MacAdam's ellipses, drawn on one diagram
Drawn at its defaults, in diagrams, and what survives being drawn on another.
It reads 3 options and
no others: show, plane, magnify.
Called by 5 essays
the blast radius of changing it
No diagram makes them circles
Every chromaticity diagram is a projective picture of the same measurement, so how badly MacAdam's ellipses fail to be circles can be minimised over the whole family of them. The best plane there is still leaves the average ellipse twice as long as it is wide — which makes the residual a fact about the eye rather than about anybody's choice of primaries.
Difference and uniformityA difference needs a basis too
A linear change of coordinates leaves every colour match exactly where it was. A cube root does not commute with one — so a lightness–chroma space, and every colour difference computed in it, is a property of the basis that happened to be in place before the nonlinearity. CIELAB's basis was chosen in 1931 for reasons that had nothing to do with difference.
What the brain doesOne matrix doing two jobs
CIECAM16 adapts in CAT16 and then applies its response compression in the same axes, so a single matrix decides both how well the model handles a change of light and how uniform the space it produces is. The two jobs have different best answers, and the matrix was chosen against only one of them.
Difference and uniformityA compression goes below the floor
Elsewhere this collection minimised the anisotropy of MacAdam's ellipses over every chromaticity diagram there is, found 2.02, and called the residual a property of the eye. It is a property of the eye seen through a projective picture. A cube root after the right basis reaches 1.61 on the same twenty-five ellipses.
Difference and uniformityThe exponent was never the argument
A century of colour science has argued about whether the eye's response is a cube root, a square root or a logarithm. Minimise the anisotropy of MacAdam's ellipses over every basis, at each of eight exponents, and the floor moves by under three per cent between a cube root and a tenth root — while the basis moves it by a factor of two.