Colour — an atlas
An exhibition in twelve rooms 62 sources · 12 instruments
Object 0 The sRGB gamut, sliced at OKLCH lightness 0.75. Hue runs around the circle, chroma outwards. The ragged edge is the limit of your screen.

How light becomes colour — and what your brain does with it

Colour is not a property of light, nor of paint, nor of pixels. It is something a nervous system makes from them. This atlas walks through that making, from photons to words. Every room holds a working instrument built from the published equations, and every claim links to its source.

The visible spectrum, computed from the CIE 1931 standard observer.1,2 No screen can show it exactly; see Room V.

Floor plan

The rooms run from physics to physiology, perception, language and design. Each can be visited on its own, but they build: the three numbers of Room II explain the illusions of Room III, and those explain why the tools in Rooms X–XII are designed the way they are.

  1. ILightNewton’s prism, and why rays are “not coloured”.
  2. IIThree ConesEvery colour you see arrives as three numbers.
  3. IIIMetamersDifferent light, identical colour, until the lamp changes.
  4. IVPaint & LightWhy yellow and blue make green only in the paint box.
  5. VThe HorseshoeThe 1931 map of every colour a person can see.
  6. VIEqual StepsWhy evenly spaced numbers are not evenly spaced colours.
  7. VIINothing AloneOne colour, two appearances; an image that isn’t there.
  8. VIIIConstancyA lemon stays yellow from noon to candlelight.
  9. IXNamingLanguages carve the same space in different places.
  10. XOther EyesDesigning for the one in twelve men who see differently.
  11. XIHarmonyWhat the colour wheel promises, and what the data show.
  12. XIIColour That WorksRainbows, colour maps, contrast, and colour in games.
Room IPhysics1666 – 1704

Light

Light is where colour starts, but the colour isn’t in the light.

In 1672 a young Cambridge professor sent the Royal Society an account of an experiment with a prism in a darkened room. Isaac Newton let a thin beam of sunlight through a hole in his shutter and watched it spread into an oblong band of colours. A second prism, he reported, could not split any single colour of that band further, and recombining the band gave white again.3 White was not pure. It was a mixture.

What separates the colours is refrangibility, the amount each ray bends as it passes through glass. We now describe the same property as wavelength. The human eye responds to electromagnetic radiation from roughly 380 to 750 nanometres, a tiny window in a spectrum that runs from radio waves kilometres long to gamma rays smaller than an atom.

Newton’s most important sentence about colour is also his most modern. In the Opticks he warned against the natural assumption that the rays themselves are red or blue:

“For the Rays to speak properly are not coloured. In them there is nothing else than a certain Power and Disposition to stir up a Sensation of this or that Colour.”
Isaac Newton, Opticks, 17044

Nothing that follows makes sense without this distinction. A wavelength is a physical quantity. A colour is an experience. The rest of this atlas is about the machinery that turns one into the other.

550nm

Drag to change the wavelength of a monochromatic light between 380 and 730 nanometres.

Frequency
545THz
Photon energy
2.25eV
Luminous efficiency
0.99V(λ)
Nearest sRGB
#9dff00

The wave is drawn to scale: its length is proportional to the wavelength. The number on the right is the V(λ) luminous efficiency of that light: how bright it looks for the same power. It peaks near 555 nm.

Plate I · A single wavelength A monochromatic light, shown as the closest colour sRGB can make. Spectral colours lie outside every display gamut. At the extremes of the range they fade because the eye barely responds there. Colour from the CIE 1931 2° observer (analytic fit).2 Frequency ν = c/λ; energy E = hc/λ. V(λ) is the ȳ function.
Room IIPhysiology1802 – 2000

Three Cones

Every colour you have ever seen reached your brain as three numbers.

In his Bakerian Lecture of 1801, published in 1802, Thomas Young noticed a problem of scale. A retina could not contain a separate detector for every wavelength, so, he argued, “it becomes necessary to suppose the number limited,” and he proposed three.5 Hermann von Helmholtz and James Clerk Maxwell developed the idea over the following half-century. Direct evidence came much later.

In 1980 Bowmaker and Dartnall measured single cones taken from a human eye. They found three classes of photopigment, with peak sensitivity at about 420, 534 and 564 nm.6 These are the short-, middle- and long-wavelength cones: S, M and L. In 1986 Nathans and colleagues isolated the genes that encode them.7 The L and M genes sit side by side on the X chromosome, which is why red–green colour deficiency is so much more common in men (Room X).

The key fact about a cone is what W. A. H. Rushton called the principle of univariance.8 A cone reports one thing only: how many photons it caught. It cannot tell a dim light at its favourite wavelength from a bright light at one it barely responds to. Wavelength information survives only in the ratio of the three cone signals. The whole of colour vision is built on those three numbers.

Modern colour science uses carefully measured “cone fundamentals”, such as those of Stockman and Sharpe, which include the filtering of the lens and macula.9,10 The instrument below uses the simpler pigment templates of Govardovskii and colleagues, which describe the shape of any visual pigment’s absorption from its peak alone.11

Isolate one cone (univariance)

Plate II · The trichromatic code Relative absorption of each human cone pigment at the chosen wavelength. The three bars are the only information about that light that leaves the eye. Isolate one cone to see univariance: for every response there are two wavelengths, one either side of the peak, that produce it. Govardovskii et al. A1 template (α + β bands), peaks at 420 / 534 / 564 nm.11,6 Pigment absorbance, not corneal sensitivity.
Room IIIColorimetry1958 – 1982

Metamers

Two surfaces can reflect very different light and still look identical, until the lamp changes.

A spectrum is a detailed thing: a separate intensity at every wavelength. Three cones reduce that detail to three numbers. Countless different spectra must therefore produce the same three numbers, and so the same colour. Such physically different but visually identical stimuli are called metamers.

In 1958 Günter Wyszecki described how to construct them. Some spectral patterns are perfectly invisible to a trichromatic observer. Their effects on the three cone types cancel out exactly. Wyszecki called them metameric blacks.13 Add one to any reflectance and the colour does not change under that light. Every spectrum can be split into a “fundamental metamer” that the eye sees and a metameric black that it cannot.14

That invisibility holds only under the light used to build it. The two surfaces below were computed to match exactly under daylight. Under incandescent light the hidden differences in their spectra reach the eye, and the match fails. This is the old problem of the jacket and trousers that matched in the shop and not at home. It also troubles printers, dyers, car makers and anyone who renders images using only three channels.

Look at the chart. The two reflectance curves cross several times. That is not a coincidence. For a trichromatic observer, two spectra that match must cross at least three times.

Sample A
Sample B
Illuminant
6500K
Difference ΔE00
0.00
Verdict
Indistinguishable
Sample ASample BLight (relative power)
Plate III · A metameric pair Sample B is sample A plus a metameric black built for a 6500 K light. Under that light the difference is exactly zero. Move the lamp and it appears. The viewer is assumed to adapt fully to each light, so only the mismatch changes. Spectral simulation at 5 nm; Planckian illuminants; CIE 1931 observer; CAT16 adaptation; CIEDE2000.13,16,17
Room IVPigment & light1931 – 2021

Paint & Light

Why blue and yellow paint make green, but blue and yellow light make something close to white.

Mix two lights and their energies add, wavelength by wavelength. A blue light and a yellow light between them cover most of the spectrum, so the mixture looks nearly white. This is additive mixture, and it is how every screen works.

Mix two paints and something different happens. Each pigment absorbs part of the spectrum, and in a mixture a wavelength survives only if both pigments let it through. A typical blue reflects short and middle wavelengths. A typical yellow reflects middle and long ones. The only light both reflect is the middle band, which we see as green. Physicists call this subtractive mixture, though “multiplicative” would be more accurate.

Real paint is more complicated, because pigment particles scatter light as well as absorb it. The standard account is the two-constant model published by Kubelka and Munk in 1931.18 In 2021 Sochorová and Jamriška showed how to run that model fast enough for digital painting. Their result is a brush that mixes blue and yellow into green, as real paint does, instead of into grey.19

The instrument below uses a simpler, idealised version. Each pigment’s reflectance is a smooth curve, and mixing takes a weighted geometric mean of the curves. It shows the essential physics, and it shows why averaging hex codes, as most software does, matches neither paint nor light.

Pigment one
Pigment two

As paintReflectances multiplied: a subtractive mixture

As lightTwo lamps overlapping: an additive mixture

As numbersThe average of the two sRGB codes

Pigment onePigment twoPaint mixture
Plate IV · Three ways to mix One pair of colours, mixed three ways. The pigments are idealised: smooth, single-band reflectances rather than measurements of real paints. Their behaviour is still the textbook one. Sigmoid-polynomial reflectances.15 Paint = weighted geometric mean of reflectance; light = linear mix of XYZ; lit by a 6500 K Planckian.
Room VColorimetry1929 – 1931

The Horseshoe

In 1931, the CIE drew every colour a standard observer can see on a single sheet.

At the end of the 1920s two British researchers, William David Wright at Imperial College and John Guild at the National Physical Laboratory, ran the same experiment on a small group of observers. Each person looked at a split field. One half showed a pure spectral light. In the other half the observer mixed three primary lights until the two halves matched.20,21 The settings, averaged and combined, became the CIE 1931 standard observer: three colour-matching functions that predict whether two lights will match for a typical person.1

Those functions give every light three coordinates, X, Y and Z. Divide out overall intensity and two remain, x and y. Plotted on a plane, the pure spectral colours trace a curved edge, the spectral locus. A straight line, the line of purples, closes it. Every colour a person can see lies inside this horseshoe.

Every display also lies inside it, as a triangle whose corners are its red, green and blue primaries. Any colour inside the triangle can be mixed from them; nothing outside can be. The triangles below are sRGB, used by most of the web; Display P3, used by modern phones; and Rec. 2020, the target for ultra-high-definition video.22 None of them covers the whole horseshoe, and no three real primaries could.

One caveat. The diagram is excellent for predicting matches but poor at showing how different two colours look. Equal distances in x,y are not equal steps in appearance. That problem is Room VI.

Move across the diagram.
Area in sRGB
—
in Display P3
—
in Rec. 2020
—

Coverage is measured as area in the x,y plane. The plane is not perceptually uniform, so treat these percentages as rough indications, not as measures of how many colours you can see.

Plate V · CIE 1931 chromaticity The spectral locus, labelled in nanometres, with three standard display gamuts and the path of a heated black body from 1000 K to 25 000 K. Hover or drag to read coordinates and check whether a point falls inside each gamut. Locus from the analytic CIE 1931 fit;2 primaries from CSS Color 4;22 Planckian locus by numerical integration of Planck’s law.
Room VIPerception1905 – 2020

Equal Steps

Numbers that are evenly spaced do not give colours that look evenly spaced.

In 1905 the painter Albert Munsell published A Color Notation, which organised colours by hue, value and chroma in steps chosen by eye to look equal.23 Colour scientists spent the following century trying to reach the same goal with mathematics.

The difficulty became clear in 1942. David MacAdam measured how precisely an observer could match colours at 25 points on the chromaticity diagram. The regions of “no noticeable difference” turned out to be ellipses, and they varied greatly in size and orientation: small in the blues, enormous in the greens.24 Equal distances on the horseshoe are not equal differences to the eye.

CIELAB, standardised in 1976, bent the space to even out those ellipses.25 Its successor formulas culminated in CIEDE2000, which adds corrections for lightness, chroma and hue, including an awkward rotation term for blues.26 Sharma, Wu and Dalal’s implementation notes are the reference that most software, including this page, is tested against.17 In 2020 Björn Ottosson proposed OKLab, a simple space tuned for image processing. It was adopted into CSS within a few years.27,22

Designers meet this problem constantly. Colour pickers usually work in HSL, which is a geometric rearrangement of RGB, not a model of perception. At the “same” HSL lightness, yellow is far brighter than blue. Gradients interpolated in sRGB sag into grey in the middle. The instrument shows both effects.

View
HSL hue sweep, S 100 %, L 50 %“same lightness”, according to the numbers
OKLCH hue sweep, L 0.72, C 0.12same perceptual lightness

Each ramp runs between the same two colours. The bars show the CIEDE2000 difference between each pair of neighbouring steps. Even bars mean the steps look even.

sRGB step spread
—
OKLab step spread
—
Interpolated in sRGB
Interpolated in OKLab
Plate VI · Two kinds of even Top: two hue sweeps, each labelled as “constant lightness” by its own system. The line under each ramp plots its perceptual lightness. Switch to “Lightness only” to see it. Below: a ramp between any two colours, interpolated two ways. Lightness = OKLab L. Step differences = CIEDE2000, validated against Sharma et al.’s test data.17,27 Spread = max ÷ min step.
Room VIIPerception1810 – 2012

Nothing Is Seen Alone

The same colour looks different depending on what is next to it, and on what you were looking at a moment ago.

In the 1820s the chemist Michel-Eugène Chevreul became director of dyeing at the Gobelins tapestry works in Paris. Weavers complained that some of his black wools looked weak. Chevreul found nothing wrong with the dyes. The blacks looked dull because of the colours woven next to them. His 1839 book set out a law of simultaneous contrast: neighbouring colours push each other apart in lightness and hue. He separated this from successive contrast, the change in how a colour looks after you have stared at another.28

The painter and teacher Josef Albers made these effects the core of a course at Yale. In Interaction of Color (1963) students learn to make one colour look like two, and two colours look like one, using nothing but their surroundings.29 Plate VII-a is an Albers exercise. The two small squares are always the same colour.

Contrast is not only a local effect of neighbouring cells. In a well-known series of displays, Edward Adelson showed that the same grey patch looks lighter or darker depending on how the brain interprets the scene. The deciding factor is whether the patch seems to lie in shadow, behind a transparent filter or in the open.30

Successive contrast

Goethe devoted pages to coloured afterimages.31 Stare at a red patch and then look at a white wall, and a green-blue ghost appears. Ewald Hering took such pairings (red with green, yellow with blue) as evidence that colour is coded in opposed channels. In 1957 Leo Hurvich and Dorothea Jameson measured those channels and reconciled them with Young’s three cones: three receptors feeding two colour-opponent channels and one achromatic channel.32 Recordings from primate retina suggest that afterimage signals begin in the retina’s ganglion cells, before the cortex.33

Study
Plate VII-a · After Albers The inner squares are identical: . Join them with a strip of the same colour and the difference fades, sometimes not completely. Flat colours only. In the grey and violet studies the grounds share the figure’s OKLCH lightness, so they shift its hue alone; the ochre study adds a lightness contrast.

An adapting image in unusual colours is shown for twenty seconds, then replaced by a black-and-white version of a landscape. Most viewers briefly see the landscape in natural colours.

Ready
Plate VII-b · A colour that isn’t there Keep your eyes on the central dot while the counter runs. When the image turns black and white, keep looking at the dot. For a few seconds most people see the landscape in natural colours. That colour is produced by your adapted visual system; the screen is showing none. The adapting image has each region’s OKLab chroma reversed (a,b → −a,−b) around a common mid-lightness. The test image is the landscape’s lightness alone.
Room VIIIPerception1959 – 2017

The Colour of Things

A lemon looks yellow at noon and by candlelight. The eye, not the light, keeps it that way.

The light reflected from a surface depends on two things: the surface and the light falling on it. Illumination varies enormously. A candle gives off many times more long-wavelength than short-wavelength energy, and a north-facing sky the reverse. Yet objects look much the same under both. This is colour constancy, and it is one of the main things colour vision is for.34,35

From the 1950s onwards Edwin Land, inventor of the Polaroid camera, demonstrated constancy with large collages of coloured paper he called “Mondrians”. He adjusted three projectors until a patch that looked red sent the eye exactly the light that a green-looking patch had sent a moment before. Observers still called it red. Land’s retinex theory argued that the visual system compares each region with the whole scene, not with some absolute standard.36,37

The simplest account is older. In 1902 Johannes von Kries suggested that each cone class adjusts its own sensitivity, so that the average light in a scene looks neutral. Modern chromatic-adaptation transforms such as CAT16 are refined versions of this idea.16,38 In the plate below, the left image shows the light that reaches the eye. The right shows the same scene after a von Kries adaptation to the illuminant.

Constancy is good but not perfect. How well it works depends on what the brain assumes about the light. In February 2015 a photograph of a striped dress divided the internet: some saw white and gold, others blue and black. Studies of the image found that viewers who assumed a bluish, shadowed light and those who assumed a warm, artificial one ended up seeing different dresses.39,40

The light that arrives
After adaptation

Move the light from candle to blue sky. The left image swings through orange and blue. On the right, most patches hold their colour. A few shift, because von Kries adaptation cannot fully correct surfaces whose spectra interact with the light in complicated ways.

Plate VIII · A Mondrian for Land Twenty surfaces, each with a smooth reflectance spectrum, lit by a Planckian light from 1800 K to 12 000 K. Left: the colour signal rendered with a fixed daylight white. Right: the same scene after CAT16 adaptation to the light’s white point. Spectral rendering at 5 nm; CIE 1931 observer; CAT16 with full adaptation (D = 1).16,15
Room IXLanguage1969 – 2017

Naming

Every language divides the same continuous space of colours, but not every language divides it in the same places.

Colour varies continuously, but languages name it in blocks. For much of the twentieth century anthropologists assumed those blocks were arbitrary. In 1969 Brent Berlin and Paul Kay challenged that view. After comparing colour terms across twenty languages and surveying reports of many more, they claimed that languages draw from a small set of basic colour terms. The best examples of those terms cluster in similar places across languages, and languages tend to add terms in a partly fixed order.41

The strong version of the claim has been revised many times. Kay and McDaniel connected the sequence to opponent-colour physiology and recast its first stage as “light-warm” versus “dark-cool”, not “white” versus “black”.42 The World Color Survey then gathered naming data from 110 unwritten languages.43 Its data suggest why the patterns exist: Regier, Kay and Khetarpal showed that the observed systems come close to optimal ways of dividing perceptual colour space into a given number of categories.44

Does the word change the seeing? Russian has no single everyday word for “blue”. It requires a choice between голубой (goluboy, lighter blue) and синий (siniy, darker blue). Winawer and colleagues found that Russian speakers told blues apart faster when the two fell on opposite sides of that boundary. The advantage disappeared when the speakers were given a verbal task to do at the same time, and English speakers showed no such effect.45

Colour naming also reflects what people need to talk about. Across languages, Gibson and colleagues found that warm colours are communicated more precisely than cool ones. The objects people pick out and name tend to be warm-coloured, while backgrounds such as sky, water and foliage tend to be cool.46

голубойgoluboy · lighter blueсинийsiniy · darker blue
blue · English: one basic term
Plate IX · A sequence and a boundary Top: the order in which Berlin and Kay proposed languages add basic colour terms (stages I–VII). Treat it as a strong tendency with documented exceptions, not a law. Below: one run of blues, which English names with one word and Russian divides into two. The mark shows roughly where the boundary falls. Swatches are illustrative focal colours chosen in OKLCH, not survey data. The goluboy/siniy boundary position is schematic.41,42,45
Room XPhysiology & design1997 – 2012

Other Eyes

About one man in twelve of Northern European descent cannot tell apart some of the reds and greens on this page.

Because the L and M cone genes lie on the X chromosome (Room II), inherited red–green colour deficiency mostly affects men. In his worldwide review, Jennifer Birch put its prevalence at about 8% of men and 0.4% of women of European origin, and lower in most other populations.47 Some people lack one cone class altogether (dichromats: protanopes lack L, deuteranopes lack M, tritanopes lack S). More have a cone class whose sensitivity is shifted (anomalous trichromats).

Brettel, Viénot and Mollon showed how to simulate what a dichromat sees. They drew on reports from rare people with normal colour vision in one eye and a deficiency in the other, and projected each colour onto the reduced set of colours a dichromat can distinguish.48 Machado, Oliveira and Fernandes later produced a physiologically based model that also covers anomalous trichromacy of any severity.49

For a game designer the lesson is direct. Loot rarity tiers, team colours, health bars and minimap markers are among the most common colour codes in games. Several of them rest on exactly the red–green and blue–purple distinctions that fail first. The fix is not a special “colourblind mode” added at the end. It is redundant coding: shape, pattern, position or text carrying the same information as the colour.

Viewer

Minimap · allies and enemies

Status

Loot

Ally vs enemy
—
Uncommon vs legendary
—
Rare vs epic
—
Health full vs low
—
Plate X · A game HUD, four ways A typical heads-up display, using conventions common in many genres, seen through simulated dichromacy. Turn on redundant cues to see how shape and text keep the information readable when colour fails. Machado et al. matrices, severity 1.0, applied in linear sRGB.49 Differences in CIEDE2000.17
Room XIAesthetics1944 – 2013

Harmony

Colour wheels promise rules for harmony. The experiments tell a subtler story.

Art schools teach colour harmony as geometry: complementary pairs opposite each other on a wheel, triads at 120°, analogous schemes of neighbours. In 1944 Parry Moon and Domina Spencer tried to make the tradition rigorous. They proposed that combinations are harmonious when their separations in a Munsell-like space are identical, small or clearly contrasting, and inharmonious when they fall in the “ambiguous” gaps between.50

Experiments have been less tidy. Ou and Luo asked observers to rate hundreds of colour pairs and built a predictive model. In their data harmony depended strongly on lightness: pairs with a clear lightness difference, or with high lightness overall, tended to be rated harmonious. Hue relationships mattered less than the colour wheel suggests.51 Schloss and Palmer separated three judgements that are often run together: how much people like a pair, how harmonious they find it, and how similar the colours are. Harmony rose with hue similarity. Liking depended strongly on how much people liked the individual colours, and on lightness contrast between figure and ground.52

Why do people like particular colours at all? Palmer and Schloss’s ecological valence theory proposes that we like colours in proportion to how much we like the objects associated with them: clear sky and clean water, but not rotten food or faeces. In their study with American participants, those associations accounted for about 80% of the variance in average colour preference.53,54

The generator below keeps the wheel but runs it in a perceptual space, OKLCH, and lets you control the one variable the data single out: lightness contrast.

An exhibition of colour
Inter­action
Scheme
Title contrast
—
WCAG 2.2
—
Lightness range
—
Plate XI · A poster generator Five colours from a classical scheme, placed at chosen lightness levels in OKLCH and composed into a poster. Click a swatch to copy its hex code. Lightness contrast decides how legible the title is and changes the poster’s character more than the hue angles do. OKLCH with CSS Color 4 chroma reduction into sRGB.22 Contrast ratio as defined in WCAG 2.2.55
Room XIIVisualisation & games1994 – 2020

Colour That Works

In a map, a chart or a game, colour carries information before it decorates.

The rainbow colour map, and its engineering descendant “jet”, has been the default in scientific software for decades. It has also been criticised for decades. Borland and Taylor summarised the case in 2007. The rainbow has no perceptual order (is yellow “more” than blue?). Its lightness rises and falls, so it draws bright bands where the data have none. It is poor for people with colour-vision deficiency.56 Crameri, Shephard and Heron documented how widespread the problem still was in 2020 and how it can distort readers’ conclusions.57

Design principles for better maps are well established. Lightness should change monotonically and, ideally, uniformly. Hue can add discrimination but should not carry the order on its own.58,59 Liu and Heer’s experiments confirmed the practical point: rainbow maps performed poorly in their tasks, while perceptually ordered multi-hue maps did well.60

Colour in games

Games use colour for both jobs at once: to make players feel something and to tell them something. Emotion research finds that brightness and saturation predict responses better than hue does. Valdez and Mehrabian found brighter colours rated more pleasant and more saturated colours more arousing.61 Geslin, Jégou and Beaudoin found that the brightness and saturation of video-game scenes were associated with the emotions players reported.62 For information, the accessibility threshold is concrete: WCAG 2.2 asks for a contrast ratio of 4.5:1 for normal text and 3:1 for large text and essential interface graphics.55

Colour map
Seen as

The data are one smooth hill with a gentle secondary rise, and nothing else. Any sharp band or “ridge” you see in the jet or HSV rendering is an artefact of the colour map. The curve plots each map’s perceptual lightness from low values to high: it should climb steadily.

Plate XII · Four maps, one dataset The same smooth field under four colour maps and three kinds of viewer. Switch to “Lightness” to see what survives in greyscale. That is also, roughly, the information available to anyone who cannot use the hue. Field: sum of anisotropic Gaussians. Lightness: OKLab L. Deuteranopia: Machado et al. 2009.27,49
The rays are not coloured.

Everything in these twelve rooms follows from Newton’s sentence. Colour is not a property of light, paint or pixels. The nervous system makes it from three numbers, then shapes it by context, memory and language. That is why colour can be measured precisely and still surprise the person measuring it. It is also why people who design for the eye, whether painters, engineers or game designers, need both the equations and the experiments.

Appendix A

Methods & limitations

Every instrument in this atlas runs live in your browser from published equations; nothing is a pre-rendered image. This appendix states what each one computes and where it simplifies, so that the demonstrations can be checked and not only admired.

Colour-matching functionsCIE 1931 2° observer via the multi-lobe Gaussian fit of Wyman, Sloan & Shirley.2 Where the fit drifts from the tabulated data in the far tails (below 425 nm, above 645 nm), chromaticity is held constant; the true locus is nearly a point there. Spectral integration uses 5 nm steps from 380 to 730 nm.
Displaying spectral coloursMonochromatic lights are out of gamut for every display. For the spectrum, 15% of the most negative linear-sRGB component is added back as white, remaining negatives are clipped, and brightness is weighted by luminous efficiency (ȳ0.3). The horseshoe fill in Plate V clips and normalises. These are conventional guides, not exact colours.
Cone pigmentsGovardovskii et al. (2000) A1 template, α and β bands, with human peaks at 420, 534 and 564 nm.11,6 These describe pigment absorbance. They omit lens and macular filtering, so they differ from corneal cone fundamentals such as Stockman & Sharpe (2000).9
IlluminantsPlanck’s law with c₂ = 1.4388 × 10⁻² m·K. CIE Illuminant A is itself Planckian at 2856 K. “Daylight” is approximated by a 6500 K Planckian, not by the CIE D65 tabulation. Computed chromaticities agree with the published black-body values to within about 0.002.
ReflectancesSmooth spectra in the sigmoid-polynomial family of Jakob & Hanika (2019);15 the Mondrian papers mix such a spectrum with a flat grey to soften it. The metameric pair adds to one of them a metameric black: a spectral pattern, found by orthogonal projection, that has zero effect on X, Y and Z under 6500 K.13,14
MixingSubtractive mixing is a weighted geometric mean of reflectances. That is an idealisation; it ignores the scattering that Kubelka–Munk theory models.18,19 Additive mixing is linear in XYZ. “Numeric” mixing averages gamma-encoded sRGB values.
AdaptationCAT16 von Kries transform with full adaptation (D = 1), from the illuminant’s white point to D65.16 Real observers adapt incompletely, particularly to very warm light.
Colour spaces & differencesRGB (IEC 61966-2-1) with D65 white; CIELAB per CIE 15; CIEDE2000 per Sharma et al. This implementation reproduces their published test pairs to four decimal places.17 OKLab and OKLCH per Ottosson, with CSS Color 4 chroma reduction for out-of-gamut colours.27,22
Colour-vision deficiencyMachado et al. (2009) matrices for protanopia, deuteranopia and tritanopia at severity 1.0, applied to linear sRGB.49 Simulations indicate which colours become confusable. They do not reproduce anyone’s experience.
ContrastWCAG 2.2 relative luminance and contrast ratio (L₁ + 0.05)/(L₂ + 0.05).55 The newer APCA method is not used, as it is not yet part of a W3C Recommendation.
What these demos are notThey are not calibrated. Your display, its settings, the room light and your own eyes all change what you see. The underlying numbers are correct; the experience on your screen is approximate.
VerificationEvery DOI in the sources below was resolved against Crossref’s metadata while the atlas was being built, and titles, authors, volumes and pages were checked against the record. Web sources were checked for availability.

Appendix B

Sources

Numbered in order of first citation. Journal articles link to their DOI; books and archives link to a publisher, library or public-domain full text where one exists.

62Sources cited
48With a verified DOI
1672–2024Span of publication
  1. 01Smith, T., & Guild, J. (1931). The C.I.E. colorimetric standards and their use. Transactions of the Optical Society, 33(3), 73–134. doi:10.1088/1475-4878/33/3/301
  2. 02Wyman, C., Sloan, P.-P., & Shirley, P. (2013). Simple analytic approximations to the CIE XYZ color matching functions. Journal of Computer Graphics Techniques, 2(2), 1–11. jcgt.org/published/0002/02/01/
  3. 03Newton, I. (1672). A letter of Mr. Isaac Newton … containing his new theory about light and colors. Philosophical Transactions of the Royal Society of London, 6(80), 3075–3087. doi:10.1098/rstl.1671.0072
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