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=2.0,
# contours_arg=(-np.pi / 2, 0, np.pi / 2, np.pi),
# emphasize_abs_contour_1: bool = True,
# add_colorbars: bool = True,
# add_axes_labels: bool = True,
# saturation_adjustment: float = 1.28,
# min_contour_length = None,
# linewidth = None,
)
plt.show()
Historically, plotting of complex functions was in one of three ways
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Only show the absolute value; sometimes as a 3D plot |
Only show the phase/the argument in a color wheel (phase portrait) |
Show contour lines for both arg and abs |
Combining all three of them gives you a cplot:
See also Wikipedia: Domain coloring.
Features of this software:
- cplot uses OKLAB, a perceptually
uniform color space for the argument colors.
This avoids streaks of colors occurring with other color spaces, e.g., HSL.
- The contour
abs(z) == 1
is emphasized, other abs contours are at 2, 4, 8, etc. and
1/2, 1/4, 1/8, etc., respectively. This makes it easy to tell the absolte value
precisely.
- 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)
Riemann sphere
cplot can also plot functions on the Riemann
sphere, a mapping of the complex
plane to the unit ball.
import cplot
import numpy as np
cplot.riemann_sphere(np.log)
Gallery
All plots are created with default settings.
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1 / z |
1 / z ** 2 |
1 / z ** 3 |
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np.real |
z / abs(z) |
np.conj |
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z ** z |
(1/z) ** z |
z ** (1/z) |
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np.sqrt |
z**(1/3) |
z**(1/4) |
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np.exp(1 / z) |
z * np.sin(1 / z) |
np.cos(1 / z) |
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secans hyperbolicus |
cosecans hyperbolicus |
cotangent hyperbolicus |
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np.arcsin |
np.arccos |
np.arctan |
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np.arcsinh |
np.arccosh |
np.arctanh |
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Hurwitz zeta function with a = 1/3
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Hurwitz zeta function with a = 24/25
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Hurwitz zeta function with s = 3 + 4i
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Jacobi theta 1 with q=0.1 * exp(0.1j * np.pi))
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Jacobi theta 2 with the same q
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Jacobi theta 3 with the same q
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Bessel function, first kind, order 1 |
Bessel function, first kind, order 2 |
Bessel function, first kind, order 3 |
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Bessel function, second kind, order 1 |
Bessel function, second kind, order 2 |
Bessel function, second kind, order 3 |
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Hankel function of first kind (n=1.0) |
Hankel function of first kind (n=3.1) |
Hankel function of second kind (n=1.0) |
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tanh(pi / 2 * sinh(z)) |
sinh(pi / 2 * sinh(z)) |
exp(pi / 2 * sinh(z)) |
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Lambert series with 1s |
Lambert series with von-Mangoldt-coefficients |
Lambert series with Liouville-coefficients |
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
- empet, Visualizing complex-valued functions with Matplotlib and Mayavi, Domain coloring method, 2014
- 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
- Ricky Reusser, Domain Coloring with Adaptive
Contouring, 2019
- Ricky Reusser, Locally Scaled Domain Coloring, Part 1: Contour
Plots, 2020
- David Lowry-Duda, Visualizing modular forms, 2020
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.