Morphet & Symanzik (2010) propose different novel cyclical color ramps by taking ColorBrewer ramps and wrapping them on the circle. All other previous continuous circle ramps I had seen prior were always rainbow scales, and there is plenty discussion about why rainbow color scales are bad so we needn’t rehash that here (see Kosara, Drew Skau, and my favorite Why Should Engineers and Scientists Be Worried About Color? for a sampling of critiques).
Below is a picture of the wrapped cyclical ramps from Morphet & Symanzik (2010). Although how they "average" the end points is not real clear to me from reading the paper, they basically use a diverging ramp and have one end merge at a fully saturated end of the sprectrum (e.g. nearly black) and the other merge at the fully light end of the spectrum (e.g. nearly white).
The original motivation is for directional data, and here is a figure from my paper Viz. JTC lines comparing the original rainbow color ramp I chose (on the right) and an updated red-grey cyclical scale on the left. The map is still quite complicated, as part of the motivation of that map was to show how plotting the JTC the longer lines dominate the graphic.
But I was interested in applying this logic to showing cyclical line plots, e.g. aoristic crime estimates by hour of day and day of week. Using the same Arlington data I used before, here are the aoristic estimates for hour of day plotted seperately for each day of the week. The colors for the day of the week use SPSS’s default color scheme for nominal categories. SPSS does not have anything as far as color defaults to distinguish between ordinal data, so if you use a categorical coloring scheme this is what you get.
The default is very good to distinguish between nominal categories, but here I want to take advantage of the cyclical nature of the data, so I employ a cyclical color ramp.
From this it is immediately apparent that the percentage of crimes dips down during the daytime for the grey Saturday and Sunday aoristic estimates. Most burglaries happen during the day, and so you can see that when homeowners are more likely to be in the house (as oppossed to at work) burglaries are less likely to occur. Besides this, day of week seems largely irrelevant to the percentage of burglaries that are occurring in Arlington.
I chose to make during the week shades of red, the dark color split between Friday-Saturday, and the light color split between Sunday-Monday. This trades one problem for another, in that the more fully saturated colors draw more attention in the plot, but I believe it is a worthwhile sacrifice in this instance. Below are the Hexidecimal RGB codes I used for each day of the week.
Sun - BABABA Mon - FDDBC7 Tue - F4A582 Wed - D6604D Thu - 7F0103 Fri - 3F0001 Sat - 878787