One use of Fractal Engineering is in Fractal Antennas:

An Overview of Fractal Antenna Engineering Research


Recent efforts by several researchers around the world to combine fractal geometry with electromagnetic theory have led to a plethora of new and innovative antenna designs. In this report, we provide a comprehensive overview of recent developments in the rapidly growing field of fractal antenna engineering. Fractal antenna engineering research has been primarily focused in two areas: the first deals with the analysis and design of fractal antenna elements, and the second concerns the application of fractal concepts to the design of antenna arrays. Fractals have no characteristic size, and are generally composed of many copies of themselves at different scales. These unique properties of fractals have been exploited in order to develop a new class of antenna-element designs that are multi-band and/or compact in size. On the other hand, fractal arrays are a subset of thinned arrays, and have been shown to possess several highly desirable properties, including multi-band performance, low sidelobe levels, and the ability to develop rapid beamforming algorithms based on the recursive nature of fractals. Fractal elements and arrays are also ideal candidates for use in reconfigurable systems. Finally, we provide a brief summary of recent work in the related area of fractal frequency-selective surfaces.

And another use of Fractals, this time Engineered as an improved cooling method is this MRI improvement:

Goodbye wires and formers: 3-D additive manufacturing and fractal cooling applied to construction of MRI gradient coils


The high pulse frequencies employed in MRI gradient and RF coils call for the use of dedicated construction techniques involving special wires and cooling systems. These requirements are needed because conventional (e.g., solid-core) wires exhibit skin effects at frequencies above 10 kHz, which effectively concentrate all the current in the periphery of the wire, leading to heating losses due to high resistance. To mitigate the resistance problem due to skin-depth, many gradient coils (and some RF coils) employ cords of twisted and/or woven thin insulated wires (e.g., Litz wires) that force currents to traverse the entire wire cross-section. Litz wires are hard to configure into the complex designs required for gradient coils, due to a minimum turning radius of several millimeters and the asymmetric bending forces required for winding the wires onto formers. Another challenge in MRI gradient coil manufacturing is the ability to cool RF and gradient coils, especially at high pulse rates. Our approach to this problem has been to replace traditional wire-coil construction methodology with multi-layer additive manufacturing methods, which lend themselves to design and manufacture automation. Additive manufacturing can enable dramatic (i.e., nearly three-fold) improvement in cooling efficiency, through the use of bio-mimetic fractal approaches. Building gradient and/or RF coils layer by layer, we have added conductive, insulating and cooling elements with appropriate interconnects as necessary. A prototype multi-layer Litz wire structure was developed, with fractal cooling, which showed superior performance (in terms of 80% reduced resistive losses at high frequency) to the comparable non-Litz wire configuration.

Fractal cooling patter for MRI circuit:

Fractal cooling patter for MRI circuit

I would like to know more practical uses for this technology, with a preferred focus on Fibonacci sequence, if possible.


2 Answers 2


It looks like this paper uses fractals to prevent current crowding in a high power MOSFET.

In high power transistor design, you want to maximize current by minimizing resistance.

Power transistor fractal evolution

If you start with a single basic transistor (fist order) with two metalization finger contacts, the wider the transistor is, the lower the transistor active region resistance is. Conversely, your metalization resistance increases because the fingers are getting longer as. You can increase the metal finger thickness to combat this, but then you're simply scaling the entire structure in both the X and Y direction to increase the current. Instead, if we add fingers to the initial two fingers (beginning the fractal), the active area resistance can drop because the transistor channels are now much wider than they are across. The author then extends this into a 2-D pattern for even more efficiency.

The issue is on-resistance would now be dominated by metalization and the current at any specific section of the transistor would become highly non-uniform as shown in their Figure 3. enter image description here

In figure 3B, they show a comb-structure (2nd order) and show the highly non-uniform current crowding that occurs. To resolve that, they go further beyond 2nd order and add in metalization that's tapered to help support uniform current transfer between each side of the transistor in Figure 3a.

  • \$\begingroup\$ I feel like you may have thermal issues in a design like this, but I can't put my finger on why I feel that way. \$\endgroup\$
    – Hearth
    Oct 10, 2021 at 0:03
  • \$\begingroup\$ @Hearth -- Did you read the cited paper. I couldn't because I don't have IEEE access. I found a related paper, "Design and Characterization of Highly-Efficient GaN-HEMTs for Power Applications" which I believe to be very closely related to the one cited by horta (becauses it contains these same diagrams in black and white). If you read the paper, maybe you will either be satisfied, or you can put your finger on what's bothering you. Page 70 begins section "4.4.5 Fractal-Structures for Power Devices". I believe, the Fractal design solves the thermal issues. \$\endgroup\$ Oct 10, 2021 at 1:28
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    \$\begingroup\$ @Hearth Thermal issues are exactly what the fractal design is working to resolve. Current crowding causes thermal hot-spotting. The fractal design allows more even thermal loading across the entire chip. That does mean overall, this chip will be capable of running hotter compared to a non-fractal design. \$\endgroup\$
    – horta
    Oct 10, 2021 at 1:46

I thought I had stumbled on a way to use Fibonacci to filter the input/output of a power converter, by using LC filters according to a Fibonacci progression of values, but as was pointed out to me, my example did not necessarily prove anything.

Therefore, in place of my original answer, I have improved my answer by merely providing one good example of Fibonacci technology in Electrical Engineering, of which you may not be aware. I hope you like it.

Modified Fibonacci Search Based MPPT Scheme for SPVA Under Partial Shaded Conditions


This paper presents the modified Fibonacci search based MPPT scheme for a solar photo voltaic array (SPVA) under partial shaded conditions. The real Fibonacci search based MPPT fails to track the global peak (GP) under partial shaded conditions. This paper improves the method so that the proposed method tracks GP for all the shaded conditions. It is checked for different shading patterns through simulation and verified experimentally.

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    \$\begingroup\$ I recognize the same fractal fever that many caught when learning about them, but Fibonacci is not a fractal. It may have some self-similarity in the way it converges, but no more than e.g. exp(x) is self-similar. Interesting thoughts, though, the antenna part more than others, but still have nothing to do with Fibonacci. Which means the question and the answer have very little to do one with another. \$\endgroup\$ Oct 8, 2021 at 8:13
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    \$\begingroup\$ and this is not a practical use \$\endgroup\$
    – user253751
    Oct 8, 2021 at 8:15
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    \$\begingroup\$ @MicroservicesOnDDD The definition of a fractal is not self-similarity alone--otherwise, a plain line would be a fractal. \$\endgroup\$
    – Hearth
    Oct 9, 2021 at 4:56
  • 2
    \$\begingroup\$ @MicroservicesOnDDD Using "shooting" and "killing" means a personal take on the matter and, thus, opinionated (the "I want to believe" part), much like your interpretation of the "concerned" part of my nick name (implying I should be concerned about you, or your answer). 3 downvotes (still none mine) should make you consider that it's other people, too, that disagree. Nobody's perfect, and good for you that you're learning through mistakes (IMO the longest lasting lessons), but opinionated means blindness; I would run as fast as I could from that. \$\endgroup\$ Oct 9, 2021 at 16:04
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    \$\begingroup\$ Now it's something else. Now, you've focused on finding the links between what you're concerned with (no pun), and the modified question. I say modified because you've changed it and, thus, its meaning, which can be considered "sleight of hand" (I'll leave it, though). It's no longer you, blindly gazing at the wonders of fractals, it's about practical use of fractals and their applications in real life cases (except the slightly victimized "-5" part; that could be omitted, but I'm probably nitpicking). Only now your answer addresses these concerns. Therefore a deserved +1. \$\endgroup\$ Oct 10, 2021 at 8:55

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