Colour: perceptual uniformity, accessibility and the colour-map debate

A colour scale stacks three decisions: whether the values are ordered or categorical, whether the ramp preserves perceived order, and whether the reader can see it at all. The field answered the first two by converging on perceptually uniform, colour-vision-safe maps. It then turned that convergence into advice strong enough to read as a prohibition on the rainbow. This third of ten units, after the second built the grammar, argues that the convergence on colour is real but narrower than the advice it produced. Accessibility is the hard limb, and ordered-reading accuracy is solid. The strongest recent work still shows the condemned map is not uniformly bad, because the tasks it suits were never the ones the critique measured.

A ramp in lightness, and the guidance that became a tool

Ware (1988) tested colour sequences on univariate maps against a theory of what each should carry: a spectrum-like scale should convey amount well but form poorly, a grey scale the reverse. His experiments found simultaneous contrast a major source of reading error and only partly confirmed the form half. Brewer (1994) separated sequential, diverging and qualitative schemes and warned against hue for ordered data. Harrower and Brewer (2003) then packaged the guidelines as an online tool. It matched schemes to data type and to the end-use environment. The advice was available and usable in the early 2000s. The persistence of poor colour documented later is therefore a mismatch between what the field knew and what it did.

The construction problem for a diverging ramp was solved in the same way. Moreland (2009) set out a map that runs through a neutral midpoint and stays smooth in lightness and chroma. He gave an algorithm for generating custom versions, because an ad hoc diverging palette produces unequal steps and a false boundary at the centre. Most scientific tools still defaulted to the rainbow, and the remedy arrived as a better construction rather than as evidence about the reader.

The critique of the rainbow, and the persistence of the practice

Borland and Taylor (2007) catalogued the rainbow map's problems. These included false boundaries where the data is smooth, non-uniform lightness, and unreadability for colour-vision-deficient readers. They argued for replacement. Crameri, Shephard and Heron (2020) showed how little had changed. Colour maps that distort data through uneven gradients, or that are unreadable to those with colour-vision deficiency, remain prevalent in science, with rainbow-like and red-green maps among them. The authors offer scientifically derived maps as the remedy. That paper is a guide rather than a controlled trial.

Accessibility is a hard constraint, and it has a number

The accessibility limb is the least vulnerable to revision and it has a number. Nunez, Anderton and Renslow (2018) noted that colour-vision deficiency affects more than 4 per cent of the population, then built a module optimising colormaps for deficient and typical viewers at once. Their map cividis is perceptually uniform in hue and brightness, increases in brightness linearly, and is read nearly identically by both groups. Failing that constraint costs a fixed share of any audience, whatever task the map suits. The fixed share includes the older reader as well as the colour-vision-deficient one, so a palette calibrated on the standard observer leaves part of the audience to a special case.

The evidence beneath the advice was thin, and the reader-outcome test came late

Reading out of a colormap was until recently studied less than building one. Zhou and Hansen (2016) grouped colormap generation into procedural, user-study based, rule-based and data-driven families, a taxonomy that shows how much of the effort goes into producing maps rather than testing them. Reda, Nalawade and Ansah-Koi (2018) showed that a single best colormap is not well posed. Spatial frequency significantly affected the effectiveness of the encoding, while the precise effect was task-dependent. No colormap was best across data of different spatial structure.

Liu and Heer (2018) supplied the controlled comparison. Readers made relative distance judgements among colour triplets from four single-hue and five multi-hue maps, viridis and a rainbow included. Single- and multi-hue maps both supported accurate decoding when well designed. Single-hue maps erred more over small value ranges. Perceptual space plus colour naming predicted performance better than either alone, though the overall prediction was poor.

What the condemned map is good for

Reda, Zaid and Nacenta (2023) reopened the question as one about categorisation. They introduced a method to detect latent colour categories in a colormap, then ran three crowdsourced experiments. Observers were more likely to discriminate global, distributional features when viewing colourful, categorising scales such as rainbow and diverging. The same maps made localised features defined by small variations less noticeable. The authors conclude that the costs and benefits are complementary. They also name conditions under which such designs are more harmful than useful. Ware, Stone and Szafir (2023) made the same case in a position piece, arguing that the rainbow's useful properties were underappreciated and that avoidance had hardened into dogma. It is an argument rather than a controlled study.

The palette's own criterion is an engineering proxy, not a perceptual law

Schloss and colleagues (2019) found that readers' inference of which colour means more is governed by background and apparent opacity as well as lightness. A dark-is-more bias holds when opacity appears constant, and an opaque-is-more bias competes with it when it does not. Colour-to-meaning is partly conventional, so a uniform ramp with its direction reversed is uniform and unreadable at once. Bujack and colleagues (2022) then found that perceived colour space does not obey the additivity axiom of a Riemannian metric, because large colour differences are perceived as less than the sum of small ones. The colour-difference measure in use holds only for small differences. The criterion on which uniformity rests is therefore an engineering proxy rather than a perceptual law.

Contested question: is the consensus narrower than the advice, or right for narrower reasons?

Two positions, not a verdict. One holds that the consensus is narrower than the advice it produced, so the counsel to abandon rainbow-like maps outran the studies behind it. Reda, Zaid and Nacenta (2023) find real affordances for global, distributional features and a complementary trade-off. Ware, Stone and Szafir (2023) argue that avoidance had hardened into dogma. Reda, Nalawade and Ansah-Koi (2018) show that the best map depends on task and data, which cuts against any single palette rule.

The other holds that the advice is right for narrower reasons. Liu and Heer (2018) found that uniform single- and multi-hue maps both support accurate reading, while single-hue maps err more over small value ranges. Nunez, Anderton and Renslow (2018) make colour-vision safety a quantified constraint that no task benefit answers. Crameri, Shephard and Heron (2020) document distortion and inaccessibility as live practice, so avoiding the rainbow is a defensible default for the default task of ordered comparison.

What would settle it is two studies, and neither is in this unit's list. One is a pre-registered task battery comparing ordered-reading accuracy and colour-vision safety for the same palettes over global and local feature judgements. The other recruits colour-vision-deficient participants rather than simulating them.

The two positions rest on different evidence. The revisionist position rests on three crowdsourced experiments on categorisation (Reda, Zaid and Nacenta, 2023) and on a position piece rather than a study (Ware, Stone and Szafir, 2023). The consensus position rests on controlled reading experiments (Liu and Heer, 2018), a quantified accessibility constraint (Nunez, Anderton and Renslow, 2018) and a survey of live practice (Crameri, Shephard and Heron, 2020). While the dispute is open, default to a perceptually uniform, colour-vision-safe ramp, and reserve a categorising map for global, distributional readings where its cost is measured.

The strongest counter-argument

The strongest objection is that the unit overstates the unsettledness. The revisionist results concern feature discrimination, that is, whether readers notice global distributions or localised detail. They leave untouched the two claims the guidance rests on. Non-uniform ramps mislead ordered comparison, and hue-heavy maps fail for a fixed part of the audience. Reda, Zaid and Nacenta themselves report conditions in which colourful maps are more harmful than useful, and no source here defends the rainbow for accessibility. On that reading the advice should have been a default rather than a blanket rule. The reply is that the published guidance held that the rainbow map is still considered harmful. That guidance was broader than the evidence Reda and colleagues (2023) and Ware, Stone and Szafir (2023) now present, and narrower than the trade-off those experiments measured.

Where the area is heading

The direction is towards conditional guidance and explicit criteria. Reda, Zaid and Nacenta (2023) supply task-conditional recommendations and name the conditions under which categorising maps mislead. Nunez, Anderton and Renslow (2018) make accessibility a computable optimisation target. Bujack and colleagues (2022) open the work of rebuilding the colour-difference metric for large differences.

The sources this unit rests on

Each note states what the cited document did and found, from the resolved record and the abstract, and from the full text where that was reachable.

• Borland, D. and Taylor, R. M. (2007). Rainbow Colour Map (Still) Considered Harmful. doi:10.1109/mcg.2007.323435 Catalogued the rainbow map's problems, including false boundaries, non-uniform lightness and unreadability for colour-vision-deficient readers, and argued for replacement. Its title concedes that the map had already been criticised and the community needed telling again.
• Brewer, C. A. (1994). Colour Use Guidelines for Mapping and Visualization. doi:10.1016/b978-0-08-042415-6.50014-4 Set out guidelines matching colour schemes to data types, separating sequential, diverging and qualitative schemes and warning against hue for ordered data. It supplies the taxonomy showing colour as three problems wearing one name.
• Bujack, R., Teti, E., Miller, J., Caffrey, E. and Turton, T. L. (2022). The non-Riemannian nature of perceptual colour space. doi:10.1073/pnas.2119753119 Tested whether perceived colour space obeys the additivity axiom of a Riemannian metric and found that it does not, because large colour differences are perceived as less than the sum of small ones. The colour-difference measure in use thus holds only for small differences.
• Crameri, F., Shephard, G. E. and Heron, P. J. (2020). The misuse of colour in science communication. doi:10.1038/s41467-020-19160-7 Documented that colour maps which distort data through uneven gradients, or which are unreadable to readers with colour-vision deficiency, remain prevalent in science, naming rainbow-like and red-green maps, with scientifically derived maps offered as the remedy. It is a guide rather than a controlled trial, and it shows the problem persisted after the warning.
• Harrower, M. and Brewer, C. A. (2003). ColorBrewer.org: An Online Tool for Selecting Colour Schemes for Maps. doi:10.1179/000870403235002042 Described an online tool that matched colour schemes to data type, number of classes and end-use environment, with tutorials and test-drive views, turning the guidelines into a choice with feedback. It dates the advice, showing it was usable before the practice it was meant to change.
• Liu, Y. and Heer, J. (2018). Somewhere Over the Rainbow: An Empirical Assessment of Quantitative Colormaps. doi:10.1145/3173574.3174172 Ran experiments in which readers made relative distance judgements among colour triplets from four single-hue and five multi-hue colormaps, characterising speed and accuracy. Both families supported accurate decoding when well designed, single-hue maps erred more over small value ranges, and perceptual space plus colour naming predicted performance only poorly.
• Moreland, K. (2009). Diverging colour maps for scientific visualization. doi:10.1007/978-3-642-10520-3_9 Described how to construct diverging colour maps that run through a neutral midpoint and stay smooth in lightness and chroma, with an algorithm for generating custom maps. Most scientific visualisation tools still used the rainbow. It solves the ramp as a construction problem and tests no reader.
• 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. doi:10.1371/journal.pone.0199239 Built a module that optimises colormaps for colour-vision-deficient and typical viewers at once, and reported cividis, perceptually uniform in hue and brightness and read nearly identically by both groups. It gives the accessibility claim its number, more than 4 per cent of the population.
• Reda, K., Nalawade, P. and Ansah-Koi, K. (2018). Graphical Perception of Continuous Quantitative Maps: the Effects of Spatial Frequency and Colormap Design. doi:10.1145/3173574.3173846 Tested how colormap design and the spatial frequency of the data interact in reading continuous maps, and found spatial frequency significantly affected the encoding's effectiveness while the precise effect was task-dependent. No single colormap was best across data of different spatial structure.
• Reda, K., Zaid, I. and Nacenta, M. A. (2023). Rainbow colormaps: what are they good and bad for? doi:10.1109/tvcg.2022.3214771 Ran three crowdsourced experiments on how colour categorisation affects the reading of scalar fields, having introduced a method to detect latent colour categories in a colormap. Colourful, categorising scales such as rainbow and diverging helped readers discriminate global, distributional features while making localised features less noticeable, a complementary trade-off.
• Schloss, K. B., Gramazio, C. C., Silverman, A. T., Parker, M. L. and Wang, A. S. (2019). Mapping Colour to Meaning in Colormap Data Visualizations. doi:10.1109/tvcg.2018.2865147 Tested how readers infer which colour means more of a quantity and found the inference governed by background and apparent opacity as well as lightness, so a dark-is-more bias holds when opacity appears constant while an opaque-is-more bias competes with it when it does not. Colour-to-meaning is a contextual convention that uniformity cannot fix.
• Ware, C. (1988). Colour sequences for univariate maps: theory, experiments and principles. doi:10.1109/38.7760 Proposed principles for colour sequences on univariate maps, that a spectrum-like scale should convey amount well but form poorly and a grey scale the reverse, then tested five sequences in psychophysical experiments that partly confirmed the form half.
• Ware, C., Stone, M. and Szafir, D. A. (2023). Rainbow colormaps are not all bad. doi:10.1109/MCG.2023.3246111 A Visualization Viewpoints article that revisits Borland and Taylor (2007) in the light of recent research and argues that rainbow maps have underappreciated properties and can be useful for selected applications. It is an argument rather than a controlled study, which is why the contest is still live.
• Zhou, L. and Hansen, C. D. (2016). A Survey of Colormaps in Visualization. doi:10.1109/tvcg.2015.2489649 Reviewed colormap research and practice, grouping generation techniques into procedural, user-study based, rule-based and data-driven families and classifying maps by data type and task. Its taxonomy shows how much of the field is method for building maps and how little is measured reader outcome.