The Amazing World of Fractals

From early times, people have observed that many things from nature have the structure and texture formed from elements that repeat themselves continuously. This fact made them curious to find out more about these structures. Once this phenomenon was discovered, people tried to find the basic element, the generator, that multiplied at different scales, builds up the entire structure. These structures are called fractals. Then, they thought how could they also generate these forms. Engineers started to use them in different activities, but they are also applied in the Chaos Theory.

Fractals are everywhere, in various shapes and forms. (

Fractal Packs Educators Guide). They are actually geometric figures, like rectangles or circles, but with special properties that those figures don’t have. In the same way, a fractal repeats itself at different scales. In other words, in a fractal pattern "you can zoom in and find the same shapes forever." (

Fractal Packs Educators Guide). The main property of fractals is self-similarity. This means that we can observe the same structure as we advance into the structure. (

What are fractals?). Fractals are applied in both geometry and algebra. In geometry, fractals are created based on plane transformations. The most famous examples are the Sierpinski Triangle and the Koch Snowflake (

Useful Beauty). However, in algebra, fractals need complex numbers in order to be generated (

Fractals). Complex numbers are a combination of real and imaginary numbers (

Complex Number). Julia Set and Mandelbrot set require a lot of calculations involving complex numbers. For a better quality of the image, we need a higher number of iteration (

Fractals).

Moreover, fractals are found all over nature. Mountains, clouds, rivers, coastlines are all examples of fractals (

Fractals on the Earth). Koch Snowflake is a well-known example. It is made by replacing each segment of a generator with a smaller copy of it, then, this process repeats all over again (

Fractal Packs Educators Guide). Furthermore, fractal ferns is the best example for understanding the idea that when enlarged a small part of a figure, it is obtained the original figure (

Fractal Ferns). Similarly, spirals can be found in galaxies, but also biological spirals are found in the plant and animal kingdoms. As an illustration, the ammonite, hurricanes and fiddlehead ferns are common examples (

Fractal Packs Educators Guide).

In time, engineers began using natural fractals in order to build high-quality goods. For example, computer chips and fractal antennas are engineering devices (

Fractal Packs Educators Guide). We also find fractals in the Google Earth Program. In addition, we use fractals to find out how long the coast is (

Fractals on the Earth). Also, fractals started to be used in medicine like CT scans. In many industries, high precision fluid mixing is used and are based on fractals (

Fractal Pack Educators Guide).

In the same way, fractals are greatly used in the Chaos theory. The chaos theory is "the science of surprises" (

What is Chaos Theory). This science involves phenomena impossible to control like turbulence or brain state. These type of phenomena use fractals to be described (

What is Chaos Theory). The Butterfly Effect is "a term in chaos theory to describe how small changes to a seemingly unrelated thing or condition can affect large, complex systems" (

What is the Butterfly Effect). In addition, the weather forecasting is not accurate for a long period of time because the conditions of weather can change from one moment to another leading to errors in computers. Based on the Chaos Theory and the Butterfly Effect, Albert Einstein said that "as far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality" (

What is Chaos Theory).

All in all, fractals help us understand better how nature created the designs of its different elements. Based on this, we can simulate different natural forms and the phenomena. Using fractals in engineering devices can make them precision goods. Even though fractals are complex and based on difficult mathematics, when simulated, they are amazing patterns that represent the same shapes forever.

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Fractal Packs Educators Guide."

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Fractals In Biology."

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What are fractals?"

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Useful Beauty."

http://www.fractal.org, Accessed 23.03.2013

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Fractals."

http://www.intmath.com, Accessed 23.03.2013

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Fractals on the Earth."

http://www.fractalfoundation.org, Published 07.02.2009, Accessed 23.03.2013

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Fractal Ferns."

http://www.popmath.org.uk, Accessed 23.03.2013

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What is the Butterfly Effect."

http://www.wisegeek.org, Accessed 23.03.2013

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Complex Number."

http://www.mathsisfun.com/definitions, Accessed 23.03.2013

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What is Chaos Theory."

http://www.fractalfoundation.org, Published 19.01.2009, Accessed 23.03.2013