We sometimes need to display points, lines, or areas that stand for more than one thing, and to colour them so they are clearly distinguishable. For example, when plotting several graph lines on the same axes. Here's a little technical tip I found for choosing colour schemes: Cynthia Brewer's ColorBrewer.
Choosing colours for graph lines is one use; another is maps. This is a good cue for me to introduce ColorBrewer. Go to the above URL, look at the left hand side of the page, and click "qualitative" in the second panel down. Then click one of the colour-scheme columns in the "mini legends" panel just below. The map will change so that its different kinds of region are coloured accordingly. Once you have a scheme you like, you can get hex values for the colours by clicking "hex" in the panel below.
I used ColorBrewer for my Category Theory Demonstrations. I wanted to depict the composition of functions, inviting the reader's eye to associate items pointed to on one line with corresponding items pointed from on the line below. Like this:
square_root = { 25→5, 36→6, 49→7 }Eventually, I'll do this with diagrams, but that needs more work.
square = { -5→25, 5→25, -6→36, 6→36, -7→49, 7→49 }
square_root followed by square = {25→25, 36→36, 49→49 }.
ColorBrewer was written by Cynthia Brewer. Her home page tells me that she is a professor of geography, and that her research includes applying colour theory to map design. As well as "qualitative" schemes like the ones I've mentioned, ColorBrewer can be used to choose "sequential" schemes for quantities such as population and height, and "diverging" schemes, where there is a central value from which quantities can either increase or decrease.