An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures [LINK]
This project is a Python-based rendering or interpretation of L-systems as per the title The Algorithmic Beauty of Plants by Przemyslaw Prusinkiewicz and Aristid Lindenmayer [Book].
All the code required to get started is in the file (lsystem.py). Only a working installation of Python 3 is necessary [LINK].
L-systems lie at the heart of this project, enabling users to define custom rules for generating fractals. This project supports any fractal pattern that can be represented by iterative rewriting rules, allowing for versatile and creative fractal generation. Users can specify parameters such as step size, angle, and iteration depth, making it easy to explore a wide range of fractal patterns, from plant-like structures to classic shapes such as the Dragon Curve or Sierpiński Triangle.
Following the same rewriting rules, this project is capable of creating [Fractals] of different forms via a recursive given set of rules input by the user (see Usage section).
Here's an example of a plant-like generated L-system (Axial Tree) using the bracketed sequence X->F-[[X]+X]+F[+FX]-X F-> FF. The rest of the parameters, such as the number of iterations (n), is described below.
Enter rule[1]:rewrite term (0 when done): L->L+R+
Enter rule[2]:rewrite term (0 when done): R->-L-R
Enter rule[3]:rewrite term (0 when done): 0
Enter axiom (initial string): L
Enter number of iterations (n): 10
Enter step size (segment length): 5
Enter initial heading (alpha-0): 90
Enter angle: 90
Note: Step size (segment length) is highly dependent on screen size, etc. Adjust as needed, but a good rule of thumb is a value between 5 and 10.
| Figure | Derivation |
|---|---|
| Koch Island | F->F-F+F+FF-F-F+F w=F-F-F-F n=2 alpha0=90 angle(i)=90 |
| Koch (1st variation) | F->FF-F-F-F-F-F+F w=F-F-F-F n=3 alpha0=90 angle(i)=90 |
| Koch Islands and Lakes | F->F+f-FF+F+FF+Ff+FF-f+FF-F-FF-Ff-FFF f->ffffff w=F+F+F+F n=2 alpha0=90 angle(i)=90 |
| Cuadratic Snowflake | F->F+F-F-F+F w=-F n=4 alpha0=90 angle(i)=90 |
| Hexagonal Gosper curve | L->L+R++R-L--LL-R+ R->-L+RR++R+L--L-R w=L n=4 alpha0=60 angle(i)=60 |
| Axial Tree (node-rewriting) | X->F-[[X]+X]+F[+FX]-X F->FF w=X n=5 alpha0=90 angle(i)=22.5 |
For example, to create a Sierpiński Triangle enter the following:
Enter rule[1]:rewrite term (0 when done): L->R-L-R
Enter rule[2]:rewrite term (0 when done): R->L+R+L
Enter rule[3]:rewrite term (0 when done): 0
Enter axiom (w): L
Enter number of iterations (n): 6
Enter step size (segment length): 5
Enter initial heading (alpha-0): 60
Enter angle increment (i): 60
For questions or comments:
- Author: Gianni Perez @ skylabus.tech or at gianni.perez@gmail.com
