Bivariate colour schemes according to Cynthia Brewer. The combination of the four basic schemes, Binary, Qualitative, Sequential and Diverging, give birth to 10 colour schemes useful in cartography and visualisation. The original chart of C. Brewer contains links to examples of use. The values y, n, T, F, etc. are only illustrative of the nature of the data.  Source: Adapted from the original by the auhor. Click on the image to enlarge it.

Colour plays an important, yet not indispensable, role in data visualisation as we have seen already in other articles about colour within the scope of this digital magazine. 

Cynthia Brewer in her page Color Use Guidelines for Mapping and Visualization proposes a set of recommendations for the use of colour in cartographic and visualisation applications that we intend to review here in summarised form  as a complement of the previous article.

According to C. Brewer the simplest recommendation that one usually receives about the use of colour in cartography is using hue to represent categorical differences (blue for rivers, brown for mountains green for lowlands...) and saturation to show ordered differences (lighter green, lower lands, etc.).

One of the aspects that Cynthia Brewer highlights of colour is its three-dimensionality. We will not extend ourselves about the colour models that make its codification possible. On the computer world the RGB (Red, Green, Blue) model dominates. It combines the three primary elements of the cathodic ray tubes (CRTs) phosphor and later on the three filters of LCD displays. Printers use to adhere to the CMY model that refers to the primary Cyan, Magenta and Yellow inks. Many design programs use also HSB where the three elements are Hue (the hue of colour), Saturation (how pure it is, a saturated colour has no white in its composition) and Brightness (also called Value in the HSV model).     

The latter is closer than the others to more sophisticated perceptual models of colour and makes it simpler to specify a colour since its three dimensions refer to concepts bound to intuition, even though it is completely equivalent to RGB and both of them can be transformed one into the other very easily. 

In any case all of them are three-dimensional and, hence, it is of our interest to use cleverly each one of those dimensions. The users of our graphical representations don't ever think in technical but in perceptual terms regarding colour. For any of us it's simpler to describe a colur as for example "light blue" than giving the proportions of red green and blue or the corresponding CMY coordinates. Hence It's important to play appropriately with the perceptual magnitudes of colour.

Brewer considers 4 diferent types of colour schemes and proposes a colour system fitting each one of them:

Qualitative: data of different categories are usually represented in an effective way by means of differences in hue. For example in a road map we can use blue for rivers, brown for mountains and red for certain type of roads. Or we can associate the data coming from the results of a soccer team with one colour while we use another one for its rival team and so on for the whole league. It's important in these cases that the level of lightness and saturation along with the contrast be equivalent if all the categories are equally important.
Binary: A binary scheme is a qualitative scheme where there are only two categories. Here either a difference in hue or in lightness is enough to differentiate them. For example two kinds of gray or two different colours with equal or different lightness allow us to differentiate. Brewer considers this a particular case of the former one and recommends two levels of gray as the palette.
Diverging: In a diverging scheme data can be grouped in two sets that show two different trends around a balance or theshold point.  For example if we consider the evolution of the stock market we find tickers increasing and decreasing in value. Here the balance point is made of the tickers which percentage of increase lies around 0%. In these cases Brewer deems very useful to use a spectrum of colour with two very different hues in the extremes, for example red and blue or red and green (yellow and blue for the colour blind), that change its saturation up to a minimum (white or even black) in the threshold or equilibrium point that separates both sets.
Sequential: To represent ordered data in sequential form the common recommendation is using variations in lightness or saturation of a given hue. For example we can use a gradation of red to show increasing temperature data. Usually the darker colours are bound to higher values while clearer ones are used for lower values. But this is not indispensable, the important thing is the association of changes in lightness to changes in data values so that the phenomenon is clear from a perceptual standpoint.

Finally these four possibilities can be combined among them to obtain up to 10 commendable bivariate schemes. At the beginning of this article you can see an adaptation of the way Brewer presents said combinations. In this case the data has two variables that can be of any of the above mentioned types. 

For example we could want to represent the increase or decrease of value (diverging) in the stock market along with its volume of business (sequential). It's worth following th links of the original page of Brewer to see the multiple examples of application of these schemes. In that representation some values appear together with the colours (y, n, etc). Its only purpose is to give an example of what the values could represent. Although the matrices are 2x3 and 3x3 in dimensions it's very easy to widen the number of shades to be represented just by adding intermediate colours.

The main limitation of Brewer's colour guidelines is that it has been thought out for the representation of data variables that have a specific location in the graphic space and the colour appears precisely in that location. This covers cartographic maps, isoline maps where colour fills the space between the isolines, choropleth maps or area maps depicting categories. This limitation leaves us, nevertheless, with a wide range of applications that can benefit from the use of these guidelines.

See also the interesting interactive tool ColorBrewer devoted to help finding the appropriate colour scheme.

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