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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 colorblindness 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.

R code for converting an RGB color for color blindness. For details see the math tab and the resources section for background reading.

--- title: 'RGB color correction for color blindess: protanopia, deuteranopia, tritanopia' author: 'Martin Krzywinski' web: http://mkweb.bcgsc.ca/colorblind --- ```{r} gamma = 2.4 ############################################### # Linear RGB to XYZ # https://en.wikipedia.org/wiki/SRGB XYZ = matrix(c(0.4124564, 0.3575761, 0.1804375, 0.2126729, 0.7151522, 0.0721750, 0.0193339, 0.1191920, 0.9503041), byrow=TRUE,nrow=3) SA = matrix(c(0.2126,0.7152,0.0722, 0.2126,0.7152,0.0722, 0.2126,0.7152,0.0722),byrow=TRUE,nrow=3) ############################################### # XYZ to LMS, normalized to D65 # https://en.wikipedia.org/wiki/LMS_color_space # Hunt, Normalized to D65 LMSD65 = matrix(c( 0.4002, 0.7076, -0.0808, -0.2263, 1.1653, 0.0457, 0 , 0 , 0.9182), byrow=TRUE,nrow=3) # Hunt, equal-energy illuminants LMSEQ = matrix(c( 0.38971, 0.68898,-0.07868, -0.22981, 1.18340, 0.04641, 0 , 0 , 1 ), byrow=TRUE,nrow=3) # CIECAM97 SMSCAM97 = matrix(c( 0.8951, 0.2664, -0.1614, -0.7502, 1.7135, 0.0367, 0.0389, -0.0685, 1.0296), byrow=TRUE,nrow=3) # CIECAM02 LMSCAM02 = matrix(c( 0.7328, 0.4296, -0.1624, -0.7036, 1.6975, 0.0061, 0.0030, 0.0136, 0.9834), byrow=TRUE,nrow=3) ############################################### # Determine the color blindness correction in LMS space # under the condition that the correction does not # alter the appearance of white as well as # blue (for protanopia/deuteranopia) or red (for tritanopia). # For achromatopsia, greyscale conversion is applied # to the linear RGB values. getcorrection = function(LMS,type="p",g=gamma) { red = matrix(c(255,0,0),nrow=3) blue = matrix(c(0,0,255),nrow=3) white = matrix(c(255,255,255),nrow=3) LMSr = LMS %*% XYZ %*% apply(red,1:2,linearize,g) LMSb = LMS %*% XYZ %*% apply(blue,1:2,linearize,g) LMSw = LMS %*% XYZ %*% apply(white,1:2,linearize,g) if(type == "p") { x = matrix(c(LMSb[2,1],LMSb[3,1], LMSw[2,1],LMSw[3,1]),byrow=T,nrow=2) y = matrix(c(LMSb[1,1],LMSw[1,1]),nrow=2) ab = solve(x) %*% y C = matrix(c(0,ab[1,1],ab[2,1],0,1,0,0,0,1),byrow=T,nrow=3) } else if (type == "d") { x = matrix(c(LMSb[1,1],LMSb[3,1], LMSw[1,1],LMSw[3,1]),byrow=T,nrow=2) y = matrix(c(LMSb[2,1],LMSw[2,1]),nrow=2) ab = solve(x) %*% y C = matrix(c(1,0,0,ab[1,1],0,ab[2,1],0,0,1),byrow=T,nrow=3) } else if (type == "t") { x = matrix(c(LMSr[1,1],LMSr[2,1], LMSw[1,1],LMSw[2,1]),byrow=T,nrow=2) y = matrix(c(LMSr[3,1],LMSw[3,1]),nrow=2) ab = solve(x) %*% y C = matrix(c(1,0,0,0,1,0,ab[1,1],ab[2,1],0),byrow=T,nrow=3) } else if (type == "a" | type == "g") { C = matrix(c(0.2126,0.7152,0.0722, 0.2126,0.7152,0.0722, 0.2126,0.7152,0.0722),byrow=TRUE,nrow=3) } return(C) } # rgb is a column vector convertcolor = function(rgb,LMS=LMSD65,type="d",g=gamma) { C = getcorrection(LMS,type) if(type == "a" | type == "g") { T = SA } else { M = LMS %*% XYZ Minv = solve(M) T = Minv %*% C %*% M } print(T) rgb_converted = T %*% apply(rgb,1:2,linearize,g) return(apply(rgb_converted,1:2,delinearize,g)) } # This function implements the method by Vienot, Brettel, Mollon 1999. # The approach is the same, just the values are different. # http://vision.psychol.cam.ac.uk/jdmollon/papers/colourmaps.pdf convertcolor2 = function(rgb,type="d",g=2.2) { xyz = matrix(c(40.9568, 35.5041, 17.9167, 21.3389, 70.6743, 7.98680, 1.86297, 11.4620, 91.2367),byrow=T,nrow=3) lms = matrix(c(0.15514, 0.54312, -0.03286, -0.15514, 0.45684,0.03286, 0,0,0.01608),byrow=T,nrow=3) rgb = (rgb/255)**g if(type=="p") { S = matrix(c(0,2.02344,-2.52581,0,1,0,0,0,1),byrow=T,nrow=3) rgb = 0.992052*rgb+0.003974 } else if(type=="d") { S = matrix(c(1,0,0,0.494207,0,1.24827,0,0,1),byrow=T,nrow=3) rgb = 0.957237*rgb+0.0213814 } else { stop("Only type p,d defined for this function.") } M = lms %*% xyz T = solve(M) %*% S %*% M print(T) rgb = T %*% rgb rgb = 255*rgb**(1/g) return(rgb) } ############################################### # RGB to Lab rgb2lab = function(rgb,g=gamma) { rgb = apply(rgb,1:2,linearize,g) xyz = XYZ %*% rgb delta = 6/29 xyz = xyz / (c(95.0489,100,108.8840)/100) f = function(t) { if(t > delta**3) { return(t**(1/3)) } else { return (t/(3*delta**2) + 4/29) } } L = 116*f(xyz[2]) - 16 a = 500*(f(xyz[1]) - f(xyz[2])) b = 200*(f(xyz[2]) - f(xyz[3])) return(matrix(c(L,a,b),nrow=3)) } # CIE76 (https://en.wikipedia.org/wiki/Color_difference) deltaE = function(rgb1,rgb2) { lab1 = rgb2lab(rgb1) lab2 = rgb2lab(rgb2) return(sqrt(sum((lab1-lab2)**2))) } clip = function(v) { return(max(min(v,1),0)) } ############################################### # RGB to/from linear RGB #https://en.wikipedia.org/wiki/SRGB linearize = function(v,g=gamma) { if(v <= 0.04045) { return(v/255/12.92) } else { return(((v/255 + 0.055)/1.055)**g) } } delinearize = function(v,g=gamma) { if(v <= 0.003130805) { return(255*12.92*clip(v)) } else { return(255*clip(1.055*(clip(v)**(1/g))-0.055)) } } pretty = function(x) { noquote(formatC(x,digits=10,format="f",width=9)) } # a dark red rgb1 = matrix(c(0,209,253),nrow=3) # dark green rgb2 = matrix(c(60,135,0),nrow=3) # simulate deuteranopia convertcolor(rgb1,type="d") convertcolor(rgb2,type="d") # get color distance before and after simulation deltaE(rgb1,rgb2) deltaE(convertcolor(rgb1,type="d"),convertcolor(rgb2,type="d")) # transformation matrices for each color blindness type M = LMSD65 %*% XYZ pretty(solve(M) %*% getcorrection(LMSD65,"p") %*% M) pretty(solve(M) %*% getcorrection(LMSD65,"d") %*% M) pretty(solve(M) %*% getcorrection(LMSD65,"t") %*% M) pretty(SA) # method by Vienot, Brettel, Mollon, 1999 convertcolor2(rgb1,type="d",g=2.2) convertcolor2(rgb2,type="d",g=2.2) ```

# a dark red rgb1 = matrix(c(225,0,30),nrow=3) # dark green rgb2 = matrix(c(60,135,0),nrow=3) # simulate deuteranopia convertcolor(rgb1,type="d") [,1] [1,] 136.7002 [2,] 136.7002 [3,] 0.0000 convertcolor(rgb2,type="d") [,1] [1,] 116.76071 [2,] 116.76071 [3,] 16.73263 # get color distance before and after simulation deltaE(rgb1,rgb2) [1] 116.9496 deltaE(convertcolor(rgb1,type="d"),convertcolor(rgb2,type="d")) [1] 12.72204 # transformation matrices for each color blindness type M = LMSD65 %*% XYZ pretty(solve(M) %*% getcorrection(LMSD65,"p") %*% M) [,1] [,2] [,3] [1,] 0.1705569911 0.8294430089 0.0000000000 [2,] 0.1705569911 0.8294430089 -0.0000000000 [3,] -0.0045171442 0.0045171442 1.0000000000 pretty(solve(M) %*% getcorrection(LMSD65,"d") %*% M) [,1] [,2] [,3] [1,] 0.3306600735 0.6693399265 -0.0000000000 [2,] 0.3306600735 0.6693399265 0.0000000000 [3,] -0.0278553826 0.0278553826 1.0000000000 pretty(solve(M) %*% getcorrection(LMSD65,"t") %*% M) [,1] [,2] [,3] [1,] 1.0000000000 0.1273988634 -0.1273988634 [2,] -0.0000000000 0.8739092990 0.1260907010 [3,] 0.0000000000 0.8739092990 0.1260907010 pretty(SA) [,1] [,2] [,3] [1,] 0.2126000000 0.7152000000 0.0722000000 [2,] 0.2126000000 0.7152000000 0.0722000000 [3,] 0.2126000000 0.7152000000 0.0722000000 # method by Vienot, Brettel, Mollon, 1999 convertcolor2(rgb1,type="d",g=2.2) [,1] [,2] [,3] [1,] 0.29275003 0.70724967 -2.978356e-08 [2,] 0.29275015 0.70724997 1.232823e-08 [3,] -0.02233659 0.02233658 1.000000e+00 [,1] [1,] 131.81223 [2,] 131.81226 [3,] 36.37274 convertcolor2(rgb2,type="d",g=2.2) [,1] [,2] [,3] [1,] 0.29275003 0.70724967 -2.978356e-08 [2,] 0.29275015 0.70724997 1.232823e-08 [3,] -0.02233659 0.02233658 1.000000e+00 [,1] [1,] 122.71798 [2,] 122.71801 [3,] 48.34316

The Sanctuary Project is a Lunar vault of science and art. It includes two fully sequenced human genomes, sequenced and assembled by us at Canada's Michael Smith Genome Sciences Centre.

The first disc includes a song composed by Flunk for the (eventual) trip to the Moon.

But how do you send sound to space? I describe the inspiration, process and art behind the work.

A forest of digits

Celebrate `\pi` Day (March 14th) and finally see the digits through the forest.

This year is full of botanical whimsy. A Lindenmayer system forest – deterministic but always changing. Feel free to stop and pick the flowers from the ground.

And things can get crazy in the forest.

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day, 2018 `\pi` Day and 2019 `\pi` Day.

*All that glitters is not gold. —W. Shakespeare*

The sensitivity and specificity of a test do not necessarily correspond to its error rate. This becomes critically important when testing for a rare condition — a test with 99% sensitivity and specificity has an even chance of being wrong when the condition prevalence is 1%.

We discuss the positive predictive value (PPV) and how practices such as screen can increase it.

Altman, N. & Krzywinski, M. (2021) Points of significance: Testing for rare conditions. *Nature Methods* **18**:224–225.

*We demand rigidly defined areas of doubt and uncertainty! —D. Adams*

A popular notion about experiments is that it's good to keep variability in subjects low to limit the influence of confounding factors. This is called standardization.

Unfortunately, although standardization increases power, it can induce unrealistically low variability and lead to results that do not generalize to the population of interest. And, in fact, may be irreproducible.

Not paying attention to these details and thinking (or hoping) that standardization is always good is the "standardization fallacy". In this column, we look at how standardization can be balanced with heterogenization to avoid this thorny issue.

Voelkl, B., Würbel, H., Krzywinski, M. & Altman, N. (2021) Points of significance: Standardization fallacy. *Nature Methods* **18**:5–6.

*Clear, concise, legible and compelling.*

Making a scientific graphical abstract? Refer to my practical design guidelines and redesign examples to improve organization, design and clarity of your graphical abstracts.