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Fractal Geometry: Mathematical Foundations and Applications

Adrian Ward

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Fractal geometry is a branch of mathematics that studies the properties of fractals, which are geometric patterns that repeat themselves at different scales. Fractals are found in nature, art, and technology, and they have a wide range of applications in fields such as computer graphics, medicine, and finance.

Fractal Geometry: Mathematical Foundations and Applications

by Meagan Trayler

4.4 out of 5

Language	:	English
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Print length	:	386 pages

Mathematical Foundations

The mathematical foundations of fractal geometry were laid in the late 19th century by mathematicians such as Georg Cantor and Karl Weierstrass. Cantor developed the concept of the Cantor set, which is a fractal with a Cantor dimension of 0. Weierstrass developed the Weierstrass function, which is a fractal with a Hausdorff dimension of 2.

In the early 20th century, mathematicians such as Benoit Mandelbrot and Gaston Julia developed new techniques for studying fractals. Mandelbrot coined the term "fractal" in 1975, and he popularized the study of fractals with his book "The Fractal Geometry of Nature" in 1982.

Applications

Fractals have a wide range of applications in fields such as:

* **Computer graphics:** Fractals are used to create realistic images of natural objects such as mountains, trees, and clouds. * **Medicine:** Fractals are used to model the structure of biological tissues and to diagnose diseases such as cancer. * **Finance:** Fractals are used to model the behavior of financial markets and to predict stock prices.

Fractal geometry is a rapidly growing field of mathematics with a wide range of applications. Fractals are found in nature, art, and technology, and they have the potential to revolutionize many fields of science and engineering.

* [The Fractal Geometry of Nature](https://www.amazon.com/Fractal-Geometry-Nature-Benoit-Mandelbrot/dp/0716711867) by Benoit Mandelbrot * [Fractals: A Mathematical ](https://www.amazon.com/Fractals-Mathematical--Kenneth-Falconer/dp/0470090183) by Kenneth Falconer * [Fractal Geometry: Theory and Applications](https://www.amazon.com/Fractal-Geometry-Theory-Applications-Michael/dp/0201632817) by Michael Barnsley

Fractal Geometry: Mathematical Foundations and Applications

by Meagan Trayler

4.4 out of 5