cplot 0.7.4

Plot complex-valued functions

Plot complex-valued functions with style.

cplot helps plotting complex-valued functions in a visually appealing manner.

Install with

pip install cplot

and use as

import numpy as np

import cplot


def f(z):
    return np.sin(z ** 3) / z


plt = cplot.plot(
    f,
    (-2.0, +2.0, 400),
    (-2.0, +2.0, 400),
    # abs_scaling=lambda x: x / (x + 1),  # how to scale the lightness in domain coloring
    # contours_abs="auto",
    # contours_arg=(-np.pi / 2, 0, np.pi / 2, np.pi),
    # highlight_abs_contour_1: bool = True,
    # colorspace: str = "cam16",
    # add_colorbars: bool = True,
    # add_axes_labels: bool = True,
    # saturation_adjustment: float = 1.28,
)
plt.show()

The plot consists of three building blocks:

• domain coloring, i.e., mapping the absolute value to lightness and the complex argument to the chroma of the representing color
• Contours of constant absolute value (the contour abs(z) == 1 is highlighted, the other contours are at (2, 4, 8, etc. and 1/2, 1/4, 1/8, etc., respectively)
• Contours along constant argument (angle). For arg(z) == 0, the color is green, for arg(z) == pi/2 it's blue, for arg(z) = -pi / 2 it's orange, and for arg(z) = pi it's pink

Other useful functions:

# 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)

Gallery

All plots are created with default settings.

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

1 / z	1 / z ** 2	(z + 1) / (z - 1)

np.real	z / abs(z)	np.conj

z ** 6 + 1	z ** 6 - 1	z ** (-6) + 1

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

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

np.log	np.exp	np.exp2

np.exp(1 / z)	z * np.sin(1 / z)	np.cos(1 / z)

exp(- z ** 2)	1 / (1 + z ** 2)	scipy.special.erf

np.sin	np.cos	np.tan

sec	csc	cot

np.sinh	np.cosh	np.tanh

np.arcsin	np.arccos	np.arctan

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

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

mpmath.siegeltheta	mpmath.siegelz	Riemann-Xi

Jacobi elliptic function sn(0.6)	cn(0.6)	dn(0.6)

Bessel function, first kind, order 1	order 2	order 3

Airy function Ai	Bi	Exponentially scaled eAi

tanh(pi / 2 * sinh(z))	sinh(pi / 2 * sinh(z))	exp(pi / 2 * sinh(z))

Testing

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

tox

Similar projects and further reading

• Tristan Needham, Visual Complex Analysis, 1997
• François Labelle, A Gallery of Complex Functions, 2002
• Douglas Arnold and Jonathan Rogness, Möbius transformations revealed, 2008
• Konstantin Poelke and Konrad Polthier, Lifted Domain Coloring, 2009
• Elias Wegert and Gunter Semmler, Phase Plots of Complex Functions: a Journey in Illustration, 2011
• Elias Wegert, Calendars "Complex Beauties, 2011-
• Elias Wegert, Visual Complex Functions, 2012
• John D. Cook, Visualizing complex functions, 2017
• endolith, complex-colormap, 2017
• Anthony Hernandez, dcolor, 2017
• Juan Carlos Ponce Campuzano, DC gallery, 2018
• 3Blue1Brown, Winding numbers and domain coloring, 2018

License

This software is published under the GPL-3.0 license. In cases where the constraints of the GPL prevent you from using this software, feel free contact the author.