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Fractal Antennas

Published on Apr 02, 2024


There has been an ever-growing demand, in both the military as well as the commercial sectors, for antenna designs that possess the following highly desirable attributes: 1. Compact size 2. Low profile 3. Conformal 4. Multi-band or broadband

There are a variety of approaches that have been developed over the years, which can be utilized to achieve one or more of these design objectives. Recently, the possibility of developing antenna designs that exploit in some way the properties of fractals to achieve these goals, at least in part, has attracted a lot of attention.

The term fractal, which means broken or irregular fragments, was originally coined by Mandelbrot to describe a family of complex shapes that possess an inherent self-similarity or self- affinity in their geometrical structure. The original inspiration for the development of fractal geometry came largely from an in-depth study of the patterns of nature. For instance, fractals have been successfully used to model such complex natural objects as galaxies, cloud boundaries, mountain ranges, coastlines, snowflakes, trees, leaves, ferns, and much more.

Since the pioneering work of Mandelbrot and others, a wide variety of applications for fractals continue to be found in many branches of science and engineering. One such area is fractal electrodynamics, in which fractal geometry is combined with electromagnetic theory for the purpose of investigating a new class of radiation, propagation, and scatter problems. One of the most promising areas of fractal-electrodynamics research is in its application to antenna theory and design.

Traditional approaches to the analysis and design of antenna systems have their foundation in Euclidean geometry. There have been considerable amounts of recent interest, however, in the possibility of developing new types of antennas that employ fractal rather than Euclidean geometric concepts in their design. We refer to this new and rapidly growing field of research as fractal antenna engineering.

Because fractal geometry is an extension of classical geometry, its recent introduction provides engineers with the unprecedented opportunity to explore a virtually limitless number of previously unavailable configurations for possible use in the development of new and innovative antenna designs. There primarily two active areas of research in fractal antenna engineering.

These include:

1.) the study of fractal-shaped antenna elements, and

2.) the use of fractals in the design of antenna arrays.

The purpose of this article is to provide an overview of recent developments in the theory and design of fractal antenna elements, as well as fractal antenna arrays. The related area of fractal frequency-selective surfaces will also be considered in this article.


The term "Fractal means linguistically "broken" or "fractured" from the Latin "fractus". Benoit Mandelbrot, a French mathematician, introduced the term about 20 years ago in his book "The Fractal Geometry of Nature". However many of the fractal function go back classic mathematics. Names like G. Cantor (1872), G. Peano (1890), D. Hilbert (1891), Helge von Koch (1904), W. Sierprinski (1916) Gaston Julia (1918) and other personalities played an important role in Mandelbrot's concepts of a new geometry.

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