Mike Kaliski wrote:

As others have mentioned, several articles appeared in various magazines
about the design of fractal antennas. The basic idea is to fold a
standard length of wire using a fractal pattern so that it fits into a
smaller space. One solution I saw was to wind a wire back and forth
across and along a plank of wood using pins or slots cut in the wood to
support the turns. Taking a four inch wide piece of wood around eight
feet long and winding equispaced turns you could easily fit 24 feet of
wire along the plank.
__ __ __
|__| |__| |__| | Using a pattern like this.

Other more complex or even three dimensional designs can fit more wire
into a given space. . .

This general category of antenna is often known as a "meander line", a
technique used for making electrically short antennas which has been
known and used for a very long time. "Fractal" antennas are a more
recent idea. They're a class of meander lines using particular
algorithms to do the meandering in a particular irregular way. Among the
interesting properties of some of these antennas is the presence of
non-harmonically related multiple resonances.

Many claims have been made for "fractal" antennas, among them being that
they provide the best efficiency for a given physical area. Steve Best,
VE9SRB, has credibly refuted this claim by creating some
randomly-meandered designs which are more efficient than claimed best
fractal designs. You'll find some of the history of this in the archives
of this newsgroup. The EZNEC models he developed are still at
http://eznec.com/misc/MI2/ for anyone interested to download and review.
Those models were also used for papers he wrote on the topic in IEEE
publications and, I believe, QEX. It's not clear what advantages, if
any, "fractal" designs would have over random or other meander
topologies for amateur use. The allure of "fractal" antennas seems more
to be in the interesting mathematics and the cachet of being modern and
revolutionary than in any demonstrable performance advantage.

Meander line antennas, including "fractals", share the same properties
as other electrically short antennas: narrow bandwidth and high
conductor current. The latter can result in poor efficiency due to I^2 *
R loss. Meander lines are better than some other methods of loading and
worse than others, depending on how the meander and other methods are
implemented. It's just one of the techniques which antenna designers
have in their bag of techniques to use.

Roy Lewallen, W7EL