This random loop antenna configuration was designed by VE9SRB for comparison with the MI2 Fractal Loop antenna (concept and design by N1IR).   

The performance of the MI2 Fractal Loop antenna as described by N1IR is not disputed.  The MI2 Fractal Loop features a useful resonant resistance in a reduced physical aperture.  The general conclusion presented by N1IR is that "Fractal Loop antennas are a unique class of antennas whose LC properties - by design - force them into compressed resonance conditions."  

It is the opinion of VE9SRB that the performance of the MI2 Fractal Loop (or any Fractal Loop)  is not soley a result of the Fractal geometry.  Rather, the performance of any loop is a function of numerous design parameters, which include geometry (shape), total wire length, the occupied physical aperture and feedpoint location.  Therefore, performance similar to that of the MI2 should be achievable with an arbitrarily shaped geometry with the same total wire length and the same physical aperture.  Since no two loop configurations will be exactly identical, we should not expect performance of any two to be identical.  This is especially true if we define only one parameter in the configurations to be identical, physical aperture as an example.  In all cases, there will be numerous tradeoffs in performance relative to the various design parameters.  There will also be practical limits to the improvement of antenna performance as a function of the design parameters.   Some further specific conclusions will be presented in the random3 text file.  This will allow the readers the opportunity to review the performance of each design before addressing the conclusions.

The random geometry presented here represents one of an infinite number of possible design configurations.   The loop is defined to be "random" because the shape (geometry) of the antenna was arbitrarily chosen.  The only constrainsts in chosing the geometry were that it have the same total wire length and physical aperture as the MI2 Fractal loop.  This antenna has a total wire length of 27.564 m and has an aperture of 2.8 m (X) by 2.66 m (Y).  

The first resonant frequency is between 14.83 and 14.84 MHz, which is lower than that of the MI2 loop.   This is not considered a significant issue as resonant frequency is generally more sensitive to MOM model parameters than other performance characteristics.  The resistance at resonance is approximately 27 ohms.  The antenna gain is 1.83 dBi.  The 2:1 SWR bandwidth wrt 50 ohms is approximately 0.81%.  These performance characteristics are consistent with those of the MI2 Fractal Loop.

The one area of issue is the 2:1 SWR bandwidth.  In most cases, the 2:1 bandwidth of each loop will be very similar if the bandwidth is defined wrt the resonant resistance.  Since  we are considering the bandwidth wrt 50 ohms, a design having a resonant resistance closer to 50 ohms will have a wider bandwidth and a lower SWR.  This takes us to the Random Loop 2 design ....