This forth randomly (arbitrary) shaped loop design by VE9SRB is another attempt at achieving  performance similar to or better than the MI2 Fractal Loop with a non-fractal geometry.   In this case, the antenna wire was simply rearranged into a symetrical yet arbitray shape.

The total wire length in this design is about 26.35 m, which is only slightly less than that of the MI2 loop (27.56 m).  The physical aperture size is also slightly but not significantly smaller than that of the MI2.

The first resonance for this design occurs at about 16.06 MHz.  The resonant resistance is 32.8 ohms and the antenna gain is 1.91dBi.  The 2:1 SWR bandwidth wrt 50 ohms is about 1.62%.

For comparison, the performance of the MI2 Loop is as follows:  The first resonance occurs at about 15.155 MHz.  The resonant resistance is 28 ohms.  The antenna gain is 1.83 dBi.  The 2:1 SWR bandwidth wrt 50 ohms is about 1.05%.

With a simple rearrangement of wire geometry, performance similar to or better than the MI2 Fractal Loop is easily achieved.  This is evidence that the Fractal geometry of the MI2 Loop is not the significant parameter in the antenna's performance.  Although the antenna geometry is an important factor, other parameters such as feedpoint location (move the feedpoint 90 degrees and see what happens), total wire length, and aperture size are equally or more important than the Fractal geometry.