Nathan Cohen in the US fractalized the quad loop based on the Minkowski square and invented an array of two elements. I think the biggest advantage of fractal antennas is that we get a wide bandwidth with a small size.

This simulation shows that we can almost double the bandwidth with a 3-element array. It has a reflector, a driven element, and a director. These are the results for the 20 m band (~ 14 MHz),

Quad size ~ 290 x 290 cm (0.14 x 0.14 of a wavelength)

Element spacing ~ 280 cm

450 KHz bandwidth (VSWR < 2) around 14.5 MHz

6 dBi gain

10 dB F/B

80° beamwidth

Vertical polarization

It has less gain than could be achieved with a 3-element Yagi, but it has a relatively large bandwidth and is a very compact antenna. It does not need a matching circuit and its impedance is 50 Ohm at resonance, so it could be fed directly through a 50 Ohm coax.

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