ASSIGNMENT 1 COMPUTATION

1
ASSIGNMENT 1COMPUTATION SIMULATION (EE317)

• Submitted by
• Aashish Kajla
• Mandeep Rathee
• Eric Dankwa

2
FRACTALS

• A Fractal is a rough or fragmented geometric
  shape that can be split into parts ,each of which
  is a reduced copy of the whole a property called
  self similarity.
• The term was coined by Benoit Mandelbrot in 1975.

3
FRACTALS (Examples)
Romanesco Broccoli (Natural Fractal)
Mandelbrot set
4
OCCURRENCE OF FRACTALS

• Fractals are easily found in nature. For ex-
  snow flakes, mountains broccoli.
• Fractals are also found in African art and
  Architecture. For ex-Circular houses appear in
  circle of circle, rectangle house in rectangle of
  rectangle so on.

5
APPLICATIONS OF FRACTALS

• Soil Mechanic
• To find the Hydraulic Properties of soil.
• Fractals are used for making mathematical models
  of soil water characteristics curve (SWCC) in
  which constants are related to the fractal
  dimension of pore size distribution. It reduces
  the time as compared to usual laboratory
  experiments.

6
APPLICATION OF FRACTALS

• Fractal Antennas
• It uses a fractal, self similar design to
  maximize the length or increase the perimeter of
  material that can receive or transmit the
  electromagnetic signals.
• Compact Multi Band. Used in Cellular Phone
  Antennas Microwave Communications.

An Example of Fractal Antenna
7
APPLICATION OF FRACTALS

• Image Compression
• It is a lossy image compression method using
  fractals to achieve high levels of compression.
• This method is best suited for natural scenes
  (trees, ferns, mountains etc)

8
NEWTON RAPHSON

• Newton Raphson is best known method for finding
  successively better approximations to the roots
  of a real valued function.

Equation for Newton Raphson Algorithm
9
Application of Newton Raphson

• It is used for solving Power Flow Problems in
  bus. The performance of the Statcom and the
  load-tap-changing transformer (LTC) into the
  power flow using the NewtonRaphson method is
  tested for reliability towards the convergence,
  accuracy voltage constraint of bus voltage.

10
Application of Newton Raphson

• The Newton Raphson method is used to solve the
  non-linear equations for optimization.
• The mean squared error is the criterion on which
  optimization is based.

11
Fractals Developed
12
Fractals Developed
13
Fractals Developed
14
References

• www.wikipedia.org
• www.ieee.org

15
ANY QUESTIONS SUGGESTIONS