As known, fractal antennas are used for example in cell phones. But why is it that so many different kinds of frequencies can be filtered out of the forest of radio waves surrounding us? Is it because of the self-similarity, when you look at different scales of the antenna pattern?
Yes, it's because of self-similarity, although self-similarity alone doesn't guarantee$^1$ good performance. I believe you can understand a fractal antenna as a collection of many antennas of different size/scales put together in a very compact way.
$^1$The full-text of the paper is available here.