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I just answered this question, and I wanted to know if any particular shape has been found to be successful for anyone.

There seems to be a lot of research on IEEE that indicates that there should be specific fractals that are better than others for any particular application. Which ones have you found that work well for amateur radio applications?

I prefer PCB-printed copper to formed-wire, but anything, really, is fine.

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    $\begingroup$ "work" is a bit of an ambiguous term. For what, exactly? Because: most fractal things I've seen are very specific solutions to very specific problems and might or might not be considered "good antennas" in a more general context... $\endgroup$ Oct 13 at 11:24
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    $\begingroup$ hm, not quite sure what you aim for "well for Amateur Radio": What does that entail? Because if you want an antenna that works well in the 2m band, for example, not using a fractal antenna is wiser than using a fractal antenna. If you want to have a multi-band antenna with a suppression for specific directions and / or bands, things that are hard to design for with classical antenna shapes, then you might have a use case where a fractal antenna might be an interesting approach $\endgroup$ Oct 13 at 15:39
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    $\begingroup$ Fractal antennas also work well at trapping dryer lint, snow and ice, they're good for impressing your ham friends around the bbq, and if the fractal is carried all the way to the feedpoint, great solder wicking ability for a strong joint. $\endgroup$
    – tomnexus
    Oct 13 at 20:35
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    $\begingroup$ There are a couple of classic antennas that are actually (degenerate) fractal and work very well: several spirals, and of course, the log periodic antenna. Somehow those get left out when discussing fractal antennas. $\endgroup$
    – user10489
    Oct 13 at 23:58
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    $\begingroup$ This question seems overly-broad to me, because there are infinitely many possible fractal antennas, and because the question doesn't define the criteria for such an antenna to be considered to "work". In other words, it's open-ended and vague; how should a good answer be distinguished from a bad one? The OP might be interested in collecting stories of successful antennas, but this site, and every other Stack Exchange site, is about creating a database of high-quality answers to objectively-answerable questions. $\endgroup$
    – rclocher3
    Oct 14 at 14:10
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Note: question changed since I wrote this answer.

Two classic and highly effective fractal antennas are the log periodic antenna and the many variations (planar, conical, cylindrical, etc.) of the log spiral antenna. The main characteristic of both of these antenna families is extremely broad bandwidth, which can be attributed to the fractal self similarity at multiple scales.

Most other fractal antennas are either less well known or are less effective than an isotropic antenna or the fat wire equivalent antenna, or are extremely specialized. (If anyone knows of others, they should add another answer here!)

Around 2000, when idea of the fractal antenna was first published, there was a lot of enthusiasm, but most papers didn't include any studies of the effectiveness of such antennas. In the following years, a number of additional papers were published, finding that all the new fractal antennas they actually characterized either had lower gain or lower efficiency (or both) than similar antennas that just used fat wires instead of fractal geometry. Fractal antennas did inspire some innovations in antenna theory around the nature of what increases the bandwidth of an antenna.

In a brief search of the literature, I see a lot of fractal antennas, but the papers I found either did not mention antenna effectiveness at all, or admit poor performance. I have heard of rumors of proprietary or trade secret fractal antennas in commercial use, but until something is published about them, they are just rumors. There are two that work, so it is possible there are others.

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    $\begingroup$ I've always thought of Fractal (antennas) as being scale independent but in discrete chunks, so a Vivaldi, Log spiral, Conical log spiral etc don't really count. Things like the Sierpenski snowflake, which apparently offer performance at multiple bands. $\endgroup$
    – tomnexus
    Oct 17 at 5:13
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    $\begingroup$ The log periodic is a degenerate fractal antenna, as in, it doesn't have higher fractal dimension, but it is still a fractal antenna. $\endgroup$
    – user10489
    Oct 17 at 12:13
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    $\begingroup$ I've added some text reflecting history of the fractal antenna. Patents are a poor source of information here, as while a patent must work, it doesn't have to tell you why or if it is effective. $\endgroup$
    – user10489
    Oct 17 at 12:24
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    $\begingroup$ @user10489 but then the yagi-uda is a degenerate fractal antenna too. and, by only relatively slight extension, the dipole just as well. $\endgroup$ Oct 18 at 15:20
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    $\begingroup$ No. The yagi-uda antenna is not self-similar at multiple scales, and is not broad band. A log perodic has every element driven. The yagi has one driven element and no others, so it can't be self similar. Note that the link in the second comment calls the log periodic as "first order fractal". $\endgroup$
    – user10489
    Oct 19 at 0:10

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