Fractals in Physics discusses fractals and their applications in various fields of physics. Fractals are geometric shapes that exhibit self-similarity and have non-integer dimensions. Examples of fractals include the Sierpinski triangle and the Mandelbrot set. Fractals have been used successfully in engineering applications like chip cooling circuits and heat exchangers. They have also found applications in medicine for analyzing blood vessels and lungs. In astrophysics, fractals help explain the formation of stars. In physics, fractals can model turbulent flows, rough surfaces, antenna design, and image compression. Many scientists have found fractals to be useful tools for understanding and solving problems across various scientific domains.

1. Fractals in Physics
By
Akeel A. Khudhayir
Supervised by
Dr. Mohammed A. Habeeb

2. Outline:
Brief Introduction₪
Fractals●
Fractal Dimension●
Examples of Fractals●
History of Fractals₪
Some Applications₪
Engineering●
Medicine●
Astrophysics●
Physics●
Conclusions₪
References₪

3. 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:

4. - 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.

5. History of Fractals
1883 George Cantor●
Cantor Set
● 1904 Helge Von Koch
Koch Curve
D=1.2618

6. 1915 Vaclav Sierpinski●
Sierpinski Triangle
Mandelbrot1975 Benoit●
Mandelbrot set

7. 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

8. 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.

9. ● 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.

10. 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.

11. Conclusions
Many 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.

12. References
Lewis 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.