Fractal geometries are characterized by repetition of a basic shape at a variety of scales – for instance, the V shape in the first iteration of this fractal tree (upper left), that is repeated through a multitude of smaller and smaller V’s as the number of iterations increases….
… or the basic triangular shape of this Sierpinski gasket, which is repeated in the cutout interior triangles …
This scaled repetition is useful in electromagnetics for two reasons. The first is that it can lead to multiband or broadband performance, as similar current patterns are allowed to form in the structure at various frequencies. The second is that the dense complexity can allow electrically large structures (supporting multiple wavelengths) to fit in small physical spaces.
Both these features make fractal geometries attractive tools for improving the frequency characteristics of electromagnetic devices whose performance is tied to resonance, such as antennas and metamaterials.
The use of fractals and non-foster circuits for wideband metamaterials and antennas
