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If you are interested in color, explore my other color tools, Brewer palettes resources, color blindness palettes and math and an exhausting list of 10,000 color names for all those times you couldn't distinguish between tan hide, sea buckthorn, orange peel, west side, sunshade, california and pizzaz.

Designing for Color blindness

Color choices and transformations for deuteranopia and other afflictions

Here, I help you understand color blindness and describe a process by which you can make good color choices when designing for accessibility.

The opposite of color blindness is seeing all the colors and I can help you find 1,000 (or more) maximally distinct colors.

You can also delve into the mathematics behind the color blindness simulations and learn about copunctal points (the invisible color!) and lines of confusion.

In an audience of 8 men and 8 women, chances are 50% that at least one has some degree of color blindness1,2. When encoding information or designing content, use colors that is color-blind safe.

1About 8% of males and 0.5% of females are affected with some kind of color blindness in populations of European descent (wikipedia, Worldwide prevalence of red-green color deficiency, JOSAA). The rate for other races is lower Asians and Africans is lower (Caucasian Boys Show Highest Prevalence of Color Blindness Among Preschoolers, AAO).

2The probability that among `N=8` men and `N=8` women at least one person is affected by color blindness is `P(men,women) = P(8,8) = 1 - (1-0.08)^8(1-0.005)^8 = 0.51`. For `N=34` (i.e., 68 people in total), this probability is `P(34,34)=0.95`. Because the rate of color blindness in women is so low, for most groups of mixed gender we can approximate the probability by only counting the men. For example, in a group of 17 women the probability that at least one of them is color blind is `P(0,17) = 0.082`, which is the same probability as for 1 man, `P(1,0)`.

color receptors are reduced or absent in color blindness

The normal human eye is a 3-channel color detector3. There are three types of photoreceptors, each sensitive to a different part of the spectrum. Their combined response to a given wavelength produces a unique response that is the basis of the perception of color.

3Compared to hearing, the color vision is a primitive detector. While we can hear thousands of distinct frequencies and process them simultaneously, we have only three independent color inputs. While the ear can distinguish pure tones from complex sounds that have multiple frequencies the eye is relatively unsophisticated in separating a color sensation into its three constituent primary stimuli.

People with color blindness have one of the photo receptor groups either reduced in number or entirely missing. With only two groups of photoreceptors, the perception of hue is drastically altered.

For example, in deuteranopia, the most common type of color blindness, the medium (M) wavelength photoreceptors are reduced in number or missing. This results in the loss of perceived difference between reds and greens because only one group of photoreceptors (L) are sensitive to the wavelengths of these colors. The spectrum appears to be split into two hues along the blue-green boundary (see figure below), which is roughly where the photoreceptor sensitivities curves cross.

Color photoreceptor profile for color blindness and the appearance of art and objects. / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Each of the three kinds of color blindness are associated with reduced number of each of the three kinds of photoreceptors. In extreme cases, a given type of photoreceptors may be missing. To people with color blindness, objects appear very differently. Artwork is (left) Edvard Munch, Scream (Skrik), 1893, National Gallery, Oslo, Norway (right) Claude Monet, Coquelicots, La promenade (Poppies), 1873, Musée d'Orsay, Paris. Each of the rows in the color ramps on the right show colors that are indistinguishable for each kind of color blindness. (zoom)

Visible light is in the range of 390–700 nm. The exact definition of the upper limit varies, with some sources giving as high as 760 nm. Shorter wavelengths are absorbed by the cornea (<295nm) and lens (315–390nm). Some near infrared light also reaches the retina (760–1,400nm).

it's all the same to me

The Ishihara test is a color perception test for protanopia and deuteranopia. Think of the Rorschach test, except with a different diagnosis if you can't see a pattern.

Traditionally, the Ishihara test is performed with digits but why not use Mr. Spock4. He knows all the digits and is much more insteresting.

4In tribute to Leonard Nimoy, 1931–2015

Spock, indistinguishable to people with color blindness. / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The likeness of Mr. Spock drawn using equivalent colors (see image above) for each of the three kinds of color blindness. Image from imagebuddy. (zoom)

simulating color blindness

Color blindness comes in varying degrees and types. Let's consider total deuternanopia—where the M receptors are missing or completely dysfunctional. Because they only have two kinds of color receptors, someone with this condition will see only two dimensions of color.

To understand how to simulate color blindness we have to look briefly at how color can be represented. You're probaby familiar with the RGB color space—just one kind of many color spaces. The RGB coordinates of a color are a device-dependent output model—they tell a device, such as your monitor or TV how much of a pixel's red, green and blue to activate. Obviously, depending on which specific display panel we're talking about, the output color might actually look very different—it's a function of the actual phosphors and any calibration and adjustments.

It turns out that we can also specify color in terms of coordinates in a space based on the physiological response of the eye to the color. Since a normal eye has three photoreceptors whose sensitivity is centered on short (S), medium (M) and long (L) wavelengths, any given color (i.e. monochromatic light) creates a unique combination of S, M and L cone response.

Using a color's LMS coordinates we can simulate color blindness by modifying the coordinate that corresponds to the missing photoreceptor under the observations that (a) deuteranopes, for example, can distinguish white and greys from blues and greens and (b) colors for which the sensitivity of the missing photoreceptors is low should be perceived normally.

Using the LMS color space to simulate color blindness / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Color blindness can be simulated by considering a color's coordinates in LMS space. (zoom)

Because color blindess reduces the number of color dimensions, a large number of colors distinguishable to people with normal vision appear the same to someone with color blidness. The ramps below show these families of equivalent colors.

Color palettes and selections for color blindness / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Sets of representative hues and tones that are indistinguishable to individuals with different kinds of color blindness. (zoom)

super color vision

The opposite condition to color blindness exists too—tetrachromacy. In this case, an individual has an extra type of color receptor which improves discrimination in the red part of the spectrum. While the anatomy of their retina can be described, how true tetrachromats subjectively perceive color is unknown. And, perhaps, even unknowable.

Tetrachromacy is common in other animals, such as fish (e.g. goldfish, zebrafish) and birds (e.g. finch, starling). The dimensionality of the perceived color space isn't necessarily proportional to the number of different receptors. If the signal from 3 color receptors are combined by the brain and each processor has a weighted response to a broad range of wavelengths, then a color can be modeled by a point in 3-dimensional space, in which the receptors are the axes. This system can perceive a large number of colors.

In the extreme case where the receptors respond to a very narrow range, of which none overlap with the other, a color is one of three points in a 1-dimensional space. This sytem can perceive only 3 colors.

For example, although the mantis shrimp has 12 different color receptors, the receptors work independently, their color discrimination is poorer than ours.

news + thoughts

Propensity score weighting

Mon 04-05-2026

It is not certain that everything is uncertain. —Blaise Pascal

We have already explored how we can mitigate bias caused by confounding variables in observational studies using propensity score (PS) matching (PSM) and propensity score weighting (PSW). However, any statistical model is only as good as its assumptions and, if it is specified incorrectly, it can itself produce biased estimates of the treatment effect.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Double Robustness. (read)

This month, we explore double robustness, a powerful statistical concept that provides a valuable “safety net” against the risk of an incorrect model. It offers two opportunities, instead of just one, to obtain a valid estimate of the treatment effect — making it possible to draw credible causal inferences from observational data without having to depend on a single set of modeling assumptions.

Kurz, C.F., Krzywinski, M. & Altman, N. (2026) Points of significance: Double Robustness. Nat. Methods 23:868–869.

Nature Biotechnology cover

Thu 23-04-2026

My cover design on the 7 April 2026 Nature Biotechnology issue shows the dendrogram that represents a cluster of uniquely expressed (or downregulated) genes in human naive stem cells induced from such cells. Within each dendrogram block, the genomic barcode sequence (sampled from Supplementary Table 1) is depicted with a Code 39 barcode. The highlighted barcode is one of those used for cell isolation.

Ishiguro S. et al. A multi-kingdom genetic barcoding system for precise clone isolation (2026) Nature Biotechnology 44:616–629.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
My Nature Biotechnology phylogenetic tree cover (volume 44, issue 4, 7 April 2026). (more)

Browse my gallery of cover designs.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A catalogue of my journal and magazine cover designs. (more)

Happy 2026 π Day—
Art for the 5%

Fri 13-03-2026

Celebrate π Day (March 14th) and enjoy the art — but only if you're part of the 5%.

Go ahead, see what you can't see.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2026 π DAY | Art for the 5%. Shown in the style of Ishihara color test plates, the art is visible only to those with colour blindness. (details)

Ishihara's Tests for Colour Deficiency

Sun 08-03-2026

Authentic and accurate images of Ishihara's test plates photographed (and lovingly color-corrected) from the 38-plate Ishihara's Tests for Colour Deficiency.

I also provide the position, size, and color of each circle on each test plate.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
ISHIHARA'S TEST PLATE 6 | This plate is part of the set of transformation plates. If you see 5, you're ok. If you see 2, you're not. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
ISHIHARA'S TEST PLATE 18 | This plate is part of the set of mysterious hidden plates. If you don't see anything, you're ok. If you see 5, you're not. (details)

Symmetric alternatives to the ordinary least squares regression

Wed 23-07-2025

What immortal hand or eye, could frame thy fearful symmetry? — William Blake, "The Tyger"

This month, we look at symmetric regression, which, unlike simple linear regression, it is reversible — remaining unaltered when the variables are swapped.

Simple linear regression can summarize the linear relationship between two variables `X` and `Y` — for example, when `Y` is considered the response (dependent) and `X` the predictor (independent) variable.

However, there are times when we are not interested (or able) to distinguish between dependent and independent variables — either because they have the same importance or the same role. This is where symmetric regression can help.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Symmetric alternatives to the ordinary least squares regression. Geometry of quantities minimized in OLS and symmetric regression. OLS minimizes `\Sigma e_y^2` in `Y` ~ `X` and `\Sigma e_x^2` `X` ~ `Y`. Pythagorean regression minimizes AB (magenta). Geometric means regression (GMR) minimizes area of ABP (orange). Orthogonal regression (OR) minimizes HP (blue). (read)

Luca Greco, George Luta, Martin Krzywinski & Naomi Altman (2025) Points of significance: Symmetric alternatives to the ordinary least squares regression. Nat. Methods 22:1610–1612.

Martin Krzywinski | contact | Canada's Michael Smith Genome Sciences CentrePHSA
Google whack “vicissitudinal corporealization”
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