Colorz

Complex domain coloring

Colorz is a fun tool that generates domain coloring for the given function of a complex variable z.

In other words, colorz is yet another implementation of:

• http://www.jedsoft.org/fun/complex/
• http://mathematica.stackexchange.com/questions/7275/how-can-i-generate-this-domain-coloring-plot

Requirements

• Ruby 2.2 or greater
• RubyGems: ChunkyPNG , rgb

Setup

1. Copy colorz into your convenient directory.

• Windows users need to copy colorz.bat into the same directory.
• *nix users may need executable permission (chmod +x colorz).

2. Include the directory in PATH.

Usage

The First Result

Try below:

$ colorz

After a few seconds, the command prints a full path to the generated PNG file and ends.

$ colorz
/working/dir/colorz.png
$

The generated colorz.png is a domain coloring result of f(z) = z, where z covers from -4-4i to 4+4i.

The color in a point represents the result value of f(z) at the corresponding point on the complex plane. The hue represents the phase, as many other domain coloring methods do. A white(bright) point means the magnitude is quite near one of 2^n (n: integer including negative numbers). A black(dark) point means either the real part or the imaginary part is an integer.

Another One

Try the sine function:

$ colorz "sin(z)"

More examples are in gallery.

Options

$ colorz -h
Complex domain coloring
Usage: colorz [options] FUNCTION

Options:
    -d, --domain=MIN,MAX             coloring domain (e.g. -d=-2-2i,+2+2i)
    -i, --input-file=INPUT_FILE      file path of ruby script for a complex function
    -o, --output-file=OUTPUT_FILE    file path of output image
    -s, --size=WxH                   size(width=W, height=H) of the output image
    -t, --tile                       the right/bottom edge shows slightly inner values than the maximum

FUNCTION:
Ruby snipet that returns a value with a given parameter "z"

Tips

Get more beautiful image

Plot twice as large as the target size. When you want a 400x400 image of f(z) = 1/z for example:

$ colorz -s 800x800 -o inv2.png "1/z"

Then shrink the image to the target size. If you have ImageMagick, convert command can do that:

$ convert -geometry 400x400 inv2.png inv.png

Don't define constant in your function

Otherwise you will see a flood of warnings "warning: already initialized constant..."

Function starts with minus sign fails

The function below fails as invalid option:

$ colors "-z"

Avoid minus sign "-" at the beginning. e.g. "0-z".

Disclaimer

On this tool, I prefer visual sweetness rather than the mathematical correctness.