On Mon, 24 Nov 2008 14:02:10 -0600, Cecil Moore
wrote:

predictability
predictability

I dare say the Yea-sayers cannot predict any specific, practical,
fractal characteristic when given fractal
mathematical models.

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.

Solution:
Biconical;
LPDA
(barring, of course, no one can give the fractal mathematical models).
Of course, the joke here is that these are neither very gainful, nor
small - the presumed boon of fractal invention. Yet no other
"fractal" can describe this antenna above. Those "fractals" that come
close (maybe covering 3 of the 9 bands) aren't small or gainful
either. Sometimes you just can't win for trying either.

Going to specifics, what is the mathematical model (not just a word
salad description) for a Sierpinksi Gasket? Using that mathematical
model (what students call plug-n-chug for solving an equation), show
the free space best gain at its sixth iteration, fourth resonance (the
30M band of the description above).

What is the greatest physical dimension of this 9 band antenna? What
would be its greatest physical dimension if implemented in a fourth
iteration Triadic Cantor (if, in fact, one were possible to support
these resonances)?

So, a specific fractal antenna, a specific implementation, a specific
characteristic - and years before anyone here will offer a
demonstration of -dare I say it?- predictability. Hasn't happened
from any other correspondents here to this board in the entire history
of the topic. In that same history, not one other scribbler has
offered a link to someone who can do their work for them.

Fractals, always amusing.