At the time I started learning Mathematica (maybe version 3.0), it is almost impossible for any student not to plot space filling curves or other fancy fractals. Except for eye candy, it is quite useless for most of us. Today, it can't even be counted as eye candy any more.
Here is mine, Hilbert Space Filling Curve, which I found in pile of old files, the only thing that warms my heart a bit is that I come up with 4 dimensional version. You probably don't see 4D ones quite often. Of course, it has to be projected into 3D in some way for displaying.