This invention entails the use of fractal shapes as cores for electromagnets, and a concurrent shape of a fractal for the windings which surround it. The novelty of this invention lies not only with the shaping, but the advantage of such shaping, which includes producing a smaller form factor electromagnet for the same desired magnetic field strength, when compared to a conventional electromagnet. It will be appreciated that a range of devices including electromagnets, based on such fractal shaping, are additionally novel and include but are not limited to solenoid switches, relays, and other devices in which the fractal electromagnets are used to make a change in state of some device.