Richard Clark wrote:
For the inverse (starting with the practical instead of the
mathematical model) one very simple test:
give the mathematical model for a single fractal
antenna specifically resonant on each frequency:
1.85MHz;
3.8MHz;
7.15MHz;
10.13MHz;
14.15MHz;
18.11MHz;
21.2MHz;
24.93MHz;
28.5MHz,
to within the margins of any Ham band represented by the single
frequency offered.

Since fractal antennas are finding practical applications
when etched on a PC board, your discussion is about as
moot at a 160m rotatable Yagi proving that rotatable Yagis
are not feasible.
--
73, Cecil http://www.w5dxp.com