Background

On his web page, Kenneth Moreland suggests a number of continuous and diverge color palettes to improve scientific visualization.[fn:1] Contrasting to other approaches, they aim for a smooth variation of the hue between the extremes of a scale displayed. While this reduces the brightness of the colors to choose from, their continuous transient hue offers a better visual inspection already when print in color. Contrasting to classical “jet” or “rainbow” palettes (vide infra), they retain their information if the output is constrained to gray scale (e.g., if xeroxed).

Where possible, this project renders Kenneth Moreland’s set of .cvs palette information accessible to gnuplot as .plt files.

How to use the .plt palettes

The color palettes are provided with a varying number of explicitly defined colors. This range spans from eight up to 1024. For smaller color palettes, a copy-paste of their content into an already existing gnuplot script file may be an option. More convenient however, especially while working with larger color palettes, is to access them from gnuplot by adding the command

load "example_palette.plt"

at any point prior to the [s]plot instruction.

Each sub-folder contains the corresponding .plt files. The number in the file name indicates the number of explicitly defined colors in the file.

Palettes at disposition

For the display of continuous data, conversions of eight color palettes are provided: black-body, extended-black-body, inferno, kindlmann, extended-kindlmann, magma, plasma, and viridis.

On the other hand, palette bent-cool-warm is designed with diverge data sets in mind where highlighting the transition across a critical value is important. This may be useful to indicate relative velocities, or pressures below / above a threshold, for example. It is complemented by smooth-cool-warm. While again designed as diverging palette, the transition around the mid point now is gradual. Thus, for data close at this transition, expect less detail displayed there with with palette smooth-cool-warm , than with palette bent-cool-warm.

The display of the palette’s action is based on synthetic data computed for the Bessel function $f(x,y) = x^2 + y^2$ with a grid of 500 × 500 points in the (x,y)-plane. 1024 levels in the orthogonal z-direction accommodate the highest number of explicitly defined colors per palette file available ($n = 1024$). Next to it, a diagram depicts how the R, G, and B channel sum up to yield the RGB color displayed. In addition, the NTSC luminance value is traced. This is indicative about how the calculated result would look like for an output constrained to gray-scale. Thirdly you see the Bessel plot a twice, actually simulating the gray-scale output.

Comparison with other palettes

A few palettes are compared to those provided by Moreland. They again rely on the high level of isosamples (set iso 1024) in z-, and samples (set samples 500) in x- and y-direction.

Repositories like gnuplot-colorbrewer,[fn:2] and gnuplot-palettes[fn:3] host alternative palettes, too.

• For the display of continuous data, either one of the following instructions prior to the [s]plot instruction may initiate palettes already included in gnuplot:

  set palette gray   # gnuplot's gray palette
  set pm3d map       # access to gnuplot's default rainbow palette
  set palette cubehelix start 0 cycles -1. saturation 1
      

  Note that palette cubehelix equally counters some cases of color blindness, too.

  

  

  

  As a contrasting example, jet.pal (provided by gnuplot-palettes) mimics an elder matlab default palette with the perceptual problems meanwhile addressed by palettes by Moreland and others. address. Its definitions relevant here are:

  set palette defined (0  0.0 0.0 0.5, \
                   1  0.0 0.0 1.0, \
                   2  0.0 0.5 1.0, \
                   3  0.0 1.0 1.0, \
                   4  0.5 1.0 0.5, \
                   5  1.0 1.0 0.0, \
                   6  1.0 0.5 0.0, \
                   7  1.0 0.0 0.0, \
                   8  0.5 0.0 0.0 )
      

  

• For diverge data, using a blue-white-red transient is a good choice to begin with. For the RGB color space by the pngcairo terminal, these palettes may be defined by ‘named colors’ as with either of the example instructions below. Similar as seen with Moreland’s palettes, it is helpful to decrease the maximal luminosity, though (second example).

  set palette defined (-1 "blue", 0 "white", 1 "red")
  set palette defined (-1 "blue", 0 "light-gray", 1 "red")
      

  

  

Generation of the data

Departing from Moreland’s RGB palettes defined as floating numbers, script csv2plt.py (sub-folder tools) reformatted the entries to five decimals. Script RGB_check.py provided a control if the RGB tuples converted stay within the permitted interval of $[0,1]$.

Script palette_decomposition.py provided a quick channel-wise decomposition of the RGB color space, complemented by the NTSC luminosity. Each synopsis per .plt file displays this result in between the test plots in color and gray-scale.

Script bessel_test_center.py computed the synthetic data of the Bessel function $f(x,y) = x^2 + y^2$ eventually displayed as color plot. It called ImageMagick to convert this result into gray-scale, and concatenated the two plots with the diagram by palette_decomposition.py.

Comparison of similar palettes

Gnuplot’s rapid scrutiny about the contribution of R, G, and B channel of a palette, reported as .png, allows a programmatic visual comparison of palettes with each other. This task addressed by script vignette_comparison.py, to be run right after palette_decomposition.py, without provision of parameters from the CLI by

python3 vignette_comparison.py

Each pairwise comparison yields a new file named in the pattern of diff_fileA_fileB.png. Differences identified by ImageMagick will be indicated with bright red pixels. This reveals, for example, palette magma.pal provided by gnuplotting.org[fn:4] / gnuplot-palettes differs from all magma.plt definitions derived from Kenneth Moreland’s palettes based on floating numbers in this repository as illustrated below, or with animation magma_diff.gif (in sub-folder extra_palette_tests).

Sub-folder extra_palette_tests/magma_testing/ includes further details about this analysis and an animated .gif about all tests performed relevant here. This and all other data processing was run under Linux (Xubuntu 18.04.3 LTS) with CPython (3.6.8, October 7, 2019), gnuplot (5.2.7beta, last modified 2019-05-14), and ImageMagick (6.9.7-4 Q16).

Vector-based export

It is possible to engage gnuplot’s set terminal pdfcairo instruction to provide a native export of the results as the resolution independent .pdf format. This was tested for the palette maps of 512 explicitly defined colors with now 256 iso samples computed by gnuplot for the same Bessel function. While this document contains only the example for the continuously smooth viridis palette, tests with this and the other palettes are stored in sub-folder pdf-tests.

./pdf_tests/viridis-table-float-0512_test.pdf

Footnotes

[fn:1] http://www.kennethmoreland.com/color-advice/ [fn:2] https://github.com/aschn/gnuplot-colorbrewer [fn:3] https://github.com/Gnuplotting/gnuplot-palettes [fn:4] http://www.gnuplotting.org/