A single-turn loop inductors can be made within a single layer of conductor, but they might require significant surface area (footprint) to represent sufficient value of inductance. Fractal inductors are capable of representing increased value of inductance without increasing the footprint.
In the study presented by Shoute and Barlage6) the inductance of the base structure was 4.6 nH with resistance of 5 Ω. However, the values for the 3rd-3O configuration was 44.7 nH (increase by 9.7x) and 63.5 Ω (increase by 12.7x), respectively. According to the authors the self-inductance (due to increased length of conductor) does not sufficiently explain the increase, which must be due to some amount of mutual inductance between the neighbouring lobes of the structure. Even some professional modelling electromagnetic software is unable to model this effect seen in experiments.7)
Fractal inductors can exhibit Q factor greater than 40 at the operating frequency. The actual design depends on the type of fractal pattern used, as well as compromises in the design process (e.g. joining the neighbouring lobes). From practical viewpoint it might be more beneficial to implement fewer lobes (thus easier to manufacture) which would give equivalent inductance as more intricate pattern. This less-than-ideal behaviour can be referred to as fractal dilution.