The above is a recreation of a nice physics demonstration video from Harvard was doing the rounds recently (original). A series of pendula oscillate all with different frequency producing lots of slowly changing patterns as they swing. The key being that the length of each pendulum is arranged such the the frequency difference between adjacent pendula is constant and, as their relative phases change, lots of lovely beat patterns emerge.
The original video:
Adding a few colours and changing the plotting method for the pendula, but keeping the general equations of motions the same, produce lots of interestingly cycling patterns.
Your computer might not enjoy displaying all these Processing sketches at once, but you can see them (and their source code) over at my openprocessing.org.