A while ago I watched this video by Numberphile (a very cool channel!). In terms of the actual math, it’s pretty light, but what I love about it is the idea of creating very cool images via very simple rules.
The idea of it is this. In the video, the guy shows a way of drawing a sequence of numbers (more on that in a minute). You draw a number line, and then you draw a semicircle above the line from the first number of the sequence to the second, with a diameter equal to the distance between the points. Then, you draw a semicircle from the second to third numbers of the sequence in the same way, except this time, the semicircle goes under the number line. You continue this way as long as you want, alternating above/below for the semicircles.