Most of this diagram is a lie, and it is not the diagram's fault.
The chromaticity horseshoe is the canonical illustration of colour science, and nearly every printed copy is filled edge to edge with colour it cannot actually show. A screen reaches a triangle inside it. Everything beyond that triangle — including the whole spectral boundary, the pure wavelengths the diagram exists to place — has been quietly clipped to something reachable, and the caption never says so. These are essays about colour with the arithmetic done and the failures marked: every swatch computed from a spectrum through a named observer, and everything the display cannot reach admitting it.
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19 essays
Most of this diagram cannot be shown
The chromaticity horseshoe is the canonical illustration of colour science, and nearly every printed copy is filled edge to edge with colours the page cannot produce. The honest version marks them, and the marking covers most of the picture.
What the eye doesThree numbers
A spectrum has as many degrees of freedom as anyone cares to give it. The eye reports three. Everything colour science can do, and every way it fails, follows from that one collapse.
What light isA spectrum is not a colour
What arrives at the eye is a function of wavelength. What the eye reports is three numbers. Keeping the two apart is the single most useful habit in the subject, and almost every confusion in applied colour comes from letting them merge.
What the brain doesThese two patches are identical
It is the most repeated and least checkable sentence in visual perception, because the whole point is that it does not look true. Every instance on this site is an assertion in code that stops the build if it ever stops being the case.
Difference and uniformityHow far apart are two colours
ΔE is meant to be a distance with the property that the same number means the same perceived difference everywhere. Three successive formulae have tried, they disagree with each other by more than a just-noticeable difference, and the disagreement decides real matching questions.
Where the model breaksSeventeen observers in 1931
The standard observer that governs every colour specification in industrial use is an average over seventeen young British men, measured with equipment from the 1920s. It is known to be wrong in the blue, the correction has existed since 1951, and it has never been adopted.
What the eye doesTwo spectra, one colour
Metamerism is usually described and almost never demonstrated. It does not have to be — the metameric black space is enormous, so a matching pair can be constructed to order, verified, and then made to come apart by changing the light.
What light isBlackbody and the colour of temperature
Heat something and it glows, in a colour fixed by its temperature alone. Planck's law gives the whole spectrum from one number, and the Planckian locus is the only curve in colour science derived from physics rather than from measurements of people.
What the brain doesBrightness is inferred from edges
The Cornsweet effect makes two identical regions look different by altering nothing except a narrow band at the boundary between them. Cover the boundary and the difference vanishes, which says the visual system is reconstructing surfaces rather than reading off intensities.
Difference and uniformityMacAdam measured it
In a perceptually uniform space the just-noticeable-difference contours would be circles of equal size. MacAdam's ellipses are neither, by a factor of eighty — and transforming them into each candidate space settles which spaces improved matters and by how much.
Matching and measuringMatching is not appearance
CIE XYZ predicts when two lights will look the same under identical viewing conditions. It was never a model of how anything looks, and most of the confusion in applied colour comes from using it as one.
Where the model breaksSimulating what cannot be simulated
A colour-blindness simulation cannot show what anybody sees. What it can show is which discriminations survive, and that is a narrower claim, a checkable one, and the only one worth making.
What the eye doesWhy colour is exactly three-dimensional
Matching every wavelength with three primaries requires, for some wavelengths, a negative amount of one of them. That physical awkwardness is why the colour-matching functions were transformed into XYZ, and why the horseshoe is curved.
Difference and uniformityThe midpoint is not half
Code 128 sits halfway along the sRGB scale and carries about a fifth of white's luminance. Half the luminance is code 188. Almost every gradient, blur and resize on the web gets this wrong, and the errors are visible once known.
Where the model breaksThe display is an unknown
This site is displayed on the very apparatus it is about, and it knows almost nothing about that apparatus. Two figures here stop assuming and ask instead — a probe for the transfer function and a probe for the gamut.
What the brain doesConstancy is the default
A sheet of paper looks white in daylight and white under a tungsten lamp, although the light reaching the eye differs enormously. The visual system is solving one equation with two unknowns, and it solves it by assumption.
What light isThe illuminant is half the answer
An object has a reflectance, not a colour. The colour appears when a specified light falls on it, which is why two surfaces can match in a shop and clash outside, and why every serious matching standard names the light.
Matching and measuringWhat a gamut costs
Three primaries reach a triangle and the visible region is not a triangle, so something has to give. Widening the primaries helps, has a price in precision and compatibility, and runs into a limit that is geometric rather than technological.
Matching and measuringA hex code is not a colour
Six hexadecimal digits identify three numbers. Turning three numbers into a colour needs a colour space, a transfer function, a white point and a display, and leaving any of them unstated is the everyday version of every confusion on this site.
Threads running through
themes, not chapters
Say which colour
A swatch is a set of coordinates in a space, under an observer, on a display with a gamut. Every colour drawn here carries all four, because a hex code on its own does not identify a colour at all.
Outside the gamut
Most colours a human can see cannot be shown on this page. The usual response is to clip them silently and print the picture anyway. The response here is to mark them and say how far out they are.
Identical, and asserted
"These two patches are the same colour" is the most repeated and least checkable sentence in perception, because the whole point is that it does not look true. Every instance here is an assertion in code.
Three numbers
An infinite-dimensional spectrum is projected onto three cone responses, and everything colour science can do — and every way it fails — follows from that single collapse.
Matching is not appearance
CIE XYZ predicts when two lights will match under identical viewing conditions. It was never a model of how anything looks, and most of the confusion in applied colour comes from using it as one.
Computed, not quoted
Every swatch begins as a spectral power distribution and is carried through the colour-matching functions while the figure is drawn. None is a hex code recalled from a table.
The instrument is the reader
This is the one subject where the page is displayed on the apparatus under discussion, and the reader's own eye is the measuring device. Several figures here are experiments rather than illustrations.