Nathan Cohen in the US fractalized the quad loop based on the Minkowski square and invented an array of two elements. 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
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.