Plot complex-valued functions with style.

cplot helps plotting complex-valued functions in a visually appealing manner. The general idea is to map the absolute value to lightness and the complex argument (the "angle") to the chroma of the representing color. This follows the domain coloring approach, also described by John D. Cook and Elias Wegert in the book Visual Complex Functions (with some tweaks). Also check out the DC gallery by Juan Carlos Ponce Campuzano.

Similar projects:

• https://github.com/endolith/complex_colormap

Install with

pip install cplot

and use as

import cplot
import numpy

cplot.show(numpy.tan, -5, +5, -5, +5, 100, 100)

cplot.savefig("out.png", numpy.tan, -5, +5, -5, +5, 100, 100)
cplot.imsave("out.png", numpy.tan, -5, +5, -5, +5, 100, 100)

# There is a tripcolor function as well for triangulated 2D domains
# cplot.tripcolor(triang, z)

# The function get_srgb1 returns the SRGB1 triple for every complex input value.
# (Accepts arrays, too.)
z = 2 + 5j
val = cplot.get_srgb1(z)

All functions have the optional arguments (with their default values)

alpha = 1  # >= 0
colorspace = "cam16"  # "cielab", "oklab", "hsl"

• alpha can be used to adjust the use of colors. A value less than 1 adds more color which can help isolating the roots and poles (which are still black and white, respectively). alpha=0 ignores the magnitude of f(z) completely.

• colorspace can be set to hsl to get the common fully saturated, vibrant colors. This is usually a bad idea since it creates artifacts which are not related with the underlying data. From Wikipedia:

  Since the HSL color space is not perceptually uniform, one can see streaks of perceived brightness at yellow, cyan, and magenta (even though their absolute values are the same as red, green, and blue) and a halo around L = 1 / 2 . Use of the Lab color space corrects this, making the images more accurate, but also makes them more drab/pastel.

  Default is "cam16"; very similar is "cielab" (not shown here).

Consider the test function (z ** 2 - 1) * (z - 2 - 1j) ** 2 / (z ** 2 + 2 + 2j):

alpha = 1	alpha = 0.5	alpha = 0.0

The representation is chosen such that

• values around 0 are black,
• values around infinity are white,
• values around +1 are green,
• values around -1 are deep purple,
• values around +i are blue,
• values around -i are orange.

(Compare to the z¹ reference plot below.)

With this, it is easy to see where a function has very small and very large values, and the multiplicty of zeros and poles is instantly identified by counting the color wheel passes around a black or white point.

All plots are created with default settings.

z**1	z**2	z**3

1/z	z / abs(z)	(z+1) / (z-1)

z ** z	(1/z) ** z	z ** (1/z)

numpy.sqrt	z**(1/3)	z**(1/4)

numpy.log	numpy.exp	exp(1/z)

numpy.sin	numpy.cos	numpy.tan

numpy.sinh	numpy.cosh	numpy.tanh

numpy.arcsin	numpy.arccos	numpy.arctan

sin(z) / z	cos(z) / z	tan(z) / z

scipy.special.gamma	scipy.special.digamma	mpmath.zeta

mpmath.siegeltheta	mpmath.siegelz	Riemann-Xi

To run the cplot unit tests, check out this repository and type

pytest

This software is published under the GPLv3 license.