1. COMPUTATION AND SIMULATION (EE317) 2008-2009 ASSIGNMENT ONE By: Shimiao Cheng, Femi Adeleke, Hanieh Alirezaee abyaneh 1

2. Fractals Rough geometric shape The term was derived from the Latin fractus mathematical fractal is based on an equation that undergoes iteration It has a fine structure at arbitrarily small scales self-similar

3. Fractals in Engineering. 1.Image compression with fractals Have more than twenty years developments. Representing an image by fractals. Each fractals represents an IFS. An image represents by group of IFS codes rather than pixels. A Compression ratio as high as 10000:1. 3

4. fractals in Engineering (Continued). 2.Fractal antenna An antenna that uses a fractal. Maximize the length, or increase the perimeter, of material that can receive or transmit electromagnetic signals within a given total surface area or volume The key aspect lies in their repetition of a motif over two or more scale sizes, or 'iterations'. They are very compact, multiband or wideband, and have useful applications in cellular telephone and microwave communications. 4

5. 2. N EWTON -R APHSON M ETHOD in Engineering. Newton-Raphson method is based on the principle that if the initial guess of the root of f(x)=0 is at x i, then if one draws the tangent to the curve at f(x i ), the point x i+1 where the tangent crosses the x-axis is an mproved estimate of the root which gives x+1 = x – f(x)/f′(x) (1) The steps of the Newton-Raphson method to find the root of an equation f(x) = 0 are: Evaluate f(x) symbolically Use an initial guess of the root, x i, to estimate the new value of the root x i+1 as (1) 5

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7. Fractal images… 1 3 2 7

8. Matlab code 1. Z= Z^3-1=0 [1 st function] 2. Z = sin(Z) [2 nd function] 3. Z= Z^3-2Z+2=0 [3 rd function] 8

9. Thank you & Questions 9