lfract 1.0.0

An open-source CLI software for generating fractal images using the L-System.

L-System Fractal Generator

An open-source CLI software for generating fractal images using the L-System.

Features

• Rewrite and draw a 2D deterministic context-free L-System. (D0L)
• Support the following turtle commands:

Command	Description
F	Draw a line forward d pixels in the current heading
f	Move forward d pixels in the current heading without drawing a line
+	Turn right by δ degrees
-	Turn left by δ degrees
[	Push the current turtle's state into a stack
]	Pop a turtle's state out of the stack

• Support saving and previewing the output image
• Support changing the drawing line's width

Background

L-System (Lindenmayer System) is a string rewriting system that uses an iterative process. An L-System starts with an axiom, an initial string, that will be rewritten following a set of production rules which contains pairs of predecessors and successors. For each iteration, each symbol or character will be replaced with its corresponding successor. Any symbols without a production rule will be replaced by themselves. For example,

Axiom: N
Production Rules:

Predecessor	Successor
N	MNO
O	#

Iteration 0: N
Iteration 1: MNO
Iteration 2: MMNO#
Iteration 3: MMMNO##

For illustration, lfract reserves some characters for controlling a drawing pen called a turtle. The turtle keeps track of its position and heading throughout the evaluation process. After some finite number of iterations, the resulting string will be evaluated and an image will be drawn. (Supported turtle commands are listed in the previous section)

The current version of lfract supports only the deterministic and context-free version of the L-System. That is each rule has a probability of being applied of 1 and the location of each symbol in a string relative to other symbols doesn't matter.

Installation

This software is available to download on The Python Package Index (PyPI) and can be installed through pip.

Start by making sure that pip is installed and up-to-date

python -m pip install --upgrade pip

Run the following command on your terminal

pip install lfract

Usage

Invokes the program using lfract. There are seven optional arguments as follows:

Option	Description
-x, --axiom	Initial string or axiom, required
-r, --rules	Production rules. Uses "->" to seperate predecessor from successor, optional
-a, --angle	Turning angle, δ (degrees), default = 90
-d, --dist	Distance, d (pixels), default = 100
-n, --iters	Number of iterations, default = 0
-o, --output	Output path. If specified, the image will be saved to the given path, optional
-w, --width	Width of the drawing pen (pixels), default = 1

The user must provide at least an axiom or the initial string to the L-System. All predecessors in the set of production rules must be unique. If there are duplicates, lfract will use the latest rule.

For the full usage description of lfract, type:

lfract --help

Examples

1. Hilbert curve by Prusinkiewicz and Hanan [1]

   lfract -x X -r X->-YF+XFX+FY- Y->+XF-YFY-FX+ -a 90 -d 50 -n 5 -w 5

2. Hexagonal tiling by Prusunkiewicz and Hanan [1]

   lfract -x X -r X->[-F+F[Y]+F][+F-F[X]-F] Y->[-F+F[Y]+F][+F-F-F] -a 60 -d 50 -n 10 -w 4

3. A fractal by Surasith Boonaneksap

   lfract -x A -r A->fB+AF+Fff+Bf B->Bf-FffF-FfA-Afff -a 120 -n 7 -d 50 -w 5

Notes

• lfract adopts the L-System formal definition from [1]. It also follows the terminologies used in [1][2][3].
• Symbols in the L-System can be any Unicode characters.
• Currently not support:
  • Stochastic L-System
  • Context-sensitive L-System
  • Parametric L-System

Dependency

Pillow 4.0.0 (Depending on the Python's version, a more recent version may be required. Check Pillow's documentation)

License

MIT

References

[1]: Prunsinkiewicz, Przemyslaw and Hanan, James; "Lecture Notes in Biomathematics: Lindenmayer Systems, Fractals, and Plants" link
[2]: Wikipedia; "L-system" link
[3]: Santel, Jordan; "L-systems" link