This second randomly shaped loop design by VE9SRB was the first attempt at achieving better performance than the MI2 Fractal Loop in the same physical aperture.  The physical aperture size was the only design variable that was considered a fixed parameter.  As a result, the design options open were the feedpoint location, the total wire length and the geometry.

Improving the performance of any small loop within the same physical aperture is not necessarily a simple task.  The performance characteritics to improve upon include lowering of resonant frequency (if necessary), SWR  (requires a resonant resistance closer to 50 ohms), the bandwidth wrt 50 ohms (requires a resonant resistance closer to 50 ohms) and finally, the antenna gain.  

For the most part, the gain of the antenna is a function of the aperture size, the radiation resistance and the ohmic losses in the structure.  Since the antennas being compared have the exact same aperture size, similar radiation resistance and similar ohmic losses, we cannot expect much improvement in antenna gain.  Gain improvements in the order of 10ths of a dB would be reasonable.  This leaves lowering of resonant frequency, SWR and bandwidth the remaining performance characteristics to improve upon.  

In this comparison, lowering of resonant frequency is not an issue.  Additionally, in the confined physical aperture, lowering of resonant frequency can be achieved by increasing the total wire length regardless of antenna geometry (shape).  Improvement of SWR and bandwidth are both achieved by increasing the resonant resistance, bringing it closer to 50 ohms.

In general, with shaped small loops, the more compressed the geometry and feedpoint are wrt the center of the loop, the lower the resonant resistance will be.  As a result, it is the opinion of VE9SRB that the feedpoint should be moved to the outside perimeter of the loop.  This will also move the feedpoint to the current max.  Additionally, it is the opinion of VE9SRB that moving as much of the geometry to the outside of the loop as possible will increase the resonant resistance.
 
In the design of compressed loop antennas we must first consider that the square or circular loop with no bends will have a first resonance at a frequency where the total wire length is approximately 1 wavelength.  For example, a square loop with no wire bends occupying the same physical aperture as the MI2 loop will have a first resonance occurring near 29.2 MHz.  The resonant resistance will be approximately 134 ohms.  Adding wire length to this loop along the perimeter will lower both the resonant frequency and the resonant resistance.

The main differences between this loop and the MI2 Loop and Random 1 loop are the following:

1)  The feedpoint is moved to the edge of the loop.  This moves the feedpoint to the current max.
2)  The feedpoint and opposite edges are comprised of a straight wire section with no bends.
3)  The random geometry (wire bends) are kept away from the center of the loop as much as possible.  
4)  The wire length was not keep the same as the MI2.  It was adjusted to keep the resonant frequency as close to that of the MI2 as possible.

The total wire length in this design is about 33.74 m, which is about 26% more than that of the MI2 loop.  The physical aperture size remains unchanged at 2.8 m (X) by 2.66 m (Y).

The first resonance occurs between 14.94 and 14.95 MHz.  The resonant resistance is 32.85 ohms and the antenna gain is 1.94 dBi.  The 2:1 SWR bandwidth wrt 50 ohms is about 1.5%.

In this case, performance improvement is seen in gain, SWR and bandwidth.  The only trade off for this improved performance is some additional wire length.