Fractals also have technological applications. Antennas have always been a tricky subject. Many antenna engineers have been reduced to using trial and error because of the complex nature of electromagnetism. The usual long, thin wire isn't the best way. Antenna arrays, another approach, consist of thousands of small antennas which are either placed randomly or regularly spaced.
Fractals provide the perfect mix between randomness and order, and with fewer components.
Parts of fractals have the disorder, while the fractal as a whole provides the order. By bending wires into the shape of Koch's Curve, more wire can be fit into less space, and the jagged shape also generates electrical capacitance and inductance. This eliminates the need for external components to tune the antenna or to broaden its range of frequencies. They're also cheaper to manufacture, can operate on multiple bands, and can be put into the body of the phone. The journal Fractals showed why fractals work so well as antenna.