This is one of the first fractals I generated to help prepare for teaching my Fractals class at Rocky Mountain College. The basic idea actually comes from XKCD #543, aka Sierpinski Heart. Instead of trying to draw something with the black ink rendering the fractals, that piece renders its image in the blank space surrounded by the fractals.
I chose the five-pointed star, because it just felt like a bigger challenge; I was using bilinear interpolation which likes to take a four-sided shape and map it onto a different four-sided shape, but no matter how you frame a five pointed star in a square, you're always left with at least one triangular piece.
Honestly, it's not that interesting in the big picture. One of my students in the class took the same concept and rendered a bowling pin in the center of the start to create a fractal image of the American Bowling Association; which I actually think is more interesting. But it proved very useful in class for pointing out the self-similarity property of stars. I rendered it as a 24" square, and it was easy to see at least 9 levels of recursion.
I'll also remember this piece because when we had the "Computer Art" show at the Ryniker-Morrison Gallery, I decided to eavesdrop when an intro class was going through the exhibit. The teacher was asking the student what she thought about this piece. The student wanted to know the deeper meaning of why the level two star in the upper-right corner was upside down. The truth was, I'd never noticed it before. So much for conceptual art...