Turbo, an Improved Rainbow Colormap for Visualization

Where jet and other non-uniform maps are useful is in highlighting small fluctuations in the value. It's less about z1 > z2 and more about z1 != z2 across the image plane.

A similar problem happens with datashader in histogram normalisation mode. It's great for highlighting small variations in the underlying density and revealing detail that you'd otherwise never see, but worthless for trying to compare one density to another by eye.

Horses for courses.

I've tried inferno and viridis to visualize weather radar data, and... rainbow-like colormap simply works better. And this is true for most weather data like wind or temperature. With a uniform colormap, you wouldn't be able to see local variations, e.g. differences in temperature within the UK.

If you want to represent a one-dimensional gradient where what is most important is "hot vs cold", i.e. the extremes, then you shouldn't be using a colormap (rainbow) in the first place, you should be using a direct gradient instead, whether grayscale or interpolated between two nearby colors (e.g. red/yellow).

Colormaps are for where highlighting local variation is important -- more important than indicating whether something is closer to one extreme or another. In the examples, this means being able to distinguish the patterns of the objects. In math plots, it means helping to see the shapes of curves. In weather maps, that means judging variation within your state, even while the map ranges from Alaska to Florida.

For this, it's most important to be able to maximize contrast in local differences but also have the perceptual rate of change be roughly comparable.

Rainbows maximize contrast using hue, because our eyes can simply distinguish so much more than with just brightness. Turbo makes the rate of change more constant than Jet. And Jet/Turbo most importantly double the resolution that Inferno has, going from dark-bright-dark rather than just dark-bright.

Computers are already really good at dealing with large-scale details. The human eye can notice edge-case scenarios in a large dataset pretty rapidly. I'm sold on Turbo because it lets your eyes change scale on the fly. You can be looking at the large scale and rapidly focus in on particulars within a smaller band, and back out again, as needed.

It looks like Turbo is just Jet, but plotted in CIECAM02-UCS (instead of Jet's HSV). It removes many disadvantages of Jet, while keeping Jet's advantage over Viridis/Inferno of making it easier to compare/contrast small differences.

The video and the blog post actually go over a lot of the same topics, like perceptual lightness and how Jet was found to lead to mistakes reading medical imaging.

I'm not sure what analysis you're looking for; the video's a good explanation of color theory, but its analysis of Viridis is mainly just "we plotted a line through CIECAM02-UCS color space and made it linear lightness". Turbo is the same, except the line is curvier and not linear lightness – and the blog post goes through the tradeoffs of that approach.

Anyway, as someone with protanomally: thank you! This looks so much better than Jet, and I just pinged my coworkers what they think about replacing our current rainbow map with this one. Having the d3 code already available makes that already low threshold even lower.

Per my reading of the blog post, they ran some images through a random color vision deficiency simulation website and decided that they looked good enough; while lightness plots are displayed for normal color vision, no such plots are shown for simulated color vision deficiency. Also, best I can tell, the simulator they used is based on a 1988 paper [1] instead of more recent and accurate techniques [2].

For an example of where color vision deficiency was actually properly considered for the development of a colormap, see Cividis [3].

[1] https://doi.org/10.1109/38.7759 [2] https://doi.org/10.1109/TVCG.2009.113 [3] https://doi.org/10.1371/journal.pone.0199239

The practical issue is that not many people really use Rainbow instead of Jet, for the reasons I mentioned in the article (it sacrifices too many of the 'good bits' of Jet). So instead I chose to compare to the more 'widely recommended' maps.

But you're right, I should have thrown rainbow into the mix, even if I didn't have the space to write about it.

"The background in the following images is barely distinguishable with Inferno (which is already punchier than Viridis), but clear with Turbo." (and presumably also Jet)

> Why would anyone want low-to-high-to-low colormap?

I'm assuming because "it greatly enhances detail when color can be used to disambiguate the low and high ends" and "to make cases where low values appear next to high values more distinct".

> What are the desirable properties of Jet?

Pretty much the only desirable property is that it used to be the Matlab default, and therefore has been used frequently and people are familiar with it.

Taking it as a starting point for a design is quite a poor choice. The design process here is pretty much just “we took jet and applied some blur to the apparent lightness”; this is not a principled or careful method, in my opinion.

One good use for this new color map might be: “My ignorant boss keeps insisting on using the jet color map even though it is terrible. I can drop this one in and he won’t notice the difference but it will be somewhat better, even if still problematical in many ways.”

> Why would anyone want low-to-high-to-low colormap?

This is sometimes called a “diverging” color map, and can be useful when e.g. you want to make choropleth map highlighting percentage of voters for Party A vs. Party B. You can make a 1/2:1/2 split of voters light and neutrally colored, and make the color get darker but with two different hues as the proportion gets more lopsided in favor of one party or the other.

But the lightness map on each side should still be more or less linear, and the obvious visual artifact created for the balance point has some concrete meaning.

Cf. https://www.kennethmoreland.com/color-maps/ https://www.kennethmoreland.com/color-advice/

[1]: https://arxiv.org/ftp/arxiv/papers/1712/1712.01662.pdf [2]: https://github.com/marcosci/cividis

So if you use one and only one colorspace for some heatmap visualization, I think I would greatly appreciate using Inferno (or Helix, or similar) instead of Turbo in the most cases.

But if you plot it in CIELAB or CIECAM02-UCS, it's likely not a straight vector but rather a curved path. A vector would only interpolate between ~two hues (like Vidris, Inferno), whereas Turbo covers multiple hues. Have a look at the lightness profile plots in the post, it should give you a rough idea about how the vector must look in color spaces such as CIELAB.

There are studies where doctors got to view MRI data under different color maps when screening for cancer. Using the 'right' map (which was different from their preferred choice) improved both the speed and accuracy of the diagnosis.

Basically changing color maps can radically change how you interpret the data being displayed.

That’s a reasonable discussion to have. In particular, Helvetica should not be used for setting long blocks of text.

The design choices in Helvetica make it an appropriate choice for posters, corporate logos, headings, ..., but not appropriate for research papers. Many other possible choices are more legible.