L-system Explorer

L-system Explorer Features

An L-system is a method used to model growth processes. They are named after Aristid Lindenmayer, who was the first to use them to model the growth of plants.

L-systems consist of an axiom (a simple string like "f"), and a set of production rules (such as "f=f-f++f-f"), and also an alphabet of symbols which have some pre-defined meaning and interpretation. The axiom is recursively expanded a fixed number of times according to the rules, after which a long string is generated.

Using the example above, the expansions would be:

Axiom: f
Rules: f = f-f++f-f

Level 0: f
Level 1: f-f++f-f
Level 2: f-f++f-f-f-f++f-f++f-f++f-f-f-f++f-f
Level 3: f-f++f-f-f-f++f-f++f-f++f-f-f-f++f-f-f-f++f-f-f-f++f-f++f-f++f-f-f-f++f-f++f-f++f-f-f-f++f-f++f-f++f-f-f-f++f-f-f-f++f-f-f-f++f-f++f-f++f-f-f-f++f-f

This long string by itself is useless unless some meaning or interpretation is made of it's symbols.

Main window
When L-system Explorer starts up, a window will be displayed (which we shall refer to as the "main window"). On this main window there are two pull-down boxes at the top (labeled "Group" and "L-system"). The Group pull-down box selects which L-system group to use, and the L-system pull-down box selects which L-system to use within that L-system group.

Whenever a new L-system is selected, the following six fields on the main window are updated to reflect the properties of the selected L-system:

1. Axiom - The L-system axiom
2. Rules - A list of production rules.
3. Initial Angle - Which way to face, initially (0 is considered north, 90 east, 180 south, etc.).
4. Turn Angle - How far to turn when encountering a + or -
5. Level - Initial depth to draw the L-system at.
6. Scale - Used for the % command.

There are two other fields on the main window: width and height, which determine the physical size of the L-system (the maximum of which is your screen height and width).

Version 0.55 added the support of .map and .fmap files. These files allow you to create your own custom color patterns. fmap stands for "fade colormap", and map for "standard colormap". Both .fmap and .map files will be referred to in this section as "map files."

Map files exist in two places:

Global maps:	/usr/local/share/lsysexp/maps
User maps:	~/.lsysexp/maps

If a user map file and global map file have the same name, the user map file will be used.

You can choose which map file to use under the Colors/Gradients menu. If the name of the map file is Foo.map, then you can use it by going to Colors/Gradients/Foo (If you have a lot of map files they will be split up into sub-menus under Colors/Gradients/ for convenience). If a fmap file as the same name as a map file, only one of them will be shown (in other words, don't name them the same! It wouldn't make sense anyway).

The following are all the symbols which have special meaning to L-system Explorer.

Symbol	Meaning
f	Move forward while drawing a line
g	Move forward, do not draw a line
+	Turn right A degrees, where A is the L-system turn angle. Optionally preceeded by an integer X to turn right X times. Example: 3+
-	Turn left A degrees, where A is the L-system turn angle. Optionally preceeded by an integer X to turn left X times Example: 12-
@	Multiply the current line segment length by whatever number follows @ (this number can be a fractional or floating point number). If @ is followd by Q and then a number X, the square root of the number X is used. If @ is followed by I and then a number X, the inverse of X is used. If @ is followed by IQ, or QI, then a number X, the square root of the inverse of X is used. Examples: @3.14159 @I2 @Q7.3 @QI5, @IQ5 (these both take the square root of the inverse of 5).
|	Turn 180 degrees (reverse direction). Note: This has no affect on the / and \ commands below, since you could just do /180 or \180 to get the same effect.
!	Reverse the meanings of + and - (along with \ and /, see below). In other words, all +'s encountered after a ! are treated as -'s, and vice-versa (unless another ! is encountered which switches the meanings of + and - back to the original).
%	Move forward at a length dependant to the current depth and the scale factor. % is never expanded (unlike the other draw commands, which are expanded and only used at the final depth), so at every depth where it is encountered a line is drawn. The length of this line is equal to the depth raised to the scale factor. Note: This command is has the same meaning as the | command from the book The Computational Beauty of Nature, but was renamed to avoid the conflict with the Fractint command.
[	Saves the current state (including x,y position, line length, direction, etc.). You may wish to think of this as pushing the current state on a stack.
]	Restores the previous state saved by a ]. You may wish to think of this as popping the previous state off the stack.
The following 4 commands use a different "current angle" than the f, g, +, and - commands, but have a similar meaning (note: all commands share the same "x,y position" and "line length" attributes, it's only the "current angle" attribute that differs). These are sometimes more convenient to use since you can specify the turn angles explicitly. They are also a little slower, since the turn angles have to be determined every time they are encountered. If all of your turn angles share a common multiple (besides 1!), then you should use + and - (which you can proceed with an integer X to turn X times).
d	Move forward while drawing a line
m	Move foward, do not draw a line
/X	Turn right X degrees, where X is an integer or floating pointer number.
\X	Turn left X degrees, where X is an integer or floating point number.

General syntax notes:

1. Whenever a number is expected, it will be gobbled up until a non-digit is encountered (except for floating point numbers, where a '.' is also allowed). That means that:

   f@5.34+f
   

   is different from

   f@5.3 4+f
   

   In the first case, the complete number is gobbled up, and then a single turn to the right is made, in the second, a non-digit is encountered (a space), and then four right turns are made. You can usually avoid cases like these, but if not, just stick in a space or some other meaningless character to separate the numbers.

2. All production rules must start with a letter, a-z (this also implies that there can be at most 26 rules).

3. All letters are automatically converted to lowercase.

4. Unknown characters are ignored.

• In Fractint + is left, and - is right, the opposite of L-system Explorer.

• No support for the CX, >X, and <X commands, where X is an integer. These commands are used to select colors, which L-system Explorer does automatically. This is usually all you need, though on some L-systems (plants, for instance), it would be nice to be able to have a color for the leaves and another for the branches. To do something similar the "right way" would require a bit of extra syntax, so I didn't do it.

lsyscustom format

When you first save an L-system, a file called "lsyscustom" will be created in ~/.lsysexp/ which contains a description of that L-system. Every additional L-system you create and save will be appended to this file. The format of this file is described below, in case you want to add L-systems by hand, or remove L-systems that you have saved.

Each L-system starts with a { followed by a new line, and ends with a } followed by a new line. In between the { and } are the fields, which have the format field_name : field_value, followed by a new line.

Valid field names are:

Field Name	Description
group	Name of the group where the L-system should be placed
name	Name of the L-system
axiom	Axiom of the L-system
rules	A rule of the L-system (there may be several of these, one per each rule).
level	The default recursion level to use for the L-system
a0	The initial angle for the L-system, in degrees
da	The turn angle for the L-system, in degrees
ds	The scale factor for the L-system

The field names can appear in any order. If a field is repeated (besides rules), the lowermost field is used.

You should be able to figure out what's going on by looking at the file, as it's pretty straight-forward.