A presentation about fractals and its basic features and applications in scientific areas.

1. Fractals in Physics
BY
AQEEL A. Al-Taie
March, 2016

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

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. THANK YOU