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Generating n Optimally Differentiatable colours

Mr Tufte,

I sometimes have issues with default colours in graphs being too similar to each other to be easily differentiated.

Given a number n (assume between 5 and 25 or so) is there an algorithm to generate a set of RGB colours that are most differentiatable from each other to the human eye? I believe such an algorithm may need to take into account human biology.

I firmly believe research on this subject must have been done and yet I can't find anything, not even canned lists of 12 optimally differentiatable colours for instance.

Have you come across this problem in your travels?

Thanks in advance,

-- Paul Vallee (email)

IMO The introduction to Josef Albers 'Interaction of Color" says it best.... ISBN 0-300-01846-0

[link updated February 2005]

-- Ziska Childs (email)

Check out the color brewer. I think it has been referenced on this forum before but it may be useful to your problem. It has color schemes that are optimized for cartography and organised in various categories (i.e. divergent, sequential schemes. Work was done by Cynthia Brewer hence the clever name.

-- Martin Gamache (email)

This subtle and intensely multivariate issue is discussed in detail in Imhof, Cartographic Relief Presentation. Also there are some ideas in the color chapter in my Envisioning Information, and in the smallest effective difference chapter in Visual Explanations.

The issues include the frequency distribution of the content (e.g., the pattern of variation in depths of the ocean), the non-linear link between perceived steps and display steps, the surrounding context, the context itself (do you want typography on the stepped field?), plenty of variation introduced by the printing process or by different computer monitors of wildly different color calibrations, individual variation in perceiving color steps, perceptual artifacts (edge fluting, interaction of colors),and color-perception difficiencies in a few viewers.

Some conclusions: (1) Nothing can be called "optimal", except by the marketing department. Even seeking local optimality may be naive. We can avoid pessimizing; maybe we can satisfice locally. (2) Cartographers have dealt with these issues for at least 100 years; for ideas look at good maps. Multivariate cartographic craft beats univariate or bivariate engineering. (3) At least the color scales should yield a clear sense of perceived proportionality (which disqualifies rainbow color scales). Usually this proportionality should be picked up in the value (or perhaps the saturation) of the color. If value, then a rough test of the color scale is: does it work as a gray scale? (4) The quantitative message needs to be carried not only by color but also by quantitative labels (e.g., mountain peaks labeled with specific heights). (5) Well-labeled contour lines seem to be a good start. (6) To be an alert viewer requires knowing how to read a contour map.

Serious thinking about color is very complex, at the level of molecular biology or late Beethoven string quartets.

-- Edward Tufte

A few more leads.

"Color and Culture" by John Gage

"The Island of the Color Blind" by Oliver Sacks

"Colors the Story of Dyes and Pigments" by Francois Delamare and Bernard Guineau

and the all time classic:

"The Artist's Handbook" by Ralph Mayer

Then there was the way John Gleason would start his color lecture for theatrical lighting design. "White can be any color you want it to be...." He taught color by key (major/minor), loudness, rhythm, orchestration and intervals. Above all else color denoted the level of reality.

-- Ziska Childs (email)

The subject of Ziska's link at his own site:

-- Niels Olson (email)

Scroll down to "CIELUV u*v* hue plane"

Give me strength.

-- Ziska Childs (email)

For a completely mathematical approach there are software packages that can generate color combinations (, These obviously don't take into account the viewer's perceived color.

-- Corey Newport (email)

Apologies if this has already been posted

-- Ziska Childs (email)

Something similar to the color brewer, but more dynamic: I can only get it to work in Explorer, although that may be due to some settings on my end. Does anyone know how to make this work in Mozilla (or Firefox), what the algorithms are, or who maintains this site?

-- Niels Olson (email)

ColorMixers was a mirror to a previous version of ColorMatch Remix which is now at It is cross-browser compliant, and all the code is open source and available for download. HTH. —tec

-- Thomas E. Cason (email)

This site can generate color schemes and the nice thing is the drop-down box that modifies the color scheme you've selected to that of a particular color-blind segment of the population.


-- Sean Gerety (email)

I have looked for something similar, and decided to use a hue sequencing algorithm. There are "tetrad" and "triad" algorithms that make use of the hue color wheel to generate contrasting, complementary colors, which I use on each hue in the sequence.

If you need more colors, you can then reuse the hue sequence with different value and saturation to create pastels and other effects.

This Javascript color scheme generator was helpful in visualizing the color wheel and playing with hopping algorithms. I found the 15-degree increment to be a good start.


Good luck, Casey

-- Casey Marshall (email)

Ethnic distribution maps in southwest China

Dear Paul and Professor Tufte,

I've run into precisely the same question in my research on ethnic categorization in southwest China. Following the tabulation of data in the first census of the People's Republic of China in 1953-4, the southwestern province of Yunnan clocked in with a staggering 260+ separate ethnic names. Through the taxonomic intervention of the state and social scientists, this number was reduced to about 24 over the following years.

I'm delivering a job talk soon, and I would like to produce "before and after" distribution maps, so that my audience can get a clear sense of the current demography of Yunnan, and how it compares with what Yunnan "might have looked like" had the Communist authorities honored their initial policy of ethnic self-determination and ethnonymic non-intervention. I think this would be a powerful way to convey the material and bureaucratic constraints that play a part in demography (much the way that mundane material constraints - such as the layout of standardized medical forms - cycle back and affect the number of recognized diseases, as Bowker and Star have shown in "Sorting Things Out").

Is it even possible to produce a reasonably sized map which can successfully convey the distribution of 260+ groups (some of which appeared in the census registers with populations of only 1 person!)

Tom Mullaney Columbia University

-- Tom Mullaney (email)

Does Yunnan have many small subdivisions?

-- Niels Olson (email)

Consider using a supertable, with places ordered by your most important data column. Then put rank numbers in front of each name and put those numbers, properly located, on a map.

-- Edward Tufte

An excellent paper with information spanning your threads on horizons, color, and photography. In challenging current dogma that stimulating specific cones leads to perception of a specific hue, the refutation includes numbers for just perceptible and bright light (.25 microwatts to 1.25 microwatts on the retina) and provides a host of keywords and historically significant papers.

Hofer H, Singer B, Williams DR. Different sensations from cones with the same photopigment. J Vis, 2005:5. 444-454.

-- Niels Olson (email)

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