Plotting tools for complexvalued functions
Project description
Plot complexvalued functions with style.
cplot helps plotting complexvalued 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:
Install with
pip install cplot
and use as
import cplot import numpy cplot.show(numpy.tan, 5, +5, 5, +5, 100, 100) cplot.save_fig("out.png", numpy.tan, 5, +5, 5, +5, 100, 100) cplot.save_img("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", "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 off(z)
completely. 
colorspace
can be set tohsl
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 z^{1} 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.
Gallery
All plots are created with default settings.
z**1 
z**2 
z**3 
1/z 
z / abs(z) 
(z+1) / (z1) 
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 
scipy.special.gamma 
scipy.special.digamma 
mpmath.zeta 
Testing
To run the cplot unit tests, check out this repository and type
pytest
License
This software is published under the GPLv3 license.
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