Colour under accessibility and reproduction: daltonism, greyscale, low-quality print

Colour does two jobs in a chart. It can carry identity, marking categories that have no order, or magnitude, ranking values that do.

This third of ten units argues that a palette doing either job well is a reproduction requirement, not a matter of taste. Such a palette must be perceptually uniform, so equal steps in the data produce equal steps in what the eye sees. It must also survive colour-vision deficiency, greyscale printing and a poor projector. The claims below come from the literature rather than from preference.

Colour carries two different quantities, and only one of them is ordered

The distinction between identity and order fixes the rules before any colour is chosen. Harrower and Brewer (2003) built ColorBrewer around it. The tool asks how many data classes a map has, whether the variable is sequential, diverging or qualitative, and what the end-use environment is, listing screens, printed pages, projectors and photocopies. A qualitative variable has no order, so a scheme that ramps through it lies about the data. An ordered variable read through arbitrary hues forces the reader to consult a legend at every mark.

A scale that reports value has to be perceptually uniform

Perceptual uniformity makes a colour scale behave like an instrument. Zeileis, Hornik and Murrell (2009) frame the move as one out of RGB and HSV space, whose dimensions are confounded, and into HCL space. There hue, chroma and luminance can be varied one at a time, and a designer can build a palette by traversing a path. Their sequential schemes ramp mainly in luminance, adding chroma and hue only to raise contrast between steps. Crameri, Shephard and Heron (2020) reach the same conclusion from the other direction. A map that is not perceptually uniform reports variation that is not in the data. Their remedy is scientifically derived maps, which report true variation and stay readable under colour-vision deficiency.

The rainbow default fails the test it is most often given

Rogowitz and Treinish (1998) describe the rainbow map as one that maps red to the highest value, blue to the lowest and interpolates the spectrum between them. They explain why it misleads. Colour is perceptual as well as physical, so hue, intensity and saturation are nonlinear in what they produce. Yellow appears brighter than blue at equal intensity. Borland and Taylor (2007) restated the case with worked examples on simple datasets. Liu and Heer (2018) tested the claim rather than asserting it. A rainbow map performed worse than every other colormap they measured, on time and on error.

Their experiment shows the failure depending on the comparison rather than on the palette alone. Participants judged the relative distance between colour triplets drawn from four single-hue and five multi-hue maps. Viridis held a low error rate at every span tested. Blues matched it over long spans and lost ground at the shortest one. The diverging blue-orange scheme erred most when the comparison crossed the middle of the map, where the hue reverses. A scale that is uniform along its own path is not uniform across the comparisons a reader actually makes.

Colour-vision deficiency is a population, not an edge case

Olson and Brewer (1997) tested seven pairs of maps and seven colour schemes. Each pair set a rendition potentially confusing to readers with red-green impairment against one chosen to accommodate them. On the confusing set those readers were less accurate and slower. On the accommodating set they matched normal-vision readers for accuracy, though still slower. Nunez, Anderton and Renslow (2018) report that colour-vision deficiency affects more than four per cent of the population. They add that no colour map had been optimised for it with modern colour appearance models until their work. Zeileis and colleagues (2009) give the construction: luminance contrasts, visible even to a monochromat, and yellow-blue chroma contrasts, visible to a dichromat. They check the result by emulating dichromatic vision.

Sequential, diverging and qualitative schemes obey different rules

Each class of scheme has its own construction, and mixing them is a common error. A sequential scheme encodes one direction of magnitude and ramps in luminance, as Zeileis and colleagues (2009) set out. A diverging scheme encodes distance from a meaningful midpoint by combining two opposing ramps. Moreland (2009) developed one that performs well and published an algorithm for generating custom variants. He noted that most tools still shipped a rainbow default. Ware (1988) supplies the theory. He divides a map's information into metric information, the quantity at each point, and form information, the shape of the surface. He predicts that a spectrum-like scale serves value while a grey scale serves form, since the visual system prefers form through the lightness channel.

Greyscale and low-quality print are reproduction tests, not afterthoughts

A palette has to survive the conditions it is reproduced under, which are often worse than the screen it was designed on. A reader in later life, or one whose only copy is a photocopy, is an ordinary case for a map rather than an exception. Ware's (1988) result is the sharpest statement of the risk. A grey scale is weak at conveying value but strong at conveying form. A scheme carrying form through hue alone therefore loses the structure of the data when printed in greyscale. Harrower and Brewer (2003) turn the requirement into an operational question by asking what end-use environment a map is for, with photocopies listed beside screens. Light and Bartlein (2004) sharpen the point. Expertise in designing colour graphics has not kept pace with the technology that produces them. A design mistake can leave a colour figure less effective than a greyscale display of the same data. That is what makes greyscale a test the palette has to pass, rather than a degradation it can suffer.

The contested question: is perceptual uniformity a property of the palette or of the reader?

The literature disagrees about what uniform refers to. One position treats it as a property of the palette, definable in a colour space. Bujack and colleagues (2018) review the design rules and find the terms ambiguous, because one word can stand for different concepts. They propose mathematical definitions of order, uniformity and discriminative power. A second holds that the property belongs to the reader and the mark, not the palette. Szafir (2018) measured colour-difference perception for points, bars and lines. The ability to perceive a difference varies significantly by mark type, which warns that guidance from large uniform fields may mislead for the small marks charts use. Liu and Heer (2018) found the same from the other side. Single-hue maps were accurate over large value spans but lost resolution over small ones. Dark regions on a white background produced far more error than the perceptual models predicted. A colormap uniform on paper is therefore not uniform in use.

A factorial experiment would settle it. Hold the palette constant and vary what the first position treats as irrelevant, namely mark type, the span of the values compared and the luminance of the background. Measure discrimination for each combination. If the error those factors contribute swamps the differences between palettes, uniformity belongs to the viewing situation, and the rules must be conditioned on it. If not, the palette-intrinsic account survives. Perceptual colour space and colour naming together predict performance better than either alone, though overall accuracy stays poor.

The two positions rest on different evidence. The intrinsic account rests on a theoretical framework that redefines its terms (Bujack and colleagues, 2018). The reader account rests on two controlled experiments, one measuring colour-difference perception across mark types (Szafir, 2018) and one comparing relative-distance judgements across palettes (Liu and Heer, 2018). While the dispute is open, a designer should test a palette on the mark the chart will use and the surface it will sit on, and keep luminance contrast as the property both accounts accept. The strongest objection is that the reproduction tests the unit treats as settled used large uniform fields, so the claim that a uniform palette is a reproduction requirement is unmeasured on the small marks a chart draws.

Where this is heading

The direction of travel is from a fixed list of rules towards designed and tested palettes. Zhou and Hansen (2016) survey the field and group colormap generation into four families: procedural, user-study based, rule-based and data-driven. They offer a taxonomy for finding the technique that suits a variable and task, rather than one recommended map. Crameri and colleagues (2020) push the shift from practice. They urge authors, publishers and the press to abandon colour misuse together, because a palette a journal accepts becomes the default others copy. Szafir (2018) and Liu and Heer (2018) raise the open question. It is whether the next rules state intrinsic properties of a palette, or conditions on the reader, the mark and the surface.

The sources this unit rests on

Each note states what the cited work did and found and what it adds to the argument. Identifiers and metadata were checked on 2 November 2026.

• Borland, D. and Taylor Ii, R. M. (2007). Rainbow Colour Map (Still) Considered Harmful. IEEE Computer Graphics and Applications, 27(2), 14-17. doi:10.1109/mcg.2007.323435 Restates why the rainbow colour map is a poor choice, with examples of its deficiencies even on simple datasets, and recommends better maps for several kinds of display. Names the goal of making it as rare as the goto statement in programming.
• Bujack, R., Turton, T. L., Samsel, F., et al. (2018). The Good, the Bad, and the Ugly: A Theoretical Framework for the Assessment of Continuous Colormaps. IEEE Transactions on Visualization and Computer Graphics, 24(1), 923-933. doi:10.1109/tvcg.2017.2743978 Reviews historical colormap design guidance and finds its key terms ambiguous, since one word can stand for different concepts. Proposes a taxonomy with mathematical definitions of order, uniformity and discriminative power.
• Crameri, F., Shephard, G. E. and Heron, P. J. (2020). The misuse of colour in science communication. Nature Communications, 11(1), 5444. doi:10.1038/s41467-020-19160-7 Reports that colour maps which distort data through uneven gradients, or which are unreadable to readers with colour-vision deficiency, remain prevalent in science. Presents scientifically derived maps that report true variation and are accessible.
• Harrower, M. and Brewer, C. A. (2003). ColorBrewer.org: An Online Tool for Selecting Colour Schemes for Maps. The Cartographic Journal, 40(1), 27-37. doi:10.1179/000870403235002042 Describes ColorBrewer, which selects schemes by the number of data classes, the nature of the data matched to sequential, diverging and qualitative schemes, and the end-use environment, including print, projection and photocopy.
• Light, A. and Bartlein, P. J. (2004). The end of the rainbow? Colour schemes for improved data graphics. Eos, Transactions American Geophysical Union, 85(40), 385-391. doi:10.1029/2004eo400002 Argues that expertise in designing effective colour graphics has not kept pace with the technology that produces them, and that a design mistake can leave a colour figure less effective than a greyscale display of the same data.
• Liu, Y. and Heer, J. (2018). Somewhere Over the Rainbow. Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems, 1-12. doi:10.1145/3173574.3174172 Ran relative distance judgements across single-hue, multi-hue, diverging and rainbow colormaps. Found multi-hue maps such as viridis perform well, single-hue maps lose resolution over small value spans, and the rainbow map performs worst overall on time and error.
• Moreland, K. (2009). Diverging Colour Maps for Scientific Visualization. Lecture Notes in Computer Science, 5876, 92-103. doi:10.1007/978-3-642-10520-3_9 Explores diverging colour maps for scalar fields, notes that most scientific visualization tools still use the rainbow map despite its known shortcomings, and presents a diverging map that performs well generally plus an algorithm for generating custom ones.
• Nunez, J. R., Anderton, C. R. and Renslow, R. S. (2018). Optimising colormaps with consideration for colour vision deficiency to enable accurate interpretation of scientific data. PLOS ONE, 13(7), e0199239. doi:10.1371/journal.pone.0199239 Reports that colour-vision deficiency affects more than four per cent of the population and that no colour maps had been optimised for it with modern colour appearance models. Publishes a module that makes a map uniform in a deficiency-safe space.
• Olson, J. M. and Brewer, C. A. (1997). An Evaluation of Colour Selections to Accommodate Map Users with Colour-Vision Impairments. Annals of the Association of American Geographers, 87(1), 103-134. doi:10.1111/0004-5608.00043 Tested seven pairs of maps, each pairing a confusing rendition with an accommodating one. On the confusing set, readers with red-green impairment were less accurate and slower; on the accommodating set they were as accurate as normal-vision readers, though still slower.
• Rogowitz, B. E. and Treinish, L. A. (1998). Data visualization: the end of the rainbow. IEEE Spectrum, 35(12), 52-59. doi:10.1109/6.736450 Shows that a rainbow map, mapping red to the highest value and blue to the lowest, is a common software default that misleads, because colour is perceptual and its hue, intensity and saturation are nonlinear in what they produce. Reports a perceptual rule based replacement.
• Szafir, D. A. (2018). Modelling Colour Difference for Visualization Design. IEEE Transactions on Visualization and Computer Graphics, 24(1), 392-401. doi:10.1109/tvcg.2017.2744359 Measured colour-difference perception for points, bars and lines and found the ability to perceive differences varies significantly across mark types. Builds probabilistic models so designers can anticipate reader perception.
• Ware, C. (1988). Colour sequences for univariate maps: theory, experiments and principles. IEEE Computer Graphics and Applications, 8(5), 41-49. doi:10.1109/38.7760 Divides map information into metric information, the quantity at each point, and form information, the shape of the surface. Predicts a spectrum-like scale serves value and a grey scale serves form, and finds across five colour sequences that simultaneous contrast was a major error source while the form hypothesis held only partly.
• Zeileis, A., Hornik, K. and Murrell, P. (2009). Escaping RGBland: Selecting colours for statistical graphics. Computational Statistics & Data Analysis, 53(9), 3259-3270. doi:10.1016/j.csda.2008.11.033 Argues for HCL space over RGB and HSV, whose dimensions are confounded, and gives constructions for qualitative, sequential and diverging palettes. For colour-vision deficiency it recommends large luminance contrasts, visible to a monochromat, and yellow-blue chroma contrasts, visible to a dichromat.
• Zhou, L. and Hansen, C. D. (2016). A Survey of Colormaps in Visualization. IEEE Transactions on Visualization and Computer Graphics, 22(8), 2051-2069. doi:10.1109/tvcg.2015.2489649 Surveys colormap generation and groups techniques into procedural, user-study based, rule-based and data-driven families, with a taxonomy for matching a technique to a variable and an application. Treats colour spaces and appearance models as the foundation.