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hue: fun

UCD Computational and Molecular Biology Symposium, Dublin, Ireland. 1-2 Dec 2016.

visualization + design

Brewer Palettes

Brewer Palettes at a Glance

Martin Krzywinski @MKrzywinski
All the Brewer palettes: qualitative, sequential and diverging. For each palette (e.g. spectral) the source colors are shown as well as all its n-color subsets. (zoom)

Presentation About Color and Brewer Palettes

If you're new to Brewer palettes, or color, catch up with this presentation. Color palettes matter - Brewer palettes and perceptual uniformity - Martin Krzywinski


I maintain a comprehensive database of named colors (3,116 colors), compiled from a variety of color name lists.

Visualization and Perception

Why Should Engineers and Scientists Be Worried About Color? by Bernice E. Rogowitz and Lloyd A. Treinish (IBM Thomas J. Watson Research Center, Yorktown Heights, NY).

Perception in Visualization by Christopher G. Healey (Department of Computer Science, North Carolina State University)

LAB and LCH gradient picker

Martin Krzywinski @MKrzywinski
Interactively create LAB and LCH color gradients interpolated across any number of colors.

Lch and Lab colour and gradient picker is a great tool by David Johnstone. It's a great way to generate color ramps—go ahead, go crazy!—and compare how the ramps look in different color spaces. Shame on you, HSV!

PaletteView — create continuous Brewer palettes

PaletteView is an exceptional tool by Magnaview to create continuous Brewer palettes. This tool is described in [1] and operationalizes Cyntha Brewer's color selection method into an algorithm that selects customizable color palettes from LCH space.

[1] Wijffelaars M, Vliegen R, Van Wijk JJ et al. 2008 Generating Color Palettes using Intuitive Parameters Computer Graphics Forum 27:743-750.

Brewer Palette Adobe Swatch Files

You can import Brewer palettes into Adobe applications such as Illustrator, Photoshop and InDesign using either the .ase or .ai swatch files.


Brewer palette ase swatch file for Adobe Illustrator Brewer palette ai swatch file for Adobe Illustrator Brewer palette pdf color file Brewer palette txt color file


In Illustrator, load the swatches from the swatch window menu. The swatch window can be accessed using Window > Swatches.

Select Open swatch library

then choose Other library...

and load either the .ase or .ai file — both contain the same content.

Brewer palettes are color combinations selected for their special properties for use in data visualization and information design.

The challenge

Selecting effective colors for bar plots, pie charts, and heat maps is made more difficult by the fact that the way we select color in software does not reflect how we perceive the color.

There are many examples of poor color combinations in published figures. For example, if categories are encoded with a combination of bright and dark colors, the bright colors will dominate the reader's attention. On the other hand, if two colors appear similar, the reader will instinctively perceive them as belonging to a group and infer that the underlying variables are related.

Colors with poor contrast (colors with similar perceived brightness) or simultaneous contrast (pure colors) also interfere with interpreting figures.

Selecting Colors in RGB and HSV

Most people select colors using RGB sliders, which is just about the worst way to pick a color! Consider the fact that when we look at a color, we cannot easily decompose it into its red, green and blue components. This limits usefulness of RGB for color selection.

HSV is a better color space, which defines a color based on hue, saturation and value. These are three properties that we intuitively assess when we see a color. We think of a "dark rich blue" and "light faded red", making HSV a reasonably useful model for color selection. Unfortunately, HSV has a nagging problem — although it is based on intuitive parameters, it is not perceptually uniform.

Perceptual Uniformity

A color space that is perceptually uniform defines colors based on how we perceive them. Distances between colors in the space are proportional to their perceived difference.

Above, we saw that HSV was not perceptually uniform. Moving the hue slider by 60 can have a small or large effect on a color, depending on where the slider is positioned.

Consider the following example. You have a chart that uses two colors, and orange and green. Both were chosen with S=V=100%. You now need to select a second color for each that is brighter. You cannot directly use HSV because both orange and green colors are already at full value. How do you intuitively increase brightness?

The reason why you cannot in do this in HSV is because V does not directly correspond to the color's perceived brightness. You are stuck fiddling with the saturation and value to try to select a brighter pairing.

What would be useful here is a color space which uses the intuitive parameters of HSV, but is perceptually based. In other words, instead of value, the space would define a color based on its perceived brightness. Luckily, this space exists — LCH, which defines color based on its luminance (perceived brightness), chroma (purity) and hue. Unfortunately, design and presentation software do not have LCH sliders and we cannot easily take advantage of this color space.

This is where the Brewer palettes come in.

Brewer Palettes

Brewer palettes were selected for their perceptual properties. These palettes were created by Cynthia Brewer for the purpose in cartography, but have found use in other fields.

Types of Brewer Palettes

There are three types of Brewer palettes

  • qualitative — colors do not have a perceived order
  • sequential — colors have a perceived order and perceived difference between successive colors is uniform
  • diverging — two back-to-back sequential palettes starting from a common color

Swatches of Brewer Palettes

I have prepared Brewer palette swatches in .ase or .ai format. For programming, use the plain-text version.

The image below (zoom) shows all the Brewer palettes.

Brewer palette colors - all swatches

Uses of Brewer Palettes

Qualitative palettes are excellent for bar plots and pie charts, where colors correspond to categories.

Grayscale Brewer palettes are available and are perfect for achieving good tone separation in black-and-white figures.

Sequential and diverging palettes are useful for heatmaps.

Brewer Palettes and Color Blindness

Some Brewer palettes are safe for color blindness — the pink-yellow-green (piyg) is one. For others, see colorbrewer.

I have designed 15-color palettes for color blindess for each of the three common types of color blindness.


news + thoughts

Happy 2016 `\pi` Approximation, roughly speaking

Thu 21-07-2016

Today is the day and it's hardly an approximation. In fact, `22/7` is 20% more accurate of a representation of `\pi` than `3.14`!

Time to celebrate, graphically. This year I do so with perfect packing of circles that embody the approximation.

By warping the circle by 8% along one axis, we can create a shape whose ratio of circumference to diameter, taken as twice the average radius, is 22/7.

If you prefer something more accurate, check out art from previous `\pi` days: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, and 2016 `\pi` Day.

Logistic Regression

Wed 13-07-2016

Regression can be used on categorical responses to estimate probabilities and to classify.

The next column in our series on regression deals with how to classify categorical data.

We show how linear regression can be used for classification and demonstrate that it can be unreliable in the presence of outliers. Using a logistic regression, which fits a linear model to the log odds ratio, improves robustness.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Logistic regression? (read)

Logistic regression is solved numerically and in most cases, the maximum-likelihood estimates are unique and optimal. However, when the classes are perfectly separable, the numerical approach fails because there is an infinite number of solutions.

Altman, N. & Krzywinski, M. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

Background reading

Altman, N. & Krzywinski, M. (2016) Points of Significance: Regression diagnostics? Nature Methods 13:385-386.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.

...more about the Points of Significance column

Visualizing Clonal Evolution in Cancer

Thu 02-06-2016

Genomic instability is one of the defining characteristics of cancer and within a tumor, which is an ever-evolving population of cells, there are many genomes. Mutations accumulate and propagate to create subpopulations and these groups of cells, called clones, may respond differently to treatment.

It is now possible to sequence individual cells within a tumor to create a profile of genomes. This profile changes with time, both in the kinds of mutation that are found and in their proportion in the overall population.

Martin Krzywinski @MKrzywinski
Ways to present temporal and phylogenetic evolution of clones in cancer. M Krzywinski (2016) Molecular Cell 62:652-656. (read)

Clone evolution diagrams visualize these data. These diagrams can be qualitative, showing only trends, or quantitative, showing temporal and population changes to scale. In this Molecular Cell forum article I provide guidelines for drawing these diagrams, focusing with how to use color and navigational elements, such as grids, to clarify the relationships between clones.

Martin Krzywinski @MKrzywinski
How to draw clone evolution diagrams better. M Krzywinski (2016) Molecular Cell xxx:xxx-xxx. (read)

I'd like to thank Maia Smith and Cydney Nielsen for assistance in preparing some of the figures in the paper.

Krzywinski, M. (2016) Visualizing Clonal Evolution in Cancer. Mol Cell 62:652-656.

Binning High-Resolution Data

Wed 01-06-2016

Limitations in print resolution and visual acuity impose limits on data density and detail.

Your printer can print at 1,200 or 2,400 dots per inch. At reading distance, your reader can resolve about 200–300 lines per inch. This large gap—how finely we can print and how well we can see—can create problems when we don't take visual acuity into account.

Martin Krzywinski @MKrzywinski
Nature Methods Points of View column: Binning high-resolution data. (read)

The column provides some guidelines—particularly relevant when showing whole-genome data, where the scale of elements of interest such as genes is below the visual acuity limit—for binning data so that they are represented by elements that can be comfortably discerned.

Krzywinski, M. (2016) Points of view: Binning high-resolution data. Nature Methods 13:463.

...more about the Points of View column