The best applications of fractals

The British artist William Lathamhas used fractal geometry and other computer graphics techniques in his works.

The best applications of fractals

An example of a fractal antenna: Log-periodic antennas are arrays, around since the s invented by Isbell and DuHamelthat are such fractal arrays. They are a common form used in TV antennas, and are arrow-head in shape.

Fractal element antennas and performance[ edit ] A planar array fractal antenna Antenna elements as opposed to antenna arrays made from self-similar shapes were first created by Nathan Cohen [4] then a professor at Boston Universitystarting in Cohen's efforts with a variety of fractal antenna designs were first published in Most varieties of fractal antennas are so-called "fractal element antennas".

Many fractal element antennas use the fractal structure as a virtual combination of capacitors and inductors. This makes the antenna so that it has many different resonances which can be chosen and adjusted by choosing the proper fractal design.

This complexity arises because the current on the structure has a complex arrangement caused by the inductance and self capacitance.

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In general, although their effective electrical length is longer, the fractal element antennas are themselves physically smaller, again due to this reactive loading. Thus fractal element antennas are shrunken compared to conventional designs, and do not need additional components, assuming the structure happens to have the desired resonant input impedance.

In general the fractal dimension of a fractal antenna is a poor predictor of its performance and application. Not all fractal antennas work well for a given application or set of applications. Computer search methods and antenna simulations are commonly used to identify which fractal antenna designs best meet the need of the application.

The best applications of fractals

Although the first validation of the technology was published as early as[5] recent independent studies show advantages of the fractal element technology in real-life applications, such as RFID [6] and cell phones.

Specifically quoting researcher Steven Best: Fractal antennas, frequency invariance, and Maxwell's equations[ edit ] A different and also useful attribute of some fractal element antennas is their self-scaling aspect. Rumsey [12] presented results that angle-defined scaling was one of the underlying requirements to make antennas "invariant" have same radiation properties at a number, or range of, frequencies.

Mushiake in Japan starting in [13] demonstrated similar results of frequency independent antennas having self-complementarity. It was believed that antennas had to be defined by angles for this to be true, but in it was discovered [14] that self-similarity was one of the underlying requirements to make antennas frequency and bandwidth invariant.

In other words, the self-similar aspect was the underlying requirement, along with origin symmetry, for frequency 'independence'.

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Angle-defined antennas are self-similar, but other self-similar antennas are frequency independent although not angle-defined.

This analysis, based on Maxwell's equations, showed fractal antennas offer a closed-form and unique insight into a key aspect of electromagnetic phenomena.

This is now known as the HCR Principle. Mushiake's earlier work on self complementarity was shown to be limited to impedance smoothness, as expected from Babinet's Principle, but not frequency invariance.

Other uses[ edit ] In addition to their use as antennas, fractals have also found application in other antenna system components including loads, counterpoisesand ground planes. Confusion by those who claim "grain of rice"-sized fractal antennas arises, because such fractal structures serve the purpose of loads and counterpoises, rather than bona fide antennas.

Fractal inductors and fractal tuned circuits fractal resonators were also discovered and invented simultaneously with fractal element antennas. A recent invention demonstrates using close-packed fractal resonators to make the first wideband metamaterial invisibility cloak at microwave frequencies US patent 8, Owing to the fact that DNA is a self-similar, electrically conducting molecule, it is hypothesized that DNA acts as a fractal antenna in the presence an external electromagnetic field.A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale.: 1 Several types of fractal dimension can be measured theoretically and empirically ().

Fractal dimensions are used to characterize a broad spectrum of objects ranging from the abstract to practical phenomena, including. • Fractal-shape antennas can respond to more frequencies than regular ones.

• They can be ¼ the size of the regular ones: use in cellular phones and military communication hardware. Explore the beautiful world of Fractals. This app allows you to explore the patterns in a Mandelbrot Set, Julia Sets, Burning Ship Fractal and Lyapunov Fractal.

An Introduction to Fractals

Abstract. Fractals is a new branch of mathematics and art. Perhaps this is the reason why most people recognize fractals only as pretty pictures useful as backgrounds on the computer screen or original postcard patterns. Discover a handpicked collection of the best science apps. The best STEM, astronomy, physics, math, chemistry, and science apps for Apple iOS and Android.

THE BEST SCIENCE APPS. Fractals. A mix of art and science, this beautiful app lets you move and pinch complicated fractals in real-time!. Reddit gives you the best of the internet in one place. Get a constantly updating feed of breaking news, fun stories, pics, memes, and videos just for you.

The best applications of fractals

is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Similarly the BBC had a show.

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