Wire antennas characterized by a tortuous shape, such as prefractal and meander line dipoles, can exhibit interesting multi-resonant and/or miniaturization capabilities. A key element influencing the resonant behavior of a wire dipole is its topology, and consequently the length and the relative orientation of each wire segment forming the antenna. Recent studies have pointed out the possibility of relating some mathematical quantities, depending on the antenna topology, to the resonant frequencies of a convoluted dipole. However, the fractal dimension alone, which may be significant only for prefractal antennas, does not play a decisive role in determining the resonant behavior of prefractal dipoles. Besides, several studies confirm that many convoluted (non-prefractal) radiators can have multiple resonances and/or miniaturization capabilities. Recently, another mathematical quantity, called lacunarity, has been adopted to examine the resonant behavior of some prefractal wire antennas, such as the Von Koch and the Minkowski dipoles. Lacunarity can be used to characterize both fractal and non-fractal sets, and
represents a measure of the inhomogeneity of a geometrical object, related to the distribution of the gaps in its topology. This paper investigates the possibility of using lacunarity to compare the resonant behavior of different convoluted (prefractal and non-prefractal) wire dipoles. More precisely, the purpose is to verify whether, given two convoluted wire dipoles having the same height and the same total length, the average lacunarity provides sufficient information to infer which dipole exhibits the lower resonances.
