* L-Systems

[[https://travis-ci.org/dlozeve/lsystems][https://travis-ci.org/dlozeve/lsystems.svg?branch=master]]
[[https://opensource.org/licenses/BSD-3-Clause][https://img.shields.io/badge/License-BSD%203--Clause-blue.svg]]

Generate and draw [[https://en.wikipedia.org/wiki/L-system][L-systems]]!

[[./img/demo.png]]

Check the [[https://www.lozeve.com/post/lsystems/][accompanying blog post.]]

** 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 [[https://docs.haskellstack.org/][Stack]].

From the repository, run:
#+BEGIN_SRC sh
stack build
stack exec lsystems-exe -- examples/penroseP3.json
#+END_SRC

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

For tests and documentation, run:
#+BEGIN_SRC sh
stack test --haddock
#+END_SRC

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

#+BEGIN_SRC 
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
#+END_SRC

** Examples

Examples are provided in the =examples/= directory.

*** Space-filling curves

+ [[https://en.wikipedia.org/wiki/Hilbert_curve][Hilbert curve]]
+ [[https://en.wikipedia.org/wiki/Gosper_curve][Gosper curve]]

*** Fractals

+ [[https://en.wikipedia.org/wiki/L%C3%A9vy_C_curve][Lévy C curve]]
+ [[https://en.wikipedia.org/wiki/Koch_snowflake][Koch snowflake]] and Koch curve
+ [[https://en.wikipedia.org/wiki/Sierpinski_triangle][Sierpinski triangle]] and Sierpinski arrow curve
+ [[https://en.wikipedia.org/wiki/Dragon_curve][Dragon curve]]
+ Binary tree and fractal plant

*** Tilings

+ [[https://en.wikipedia.org/wiki/Penrose_tiling#Rhombus_tiling_(P3)][Penrose P3 tiling]]

** Implementation

The program is implemented in Haskell, using [[https://hackage.haskell.org/package/gloss][Gloss]] to display the
generated L-systems.