Fractal

Draws fractals in form of PNG images, using Ruby.

Generated with fractal -w=2000 -h=1100 --scale=2.92 --def=100 mandelbrot --color=mono

Installation

RubyGems:

gem install fractal

Source:

git clone https://github.com/Demonstrandum/Fractal.git && cd ./Fractal/
gem build fractal.gemspec
gem install fractal-*.gem

Usage

The current command-line arguments possible are:

• -w=, the pixel width of the output image. (Defaults to 300), e.g. -w=500
• -h=, the pixel height of the output image. (Defaults to 300), e.g. -h=240
• --color=, (Defaults to mono), allows you to draw the image in colour or monochromatically, e.g. --color=mono or --color=multi which is the same as --color=rainbow
• -o=, (optional) is the location in which to save your image, the -o= part is not required if you just write the file location with a .png at the end.
• --def=, (optional), the 'definition' of the image, the amount of calculations performed or iterations to the formula. e.g. --def=100
• --scale=, (optional), the zoom level of the image, a higher value corresponds to a taller imaginary number line thus a smaller fractal is seen. e.g. --scale=2.25
• --offset=x,y (optional), the offset will make you able to position yourself where you like on the plan. (offsetting where the centre is, before (0,0) was the centre of the image, but now your offset is the centre). Make sure you give an x and y value as numerics, ints and floats work both and don't leave any space between the comma).
• --complex= (only needed for the Julia set) this sets a complex coordinate for the Julia set, in the form of a±bi (a and b real numbers and i is the square root of -1 which can take on all values in the complex plane), e.g. -0.8+0.4i
• Last but not least, (required), the type of fractal drawn. This argument is composed of just the fractal's name, put at any position in your list of arguments. e.g. mandelbrot or julia (only ones currently available)

Example commands are:

Mandelbrot

For the Mandelbrot set:

fractal -w=400 -h=320 --color=multi mandelbrot --scale=2 --def=200

Offset & Zoom

Using our offset argument, we can get to some very pretty places...

fractal mandelbrot --offset=-0.7463,0.1102 --scale=0.005 --def=1000 -o=close_1.png

will generate:

fractal mandelbrot --offset=-0.7453,0.1127 --scale=6.5e-4 --def=1000 -o=close_2.png

will generate:

Check out: cuug.ab.ca/dewara/mandelbrot/ for more prime locations (This is where the coordinates for the two above come from).

Julia

For the Julia set, which requires the complex coordinate argument:

fractal julia -w=1000 -h=1000 --color=multi --complex=-0.8+0.156i --def=100 --scale=1.5

which generated: