A simple implementation of a Lindenmayer system for playing around with rewriting rules, turtle graphics and fractals. Most of the code is inspired by Chapter 4 of Bio-Inspired Artificial Intelligence by D. Florreano and C. Mattiussi.

L-systems are rewriting systems that operates on strings of symbols. Given an alphabet A and a set of production rules π, the system iteratively updates the contents of an axiom ω. The system can be run to the string contents converge or for a number of iterations. The production rules are applied in parallel.

For example:

A = {a, b, +, -}
ω = a-b
π = {a → b+a-b, b → a-b+a}

should produce the following results

0: a-b
1: b+a-b-a-b+a
2: a-b+a+b+a-b-a-b+a-b+a-b-a-b+a+b+a-b
3: b+a-b-a-b+a+b+a-b+a-b+a+b+a-b-a-b+a-b+a-b-a-b+a+b+a-b-a-b+a+b+a-b-a-b+a-b+a-b-a-b+a+b+a-b+a-b+a+b+a-b-a-b+a

L-systems are no fun unless the resulting strings are interpreted and used for something. Turtle graphics are a popular way to interpret and visualize the strings.

The turtle represent a simple drawing tool, able to execute a few drawing commands such as moving forward while drawing a line, and turning left and right. A few additional commands such as moving without drawing and saving and restoring the turtle's state enables drawing of trees and other recursively branching structures.

Shown below is the result of six iterations of the above example as drawn by the turtle. Symbols a and b both correspond to draw forward, and + and - meaning turn left and turn right, respectively. The example is generated by calling:

python demo.py shrooms 6

The only dependency for running this code is python-tk.