Antennas seem simple enough, but the theory behind them, based on Maxwell's equations of electromagnetism , is almost impenetrable. Even the highest-tech receivers often depend on a scraggly wire no better than what Guglielmo Marconi used in the first radio a century ago.
Fractals help in two ways.
First, they can improve the performance of antenna arrays. Many antennas that look like a single unit, including most radar antennas, are actually arrays of up to thousands of small antennas. Traditionally, the individual antennas are either randomly scattered or regularly spaced. Second, even isolated antennas benefit from having a fractal shape. Not only can crinkling an antenna pack the same length into a sixth of the area, but the jagged shape also generates electrical capacitance and inductance, thereby eliminating the need for external components to tune the antenna or broaden the range of frequencies to which it responds.