While most of what I've read about fractals has been dubious in nature, over the years, I keep hearing that these sorts of self-similar (or approximately self-similar) geometries are useful in the manufacture of high-performance antennas at small scales, perhaps for cell phones or distributed sensing applications. Benoit Mandlebrot himself cited this as one application of his work.
Can anyone provide me an intuitive reason why a fractal geometry, as opposed to some other symmetric structure, would be optimal for compact antenna design?