LSYSTEM(1) LSYSTEM(1)
NAME
lsystem - L system fractal generator
SYNOPSIS
lsystem [options] [file]
DESCRIPTION
lsystem is a fractal generator is based on the scheme devised by
Aristid Lindenmayer (the L in Lsystem). It is a so-called string-
rewriting system, in which an input string is altered according to a
set of transform rules. The characters that make up the string, in
turn, can represent commands to a "turtle" which will draw the actual
fractal. More sophisticated Lsystem incarnations have been used to
create very lifelike renderings of plants (see "The Algorithmic Beauty
of Plants", written by Prusinkiewicz and Lindenmayer, published by
Springer Verlag).
Here's an example of a string-rewriting system. Consider the initial
condition: b And the rules are: a = ab b = a Here are the results of 5
passes through the string-rewriting engine: b (initial) a ab aba abaab
abaababa If "a" and "b" represented commands to a turtle-like drawing
routine, the output string "abaababa" could be fed to it, and it would
generate some type of figure.
OPTIONS
-o file
Write output to file.
-s Print string length info.
-v Print version info.
OPERATION
lsystem reads an L system description from the specified file and
writes drawing commands on the standard output (or a file, if
specified with the -o option). These drawing commands should be piped
through to convert them to the graphics driver of your choice.
The drawing commands are generated in two phases: the string-rewriting
phase, in which the initial string is iterated using a set of rules,
and the string-interpretation phase, where the iterated string is
passed to a `turtle' which substitutes macro definitions and executes
drawing commands.
INPUT FORMAT
The input to lsystem consists of an initialization statement and
several statements defining macros and rules. Blank lines are
ignored, and anything from a # to end-of-line is a comment. The
initialization statement has the format init <string> <iterations>
<angle> where <string> is the initial string to be iterated,
<iterations> is the number of iterations to perform, and <angle> is
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LSYSTEM(1) LSYSTEM(1)
the angle through which the turtle turns when given the appropriate
command. Strings in lsystem may consist of the letters A-Z (upper or
lower case), +, -, [ and ]. Several of these have special meanings to
the turtle, described later.
MACROS
Macros are useful to help simplify the design of fractals. They are
only used during the string-interpretation phase, when the turtle is
in operation. The format for defining a macro is <char> = <string>
When the turtle is drawing, each occurrence of <char> is replaced
(once only) by <string>.
RULES
Rules specify what replacements are done in the string in the
iteration phase. In each iteration, rules are applied to the string
in the order they were defined in the input. The format of a rule
definition is <char> -> <string> Each instance of <char> in the string
is replaced by <string>.
TURTLE COMMANDS
The turtle understands a limited set of commands. If it encounters a
foreign character, it simply ignores it. This can be useful for
building up complex strings.
F Move turtle forward one step. A line is drawn.
f Move turtle forward one step. No line is drawn.
+ Turn turtle clockwise by the angle increment.
- Turn turtle anticlockwise by the angle increment.
[ Stack turtle state. This includes position, heading and
current colour (see COLOURS, below).
] Unstack turtle state. The state is restored to the matching
[. No line is drawn if the turtle position changes.
COLOURS
You can change the colour of parts of the drawing (on those graphics
devices which support colour) by setting characters to different
colour values. In the string-interpretation phase, when the turtle
sees a character, the current colour is set to its corresponding
colour. If the character has no colour, no colour change is done.
The format of a colour command is col <char> <red> <green> <blue> This
sets <char> to have the specified RGB values. The RGB values are in
the range [0-1].
RESTRICTIONS
Complex rules and/or high iteration factors will take awhile to run
through the lsystem engine. The string may become larger than
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LSYSTEM(1) LSYSTEM(1)
available memory, too. Each pass through the lsystem engine can
produce an exponential increment in the length of the string, so ANY
amount of memory will be filled.
FILES
tab(@);
l l .
%%LIBDIR%%@Example L systems
HISTORY
This implementation of L systems is based on (and uses the same
examples from) an Atari ST version written by Mark Kimball (1991).
SEE ALSO
AUTHOR
Glenn Hutchings (zondo@hunting2.demon.co.uk)
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