Fractals in Physics

By

Akeel A. Khudhayir

Supervised by

Dr. Mohammed A. Habeeb

Outline:Brief Introduction ₪

Fractals●

Fractal Dimension●

Examples of Fractals●

History of Fractals₪

Some Applications ₪

Engineering●

Medicine●

Astrophysics●

Physics●

Conclusions₪

References₪

Brief Introduction● Fractals are the main concern of fractal geometry, which is a branch of mathematics concerned with irregular patterns made of parts that are in some way similar to the whole

● Examples of Fractals

- In nature:

- In Geometry:

Sierpinski

triangle

D=1.585

● Fractal Dimension

Shapes of Euclidean geometry are described by an integer dimension such as, a 1-Dim. for line, 2-Dim. for rectangle and 3-Dim. for cube, while a fractals are described by non-integer dimension like 1.2 and 2.3.

History of Fractals

1883 George Cantor ●

Cantor Set

● 1904 Helge Von Koch

Koch Curve D=1.2618

1915 Vaclav Sierpinski●

Sierpinski Triangle

Mandelbrot 1975 Benoit●

Mandelbrot set

Some Applications ● In Engineering A computer chip cooling circuit etched in a fractal branching pattern. The device channels liquid nitrogen across the surface to keep the chip cool.

A fractal heat exchanger

In Medicine●

Researchers at Harvard Medical School and elsewhere are using fractal analysis to assess the health of blood vessels in cancerous tumors. Fractal analysis of CT scans can also quantify the health of lungs suffering from emphysema or other pulmonary illnesses.

● In Astrophysics

Astrophysicists believe that the key for the problem of forming of stars and their positions in the universe is related to the fractal nature of interstellar gas.

● In Physics

1- The study of turbulence in flows is very adapted to fractals. Turbulent flows are chaotic and very difficult to model correctly. A fractal representation of them helps to better understand complex flows. Flames can also be simulated. Porous media have a very complex geometry and are well represented by fractal.

2- Fractals are used to describe the roughness of surfaces. A rough surface is characterized by a combination of two different fractals.

3- Using of fractals in antennae design, the resulted fractal-shaped antenna has many advantages including miniaturization, multiband performance

and high efficiency.

4- Using in image processing:-Many image compression schemes use fractal algorithm to compress computer graphics files to less than a quarter of their original size.

ConclusionsMany scientists have found that fractals and their○

geometry are powerful tools for uncovering secrets from a wide variety of systems and solving important problems in applied science.

Fractals improved our precision in describing and ○

classifying “random” or organic objects, but maybe they’re not perfect.

ReferencesLewis R., Fractals in your future. Chapter 1. Ontario 2000.

Mandelbrot, B.B., The fractal geometry of nature. San Francisco 1982.

Turner, M.J., Modeling nature with fractals, Leicester 2000.

Fractals are smart, Fractal foundation, www.FractalFoundation.org 2009.

Vicsek, Tamas, Fractal growth phenomena, New Jersey, World Scientific 1992.

Falconer, Kenneth, Fractal geometry: mathematical foundations and applications, John Wiley & sons 2003.