Martin Krzywinski / Genome Sciences Center / Martin Krzywinski / Genome Sciences Center / - contact me Martin Krzywinski / Genome Sciences Center / on Twitter Martin Krzywinski / Genome Sciences Center / - Lumondo Photography Martin Krzywinski / Genome Sciences Center / - Pi Art Martin Krzywinski / Genome Sciences Center / - Hilbertonians - Creatures on the Hilbert Curve
In your hiding, you're alone. Kept your treasures with my bones.Coeur de Piratecrawl somewhere bettermore quotes

saturation: beautiful

DNA on 10th — street art, wayfinding and font

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

Markov Chains

Tue 30-07-2019

You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts

A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Markov Chains. (read)

Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.

Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.

This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

1-bit zoomable gigapixel maps of Moon, Solar System and Sky

Mon 22-07-2019

Places to go and nobody to see.

Exquisitely detailed maps of places on the Moon, comets and asteroids in the Solar System and stars, deep-sky objects and exoplanets in the northern and southern sky. All maps are zoomable.

Martin Krzywinski @MKrzywinski
3.6 gigapixel map of the near side of the Moon, annotated with 6,733. (details)
Martin Krzywinski @MKrzywinski
100 megapixel and 10 gigapixel map of the Solar System on 20 July 2019, annotated with 758k asteroids, 1.3k comets and all planets and satellites. (details)
Martin Krzywinski @MKrzywinski
100 megapixle and 10 gigapixel map of the Northern Celestial Hemisphere, annotated with 44 million stars, 74,000 deep-sky objects and 3,000 exoplanets. (details)
Martin Krzywinski @MKrzywinski
100 megapixle and 10 gigapixel map of the Southern Celestial Hemisphere, annotated with 69 million stars, 88,000 deep-sky objects and 1000 exoplanets. (details)

Quantile regression

Sat 01-06-2019
Quantile regression robustly estimates the typical and extreme values of a response.

Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Quantile regression. (read)

Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.

Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nature Methods 16:451–452.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nature Methods 12:999–1000.

Analyzing outliers: Robust methods to the rescue

Sat 30-03-2019
Robust regression generates more reliable estimates by detecting and downweighting outliers.

Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Analyzing outliers: Robust methods to the rescue. (read)

We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.

Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.

Background reading

Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.