OOLALA: L- System Visualizer

This language is a simplified version of the one invented by Aristid Lindenmayer at the University of Utrecht that has been used to model the growth processes of plant development.

Create an interactive visualizer for L-systems, short for "Lindenmayer's system". that supports users to write basic sets of rules to generate recursive drawings.

L-systems are rules and symbols that model growth processes as shapes that are self-similar on different scales, because growth involves repetition of the same simple process (e.g. branching). They consist of an starting string (e.g., a simple string like F), a set of production rules (e.g., F-F++F-F), and an alphabet of symbols which have some predefined meaning (e.g., F means mane the turtle go forward 10 pixels with its pen down). The starting string is recursively expanded a fixed number of times according to the rules, after which a long string is generated. By increasing the expansion level the form slowly grows, becoming more complex (this is what makes fractal forms so easy to describe).

In addition to the UI features common to all applications, it should all allow the user to:

• set the length to be used for moves and the angle to be used for turns
• set the number of levels to expand the expression
  
• set the location to start the generation to a specific xy-location (default is the center of the display)
  
• set an image to be drawn (e.g., a leaf at the end of a branch)

Example

This is an example of a typical program:

Program	Expansion	Output
# Koch Snowflake start F rule 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

More examples are given here, but you are expected to make your own example files as well (including ones with syntactically incorrect programs).

Programs

The characters in the expanded string are evaluated using Turtle graphics to provide a geometrical interpretation to make their dynamics visible. Traditionally, F means to go forward (drawing a line from the current point to the next point), while + and - mean to turn (right or left). Thus, using just a few rules, it is possible to construct very complex and interesting fractals. Thus, for level 1 of the example above, your program could run the following commands (assuming the length has been set to 10 and the angle has been set to 30):

fd 10 lt 30 fd 10 rt 30 rt 30 fd 10 lt 30 fd 10

Note, the turtle should not be seen during the drawing.

Commands

Name	Description
START symbol	Set given symbol as the start of the program
RULE symbol string	Describe how the given symbol expands when evaluated in a program string
SET symbol "Logo Commands"	Define the Logo commands used to display the given symbol

Built-in Alphabet

Name	Logo Commands
F	PD FD length
G	PU FD length
A	PU BK length
B	PD BK length
+	RT angle
-	LT angle
X	STAMP

General notes about a program's syntax:

• Tokens are separated by one or more spaces, tabs, or newlines
• Command names are not case sensitive (even though they are shown below in all capital letters)
• Ignore any lines that are empty, i.e., only zero or more spaces, or begin with comment character, "#"

Resources

Experiment with L-Systems interactively.

Learn more about how algorithmic biology and other uses of L-Systems:

• Simulation Modeling of Plants and Plant Ecosystems by Przemyslaw Prusinkiewicz (original paper)
• Wildwood: The Evolution of L-System Plants for Virtual Environments by Kenrick J. Mock