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How does one algorithmically calculate a set of N colors that are both contrasting and aesthetically pleasing? For example, we want to plot an unknown number of lines on a graph that still looks good.

I'm not certain on how to quantify aesthetically pleasing, but not clashing with a given palette might be a starting point (e.g the graph borders and an associated logo are Colors A, B, and C).

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Well, there are a couple of different scheming methods known.

At Kuler, you can try scheming methods based on analogous colors, monochromatic, triad, complementary, compound and shades. Also check out the wiki page about color schemes for more examples (also check out the references for some good book references!)

I think a good way to go is to apply changes to a base color in a consistent matter, e.g. only change one variable (brightness, hue, etc) systematically.

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