractint L-System Space-filling Curves Tutorial by William McWorter.
The Science of Fractal Images
M.F. Barnsley, R.L. Devaney, B.B. Mandelbrot, H.-O. Peitgen, D. Saupe, R.F. Voss
with contributions by Y. Fisher, M. McGuire
Appendix C: A unified approach to fractal curves and plants
For many L-System examples that can be used with the Fractal Science Kit see:
Fractint L-System Tutorial by William McWorter.
Fractint L-System Space-filling Curves Tutorial by William McWorter.
Charlie Chernohorsky's FractInt@oblivion site.