In this project I use an L-System to implement Turtle graphics (i.e. a drawing produced my moving a point around and adding lines), specifically to produce simple fractal drawings.
The main point is to illustrate how complex abstractions used in the correct way can result in nice simplifications.
A Lindenmeyer System (L-System) is a type of formal grammar in which productions (i.e. rewrite rules) are applied simultaneously to a fixed initial string (the axiom).
A simple example illustrates the Cantor set:
Alphabet: { A, B }
Axiom: A
Rules: A -> ABA
B -> BBB
Expansion is as follows:
1. A
2. A B A
3. ABA BBB ABA
4. ABA BBB ABA BBB BBB BBB ABA BBB ABA
This system is context-free as there is a single letter on the LHS of each rule, and deterministic as each letter appears in at most one rule.
The code will assume systems are context-free and deterministic.
Many Wikipedia descriptions of fractals include a specification as an L-system, others can be determined by trial and error.
First install dependencies and build via stack build.
The test.svg image is produced by the command
stack run -- -i 3 --name=Sierpinsky -f test.svg
All implemented systems are in src/Systems.hs and their corresponding command flags names are listed by passing an empty string to --name:
stack run -- --name=""
Note that the output size will usually grow exponentially with the number of iterations, e.g. Koch snowflake with n=10 will produce an SVG of about 100MB. I have not really tried to optimize performance.
