6  Colour

Figure 6.1 shows a pie chart of the number of offenders for different levels of crime seriousness in 2021. In this data visualisation, the crime level, which is a qualitative variable, is encoded as colour, which is appropriate for representing qualitative values (Section 3.4). It is easy to decode the crime levels because it is easy to identify the colour for a particular crime level amongst the set of colours used.

Figure 6.1: A data visualisation of the number of offenders for different levels of crime severity. We can decode different levels of crime from the different colours of the wedges.

Figure 6.2 shows another pie chart of the same data, again encoding the qualitative level as colour. It is again easy to identify each crime level because we can easily identify each separate wedge colour. However, Figure 6.2 has an advantage over Figure 6.1 because we can also decode an ordering of the wedges from more serious crimes, which are darker wedges, to less serious crimes, which are lighter wedges.

Figure 6.2: A data visualisation of the number of offenders for different levels of crime severity. We can decode different levels of crime from the different colours of the wedges and we can decode an ordering of the levels of crime from the colours of the wedges.

The fact that there can be two data visualisations, Figure 6.1 and Figure 6.2, with the same encoding—the qualitative level of crime is encoded as the colour of the wedges—but the two data visualisations have different effectiveness suggests that there is still more to learn about the encoding of data values as colour.

This chapter covers some more details about how the colour visual feature works.

6.1 Hue, chroma, and luminance

We have so far taken a very simplistic approach to colour, treating it as if it is a single qualitative visual feature (Section 3.4). However, the perception of colour can be divided into three separate visual features: hue, chroma, and luminance (Figure 6.3).¹ Hue describes what we normally refer to as the colour name: reds, oranges, yellows, greens, blues, purples, and so on. Chroma describes the colourfulness, from bright (very colourful) to dull (grey), and luminance describes the lightness, from dark to light. Our visual system is capable of perceiving changes in hue and changes in chroma and changes in luminance.

In Section 3.4, we treated colour as a nominal visual feature, but that really strictly only applies to hue. For example, in Figure 5.5, we encoded different ethnic groups as different hues. We are very good at decoding nominal data values, or different groups, from different hues, subject to the capacity limits described in Section 3.6.

Figure 6.3: The perception of colour can be divided into three components: differences in hue, the colours of the rainbow; differences in chroma, from bright and colourful to dull and grey; and differences in luminance, from light to dark.

6.2 Ordinal visual features

Chroma and luminance are both nominal visual features in that they can be used to encode different groups, but they are also ordinal visual features because we can decode an ordering from a set of colours that differ in terms of either chroma or luminance (or both). A set of colours that transitions from darker to lighter and/or brighter to duller conveys an ordering from larger to smaller.²

This helps to explain the advantage of Figure 6.2 over Figure 6.1. In Figure 6.2, the colours differ mostly in terms of luminance and chroma so we are able to perceive changes from larger values to smaller values because the colours transition from darker to lighter.

In this sense, chroma and luminance are able to convey more information than hue because they can represent nominal differences and ordinal differences, whereas hue can only represent nominal differences.³

On the other hand, Figure 6.4 shows that chroma and luminance are even more limited than hue in terms of capacity. We can only use chroma and/or luminance to represent nominal data when there are very few different groups to represent.

Figure 6.4: Encoding qualitative values to luminance and chroma works well for representing nominal data values, but only for a very small number of values. It is possible to identify which shade of purple the single dot corresponds to amongst the three shades on the left, but it is much harder with the seven shades in the middle, and harder still for the eleven shades on the right. This figure can be compared with Figure 3.13, which demonstrates the capacity of hue for representing nominal data values.

If we encode data values to the hue of data symbols, then we can only decode nominal information from the data symbols; do the data symbols represent different groups or the same group.

If we encode data values to the chroma and/or luminance of data symbols, it is also possible to decode ordinal information form the data symbols.

6.3 Perception is relative

We saw in Section 5.4 that perception of lengths is relative. For example, small differences in length are easier to see when the lengths themselves are short (Figure 5.9).

There is a similar rule for the perception of colours. Our perception of luminance and chroma is affected by neighbouring colours.⁴ This effect is demonstrated in Figure 6.5: the same colour when surrounded by a darker background appears lighter than it does when surrounded by a lighter background.

Figure 6.5: The perception of colours is relative. In the top row, the inner rectangles are exactly the same shade of grey on the left and exactly the same shade of purple on the right. The perception of the inner rectangles is affected by the surrounding colour, so the same shade appears darker against a light background and lighter against a dark background. The bottom row draws a line connecting the two inner rectangles to show that they really are the same shade.

This effect also applies to the perception of hue. Figure 6.6 shows a pie chart of the number of offenders in each police district, with the police district encoded to the colour of the wedges. There are two issues with the perception of the wedge colours: each wedge is affected by its neighbour so that, for example, some of the blue wedges look more green at the boundary with their more blue neighbour and more blue at the boundary with their more green neighbour; furthermore, the colours in the legend are perceived differently from the corresponding colours in the wedges because the legend colours are surrounded by a light grey, rather than sharing a boundary with a neighbouring colour.

Figure 6.6: This pie chart demonstrates that the perception of hues is relative. The colours within each wedge appear to have a subtle gradient within the wedge because the perception of the wedge colour is affected differently by the neighbouring wedge colours.

The pie chart in Figure 6.6 is not an effective data visualisation because it encodes qualitative data values with many different groups as colour hue. This exceeds the capacity of the hue visual feature; it is difficult to clearly identify which wedge corresponds to which district (Section 3.6). We have just used it here to demonstrate the relative perception of colours.

Although it does not make the use of hue any more appropriate, for the purposes of demonstration, we can solve the colour perception problems in Figure 6.6 by adding a white border to all of the wedges and to the squares of colour in the legend (Figure 6.7). Now all of the wedges and all of the squares in the legend are perceived relative to a surrounding white border. This means that, not only is each wedge perceived as a solid block of constant colour, but it is easier to match the colours within the wedges with the colours in the legend.

Figure 6.7: The hues in this pie chart are perceived more accurately than those in Figure 6.6 because each wedge is surrounded by a white border.

If we encode data values as the colour of data symbols, we may have difficulty decoding the colours if the same colour is presented with different colours adjacent to it. This is an example where and encoding can be less effective because our visual system does not always faithfully decode values (Section 2.10).

6.4 Size matters

The perception of colours is also affected by the size of the coloured region. In particular, small regions of colour may blend together with neighbouring colours.⁵ For example, on the left of Figure 6.8, the yellow and blue stripes are, in reality, the same colours both in the top set of wide bars and in the bottom set of narrow bars, but the blue bars appear greener in the bottom set. The right side of Figure 6.8 shows that the same colours may appear different when they are used as fill colours for larger regions, like bars, compared to when they are used for thin lines. In this case, the blue line appears darker than the blue bars even though the two blues are exactly the same.

If we encode data values as the colour of data symbols, we may have difficulty decoding the colours if there are large differences in the sizes of data symbols. This is another example of our visual system not producing consistent results (Section 2.10).

Figure 6.8: The perception of colours varies based on the size of the coloured regions.

6.5 Colours in space

Figure 6.9 shows two-dimensional slices of the set of visible colours arranged in three dimensions.⁶ The central column of three coloured regions (surrounded by white circles) show slices of colours with constant luminance. Chroma increases outwards from the centre (indicated by a white dot) and hue changes with angle. In each slice, we can see the familiar rainbow of colours from red, through orange, yellow, green, blue, indigo, violet, and back around to red. The top slice is for high luminance (light) colours and the bottom slice is for low luminance (dark) colours.

The coloured regions to the left and to the right (surrounded by white semicircles) show slices of constant hue. In these slices, Luminance increases from bottom to top and chroma increases away from the flat side of the semicircle. For example, the top-left slice shows the same green hue at different levels of luminance and chroma.

Figure 6.9: Slices through the set of colours that are visible to humans. The central images show colours that differ in terms of chroma and hue, but share a common luminance (from lighter at the top to darker at the bottom). The images to the left and right show colours that differ in terms of chroma and luminance, but share a common hue.

Figure 6.9 provides insight into what sorts of colours are possible and what sorts of differences between colours are possible. For example, from the bottom central slice we can see that it is not possible to produce colours that have a high chroma and are very dark. In other words, there is no such thing as a very colourful black. This is also true for colours that are very light.

We can also see that the range of possible chroma values depends on both the hue and the luminance of colours. For example, the top-right slice shows that it is possible to produce a light yellow with either a low chroma or a high chroma, but we can only produce a dark yellow with a low chroma. Equivalently, the range of possible luminance values depends on both the hue and the chroma of colours. For example, we can produce both dark and light low-chroma yellows, but we can only produce light high-chroma yellows.

This means that, if we want to encode data values as the chroma of a data symbol, we can get a wider range of colours—we can get a higher decoding capacity—through careful selection of hue and luminance. For example, we can generate a wider range of light greens than dark greens (the top-left slice) and a wider range of reds that are neither too light nor too dark (the centre-right slice).

Figure 6.10 is similar to Figure 6.9 except that, instead of showing the range of colours that it is possible to perceive, it shows the range of colours that it is possible to produce using standard technology.⁷ The simple message here is that the limits on the range of colours that we can use to encode data values is much smaller than the range of possible colours. On the positive side, the range of colours that we can produce is still very large. A more important message is that the general points about differences between colours still apply. For example, the range of possible chroma values is dependent on the hue and luminance of colours.

If we encode data values as the colour of data symbols, the choice of hue, luminance, and chroma affects the capacity of decoding—how many different colours can be effectively decoded.

Figure 6.10: Slices through the set of colours that it is possible to produce on a typical computer monitor.

6.6 Colour harmony

We have seen that hue is an appropriate visual feature for encoding nominal data values because we can decode differences between hues without any implied ordering between hues. For example, blue is not larger than red.

However, it is not entirely true that there is no sense of distance between different hues. The left image in Figure 6.11 shows a colour wheel of hues for a constant luminance and chroma. Hues that are close together on this colour wheel are decoded as more similar than hues that are on opposite sides of the wheel. For example, the top two circles on the right of Figure 6.11 have hues that are both from the left side of the colour wheel so they appear similar, but the bottom two circles have hues from the left and the right side of the colour wheel so they have a greater contrast.⁸

If we encode data values as hue, it is possible to decode some hues as more similar to each other and other hues as very different from each other.

Figure 6.11: On the left, a colour wheel that shows differet hues for a constant chroma and luminance. At top-right is a pair of hues from the left side of the colour wheel and bottom-right is a pair of hues from opposite sides of the colour wheel. There is greater contrast between the bottom pair of colours and less contrast between the top pair of colours.

6.7 Colour vision deficiency

Roughly 10% of the population, primarily men, suffer from a form of colour vision deficiency (CVD). In the most common case, the viewer will have difficulty distinguishing between red and green hues.⁹ Figure 6.12 simulates how the colours in Figure 6.6 would appear to a person with severe CVD.

Figure 6.12: A data visualisation of the number of offenders for different police districts. This is how a person with severe deuteranopia might perceive the colours in Figure 6.6.

In order to avoid confusion for viewers with CVD, it may be necessary to vary luminance and/or chroma in addition to or instead of hue. For example, Figure 6.13 shows how the shades of purple in Figure 6.2 would appear to a viewer with severe deuteranopia. It is not important that a viewer with CVD perceives a different hue in this case because the more important difference is in the luminance and chroma of the colours.

When we encode data values as the colour of data symbols, some viewers will have difficulty decoding the colours if we do not take into account common forms of colour vision deficiency.

Figure 6.13: A data visualisation of the number of offenders for different levels of crime seriousness. This is how a person with severe deuteranopia might perceive the colours in Figure 6.2.

6.8 Escape capacity

We have previously identified that colour has a limited capacity (Section 3.6 and Section 6.2). In general, we cannot use colour to encode more than around 7 different categories. Section 6.5 also demonstrated that this capacity varies for different combinations of hue, chroma, and luminance.

One way to increase the decoding capacity of a colour encoding is to vary more than one of hue, chroma, and luminance at once. For example, the top row of Figure 6.14 shows a set of colours that only vary in terms of luminance—hue and chroma are held constant. In the second row of Figure 6.14, in addition to increasing luminance, we have increasing chroma, so there are larger differences between colours, but still a clear ordering. Similarly, in the bottom row of Figure 6.14, the hue changes slightly as the luminance increases so that the differences are more obvious.

In effect, this is an example of a non-linear encoding (Section 4.7) because we take a non-linear path through colour space (Section 6.5). When encoding ordinal data values as colour, the capacity can be increased by varying more than one of hue, chroma, and luminance.

Figure 6.14: The top row holds hue and chroma constant and just varies luminance. It is limited to a very low chroma. The middle row varies chroma as well as luminance, which provides a wider range of colours compared to the top row. The bottom row varies hue as well as chroma and luminance, which provides an even wider range of colours.

Another way to expand the decoding capacity of a colour encoding is to reduce the number of colours that need to be directly compared. For example, if data symbols are arranged in a very regular pattern, like in a bar plot, comparisons between neighbouring data symbols are most important. This means that we can order the colours to maximise neighbour differences rather than maximising all pairwise differences.¹⁰ Figure 6.15 demonstrates this idea with a bar plot of the crime rate in different districts for both 2011 and 2021. This bar plot uses the same set of hues as Figure 6.7, just in a different order so that adjacent bars have very different colours. It is very easy to distringuish between adjacent colours.

Figure 6.15: The hues in this pie chart are ordered so that adjacent hues are distant from each other.

A similar idea is to just reuse a smaller set of hues, which means larger differences between adjacent colours, but repeat the set. The regular arrangement of the data symbols means that we can still differentiate between repeated colours because of the bar positions (Figure 6.16). For example, we can differentiate the pink for the Wellington district from the pink for the Eastern district because Wellington is at the end and Eastern is in the middle.

When encoding nominal data values as colour, the capacity can be increased by focusing on adjacent colours rather than all pairs of colours.

Figure 6.16: The hues in this pie chart are repeated so that adjacent hues are more distant from each other.

6.9 Colour palettes

When we encode nominal or ordinal data values as colours, we have to choose a set of colours, or a colour palette. For example, in Figure 6.1 we have to choose a different colour to represent each level of crime.

This choice is difficult because there are many different colours to choose from and often there is no obvious encoding from a data value to a particular colour. For example, what specific hue, chroma, and luminance should we choose to represent a “high crime level”? As we have seen in the preceding sections, there are also many, sometimes competing, criteria involved in selecting effective colours.

As an example, we can consider the problem of selecting a set of 5 different hues to represent 5 different categorical data values, like the palette that is required to represent the difference levels of crime in Figure 6.1.

We know that it is effective to encode qualitative data values as the hue of a data symbol (Section 3.4 and Section 6.1). In order to make the individual hues easy to identify, we can place them evenly around the colour circle. If we do not want the viewer to decode any ordering of the data values from the data symbols, then we should also hold the chroma and luminance of the data symbols constant. The top row of Figure 6.17 shows a palette that follows that simple approach.

The bottom row of Figure 6.17 shows one big problem with this attempt: the hues are very hard to identify for viewers with CVD (Section 6.7).

Figure 6.17: The top row shows a colour palette that attempts to vary hue evenly, in order to allow decoding of nominal data values, while holding chroma and luminance constant, in order to avoid decoding of ordinal data values. The bottom row shows how the palette appears to a viewer with red-green CVD.

Figure 6.18 shows another big problem with the palette in the top row of Figure 6.17. An attempt to hold chroma constant for a range of hues will fail on most standard computer displays because they cannot produce high chroma for all hues (Section 6.5).

Figure 6.18: A view of the colour palette from Figure 6.17 relative to the range of colours that are possible on a standard computer monitor. The palette attempts to produce the same chroma for different hues, but only a much lower chroma can actually be achieved for some hues. The result is that the brown, green, and blue in the colour palette are less colourful than the purple and red.

Given the difficulty of selecting an effective colour palette, there is a good argument for making use of pre-existing colour palettes that have been designed by experts. For example, the ColorBrewer web site provides tools for choosing colour palettes for nominal and ordinal encodings. Another example is the Okabe-Ito palette, which is specifically designed for encoding nominal data (up to 9 categories) using colours that allow effective decoding by viewers with all types of CVD (Figure 6.19).¹¹

Selecting a colour palette is a complex task so it is a good idea to make use of an existing colour palette that has been designed by an expert.

Figure 6.19: The top row shows the first 7 colours from Okabe-Ito. The bottom row is 7 sequential “Greens” from ColorBrewer.

6.10 Case study: Diverging colour palettes

We have data on the total number of points that were scored and conceded in World Cup matches for Tier One nations at each World Cup. Table 6.1 shows a sample of these data. This an aggregated version of the data set that we saw in Table 4.2.

Table 6.1: A table of the total number of points scored and conceded by Tier One nations in Rugby World Cup matches at each World Cup. Each row represents the total points scored by one team in one World Cup. There are 100 rows in total, with just the first 6 rows shown here.

team	year	scored	conceded	diff
Italy	1987	22	95	-73
Italy	1991	27	67	-40
Italy	1995	51	52	-1
Italy	1999	10	168	-158
Italy	2003	22	97	-75
Italy	2007	30	94	-64

Figure 6.20 shows a heatmap of the points differential (points scored for minus points scored against) for Tier One nations at each Rugby World Cup. The data symbols are rectangles, the teams are encoded as the vertical positions of the rectangles, and the years are encoded as the horizontal positions of the rectangles. These are both effective encodings and we can easily decode to teams or years. The points differentials are encoded as the colour of the rectangles, but in a slightly complicated way. Positive data values encode to a shade of green, while negative values encode to a shade of brown. In both cases, we have a constant hue, with increasing chroma and decreasing luminance as the data values get further away from zero.¹²

The use of two hues creates two different groups (positive and negative values), while the changes in chroma and luminance convey changes in absolute magnitude (if only for ordinal comparisons).¹³ This means that we can easily identify positive versus negative points differentials and we can easily decode larger or smaller points differentials (within each of those groups).

A diverging colour palette is effective because it creates two distinct visual features: a nominal hue to differentiate between two groups and changes in chroma and/or luminance to encode ordinal values within each group.

Figure 6.20: A heatmap of the total points differentials for Tier One nations at individual Rugby World Cups. South Africa was excluded from the 1987 and 1991 tournament due to its apartheid policies.

6.11 Case study: The rainbow

In some fields of research, for example medical imaging and geographic imaging, a common task is to visualise numeric data values on a regular spatial grid. Figure 6.21 shows an example, where the grid is a set of longitudes and latitudes in the vicinity of New Zealand and the data values are measures of wind strength (this is the data set that we saw in Figure 2.2).

A common approach is to encode the numeric data values using colour¹⁴ and it is also common to use a rainbow colour palette for that encoding (Figure 6.21). However, there are several problems with this approach.¹⁵

Figure 6.21: A snapshot of wind strength in the vicinity of New Zealand on September 14 2024. This uses the same data as Figure 2.2, but does not show wind direction. The image uses a rainbow colour palette (from red through green and blue to violet; see Figure 6.22).

Figure 6.22 shows the spectrum of colours for rainbow palettes.¹⁶ This shows that the colours within a rainbow palette differ mostly in terms of hue and we have already established that hue is not a good visual feature for encoding quantitative data values (Section 3.4 and Section 6.1).

Figure 6.22: The top row shows the spectrum of colours from which a classic rainbow colour palette is taken. The middle row shows the changing luminance of the colours in the rainbow spectrum. The luminance of the blue colours is considerably less than the luminance of the yellows and greens and even the reds. The bottom row shows an example rainbow palette of 6 colours taken from the rainbow spectrum.

At the same time, The middle row of Figure 6.22 shows that the rainbow palette also varies in terms of luminance. We know that luminance can be an effective encoding for ordinal data values (Section 6.2), but the luminance changes in a rainbow palette are not monotonic. There are regions of almost constant luminance plus regions where luminance decreases followed by regions where luminance increases.¹⁷ This makes a rainbow palette a poor encoding even for showing the order of numeric data values.

Finally, the changes in luminance and chroma within the rainbow spectrum produce bands of colours (red, yellow, green, cyan, blue, magenta). In other words, the spectrum appears discrete rather than continuous. This can result in a decoding that adds structure (discrete levels) to numeric data values that are in reality continuous.¹⁸ For example, Figure 6.21 suggests three main regions—red-yellow, green-cyan, and blue-magenta—but the underlying data values vary more smoothly than that.

6.12 Case study: Viridis

One of the arguments for using a rainbow colour palette is that viewers like that it is colourful. We also saw in Section 6.8 that varying hue in addition to luminance can help to increase the capacity of an ordinal colour scale.¹⁹

The viridis colour palette, shown in Figure 6.23 (on the right), is an attempt to fix the problems of the rainbow palette, while still retaining a significant range of hues. Compared to Figure 6.21, it is much easier to decode regions of stronger winds and regions of weaker winds. This is because the regions of stronger winds are darker than the regions of weaker winds in Figure 6.23, rather than just being different hues in Figure 6.21.

At the same time, the image on the left of Figure 6.23 shows a colour palette that only varies in terms of luminance and we can see that it is easier to see some details in the more colourful viridis map, such as the variations in low wind strength (the yellows) over New Zealand. This is thanks to the changes in hue as well as luminance in the viridis map; the grey-scale map on the left of Figure 6.23 varies only in terms of luminance.

Figure 6.23: A snapshot of wind strength in the vicinity of New Zealand on September 14 2024. This uses the same data as Figure 2.2, but does not show wind direction. The image on the left encodes wind strength as shades of grey (darker is stronger) and the image on the right uses a viridis colour palette (Figure 6.24).

Figure 6.24 shows the spectrum for viridis colour palettes.²⁰ We can see that there is still a large range of hues, but the change in luminance is now monotonic, which at least allows decoding of ordinal data values. In addition, the range of hues has been selected to be appropriate for viewers with red-green colour blindness (Section 6.7).²¹

Figure 6.24: The top row shows the spectrum of colours from which a viridis colour palette is taken. The middle row shows the changing luminance of the colours in the viridis spectrum. The luminance change is monotonic. The bottom row shows an example viridis palette of 6 colours taken from the viridis spectrum.

6.13 Summary

Précis (click to expand/contract)

Data visualisations can be very effective for communicating information.

However, a data visualisation that is effective for communicating one type of information may be ineffective for communicating another type of information.

The goal of this book is to explain why some data visualisations are more effective than others at communicating different types of information—how data visualisation works.

We will focus on how information can be encoded to create a visual representation. We will characterise a data visualisation in terms of the encodings that it uses to convert data values into data symbols.

The effectiveness of an encoding will depend on how well we can decode the information that we want from a visual representation. We will judge a data visualisation in terms of how well data values can be recovered from the data symbols.

There are features of the human visual system that mean that we can decode some information extremely rapidly and without effort:

• A very large amount of basic information is gathered at once about simple visual features like positions, lengths, and colours.

• Large, bright, colourful items automatically attract attention.

• We automatically identify groups of items within an image based on similarity of basic visual features like position and colour, plus connecting lines and enclosing borders.

On the other hand, there are limitations of the visual system that suggest encodings that we should avoid:

• Detailed information is only available at the centre of the visual field.

• Visual memory is extremely limited.

These features suggest that encoding data values as basic visual features and generating simple, orderly data visualisations will lead to rapid and effortless decoding of information.

A simple encoding of data values to data symbols involves encoding each data value to a separate data symbol. This allows the viewer to decode and compare individual data values from the data symbols.

A simple encoding of data values to data symbols also involves encoding each data value as a basic visual feature of the data symbol, e.g., position, length, area, angle, colour, or pattern.

Position, length, area, and angle are appropriate for encoding quantitative data because we can decode numeric values from these visual features. We can decode position and length more accurately than area and angle.

Position, colour, and pattern are appropriate for encoding qualitative data because we can decode groups from these visual features. We can represent a large number of categories if we use position, but only a few categories if we use colours and patterns.

Encoding data values as the position of data symbols is very effective for decoding of both quantitative and qualitative information. However …

• For quantitative values, what we can accurately decode are comparisons between quantitative values, not absolute quantitative values.

• The decoding is most accurate for positions that share a common baseline.

• Encoding identical data values as the positions of data symbols means that the data symbols overlap, which compromises our ability to decode data values from the data symbols.

• We can encode one set of data values as horizontal positions and another set of data values as vertical positions because we can decode horizontal and vertical positions separately.

• Decoding quantitative data values from the positions of data symbols is only accurate if the encoding is linear.

Encoding data values as the length of data symbols is very effective for decoding quantitative information. However …

• Comparisons between lengths are more difficult if the lengths are far apart, especially if there are distractors in between.

• Comparisons between lengths are more difficult if the lengths do not have a common baseline.

• Comparisons between lengths are easier for shorter lengths.

Colour is really three visual features: hue, chroma, and luminance.

Hue is excellent for encoding nominal data values, though it has a limited capacity.

Chroma and luminance can be used to encode ordinal data values (as well as nominal data values), but they have even lower capacity.

When we encode data values as colours there are several caveats:

• The decoding of data values from colours is affected by surrounding colours and the size of the data symbol.

• Approximately 10% of viewers are unable to differentiate between red and green hues with similar chroma and luminance.

Selecting which colours should be used to encode data values is difficult to get right and a good solution often involves varying all of hue, chroma, and luminance at once.

Consequently, it is usually a good idea to make use of pre-existing colour palettes that have been carefully designed to avoid most problems.

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Schloss, Karen B. et al. 2023. “More of What? Dissociating Effects of Conceptual and Numeric Mappings on Interpreting Colormap Data Visualizations.” Cognitive Research: Principles and Implications 8 (38). https://doi.org/10.1186/s41235-023-00482-1.

Schloss, Karen B., Zachary Leggon, and Laurent Lessard. 2021. “Semantic Discriminability for Visual Communication.” IEEE Transactions on Visualization and Computer Graphics 27 (2): 1022–31. https://doi.org/10.1109/TVCG.2020.3030434.

Smith, Nathaniel, and Stéfan van der Walt. 2015. “A Better Default Colormap for Matplotlib.” YouTube video. https://www.youtube.com/watch?v=xAoljeRJ3lU.

Stone, Maureen. 2012. “In Color Perception, Size Matters.” IEEE Comput. Graph. Appl. 32 (2): 8–13. https://doi.org/10.1109/MCG.2012.37.

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Ware, Colin, Maureen Stone, and Danielle Albers Szafir. 2023.“Rainbow Colormaps Are Not All Bad .” IEEE Computer Graphics and Applications 43 (03): 88–93. https://doi.org/10.1109/MCG.2023.3246111.

Zeileis, Achim, and Paul Murrell. 2023. “Coloring in r’s Blind Spot.” The R Journal 15: 240–56. https://doi.org/10.32614/RJ-2023-071.

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1. The three-dimensional experience of colour arises from the fact that there are three different sorts of cones in the retina (see Section 2.1), each sensitive to a different range of light wavelengths: The L cones respond to long wavelengths (reds); the M cones respond to medium wavelengths (greens); and the S cones respond to short wavelengths (blues). The neural connections that combine the messages from the retina are also divided into three pathways: light-dark, which represents the sum of L, M, and S cones; red-green, which represents the difference between L and M cones; and blue-yellow, which represents the difference between S cones and the sum of L and M cones. For a more detailed description, see Ware (2021).

2. Schloss, Leggon, and Lessard (2021) and Schloss et al. (2023) are examples of studies that have demonstrated that viewers naturally decode darker colours to larger values.

3. The stance taken in this book, that chroma and luminance are only appropriate for qualitative (including ordinal) data, is more rigid than in many other places. Chroma and luminance are often included as an appropriate choice for encoding quantitative data values as well, albeit a poor one. For example, Cleveland and McGill (1984) includes chroma (as saturation) and Munzner (2014) includes both luminance and chroma (as saturation) in their rankings of the accuracy of different visual features.

4. This relative perception of colours is useful for being able to adapt to a wide range of lighting conditions. See Ware (2021) for a more detailed discussion.

5. Stone (2012) describes “spreading”, which means a blending or averaging of colours over small areas by the visual system: “In designing colors for digital visualization systems, one of the most critical factors is the interaction between size and color appearance.”

6. Figure 6.9 shows the extent of the optimal colour solid, which is essentially the colours that it is possible to produce by reflecting a light source off a surface that has perfect reflectance. This colour solid was determined assuming specific illumination conditions (D65), and assuming a standard human observer.

   The colours are shown in CIE \(L^*u^*v^*\) space (aka HCL space), which is (roughly) perceptually uniform so that perceptual differences between pairs of colours that are the same distance apart within the space are perceived as having the same visual difference.

   The colours shown are produced using sRGB specifications, so many of the colours, especially at high chroma, are not realistic.

7. Figure 6.10 shows the gamut of sRGB colours in CIE \(L^*u^*v^*\) space (aka HCL space).

8. In colour theory, hues that are close together on a colour wheel are referred to as analogous and hues that are opposite each other are complementary.

9. This is more commonly known as red-green colour blindness. Blue-yellow colour blindness is also possible, but much rarer. There are also four distinct categories of red-green colour blindness, though the effect on the colour perceived is similar in all cases. The images used in this book simulate deuteranomaly (the most common form of CVD).

   The approximate figure of 10% is from Ware (2021).

10. This idea is described and demonstrated in Bartolomeo et al. (2025).

11. The ColorBrewer tools are described in Harrower and Brewer (2003).

    Okabe and Ito established the Color Universal Design organization, but the associated web site is no longer available. Okabe and Ito (2008) provides a general discussion of colour-blindness, including the palette used in Figure 6.19. An earlier piece of work that produced a palette of just 4 colours is described in Ichihara et al. (2008).

    Zeileis and Murrell (2023) provides an overview of a large number of different palettes, within the context of producing data visualisations in R.

12. This colour palette is based on the BrBG diverging palette from ColorBrewer.

13. In contrast to a diverging colour palette, a colour palette for nominal data is often called a qualitative palette and a palette for ordinal or qualitative data is called a sequential palette.

14. The resulting image is often referred to as a pseudo-colour image.

15. The problems with rainbow palettes have been well-known for decades and attempts have been made to stamp out the use of rainbow colour palettes, but they remain popular in some fields of research (Borland and Taylor II 2007; Gołębiowska and Çöltekin 2022).

16. The rainbow palette is typically a fully-saturated, maximum-value spectrum of hues—the most colourful and brightest colours that a typical computer monitor can produce.

    Saturation and value are essentially less accurate versions of chroma and luminance. For example, a fully-saturated, maximum-value yellow has a higher chroma and luminance than a fully-saturated, maximum-value blue.

    The rainbow spectrum is basically a path along the boundary of the colours in Figure 6.10, visiting the most extreme points for different hues. This path clearly is not going to have a simple monotonic change in either luminance or chroma.

17. A rainbow palette is a colour encoding that is non-linear (Section 4.7).

    The representation of luminance in Figure 6.22 also shows an example of a 3d illusion (Section 2.10). The curved line combined with the gradients of grey tempt us to see a curved wall of constant height that is receding from us.

18. Heer and Stone (2012) discuss that viewers tend to group colours by discrete colour names and that those colour groups help to explain how colour palettes are decoded.

19. Liu and Heer (2018) provide evidence that colour palettes that vary in hue as well as luminance and/or chroma (multi-hue palettes) lead to faster and more accurate decoding than palettes with a constant hue (single-hue palettes). Ware, Stone, and Szafir (2023) make a similar argument.

20. There is no official publication that explains the development of the viridis colour spectrum, but there is a video on YouTube that is very good (Smith and Walt 2015).

21. Nuñez (2018) take things a step further with a cividis colour palette that provides a CVD-safe version of viridis that also has a wider and linear variation in luminance (in Figure 6.24, we can see that the changes in luminance are non-linear and do not span the full range of luminance).