• L-Systems
  • Introduction
  • L-systems
    • LSystem data type
    • JSON format for L-systems
  • Building and running
  • Examples
    • Space-filling curves
    • Fractals
    • Tilings
  • Implementation

L-Systems

https://travis-ci.org/dlozeve/lsystems.svg?branch=master

Generate and draw L-systems!

Introduction

This program can be used to generate arbitrary L-systems. It supports:

• full rewriting rules
• full representation rules
• personalized angle and segment length for the representation
• push ('[') and pop (']') operations

L-systems

LSystem data type

An L-system consists of:

• the L-system itself:

  • an alphabet
  • an axiom (i.e. the starting point)
  • a set of rewriting rules (represented as a list of tuples)

• rules to transform it into a graphical representation:

  • an angle and a length
  • a set of representation rules (which symbols mean "draw forward", "turn left", "pop a position", etc.)

JSON format for L-systems

L-systems can be specified using a straightforward JSON encoding. See the examples/ folder for examples.

Note that the rules and representation keys are associated to arrays of arrays in JSON. angle and distance are numbers. Everything else should be a string.

Building and running

You will need Stack.

From the repository, run:

stack build
stack exec lsystems-exe -- examples/penroseP3.json

This will open a window, where you can move around using the mouse and zoom by scrolling.

For tests and documentation, run:

stack test --haddock

You can choose the L-system and the number of iteration via command-line arguments, see the output of --help:

lsystems -- Generate L-systems

Usage: lsystems-exe FILENAME [-n|--iterations N] [-c|--color R,G,B]
                    [-w|--white-background]
  Generate and draw an L-system

Available options:
  FILENAME                 JSON file specifying an L-system
  -n,--iterations N        Number of iterations (default: 5)
  -c,--color R,G,B         Foreground color RGBA
                           (0-255) (default: RGBA 1.0 1.0 1.0 1.0)
  -w,--white-background    Use a white background
  -h,--help                Show this help text

Examples

Examples are provided in the examples/ directory.

Space-filling curves

• Hilbert curve
• Gosper curve

Fractals

• Lévy C curve
• Koch snowflake and Koch curve
• Sierpinski triangle and Sierpinski arrow curve
• Dragon curve
• Binary tree and fractal plant

Tilings

• Penrose P3 tiling

Implementation

The program is implemented in Haskell, using Gloss to display the generated L-systems.