1. Assignment-1 Newton Fractals Group N0:7 ReenuRaniVivekRathee 56113838 55142176 Ice-3

2. WHAT IS FRACTAL? • Derived from Latin word Fractus . • A shape that appears self-similar on multiple spatial scales. • Any piece of it looks like the whole after a change of scale. • Eg: A fern , Aerial photo graph of a coastline.

3. OCCURRENCE OF FRACTALS • Natural fractal. • Nature apparently maximizes functional efficiency while using minimum space. • Mathematical fractal. • Based on an equation that undergoes iteration , a form of feedback based on recursion. • Fractal generating software like Sterling , Ultra fractal etc.

4. USES OF FRACTALS • Data compression. • Image creation in science fiction movies , Fractal landscapes. • Characterizing metals. • Describing astronomy, meteorology, ecology and study of galaxy clusters.

5. NEWTON- RAPHSON METHOD • Most widely used for locating roots. • Can be derived using Taylor series or the geometric interpretation of the slope in figure

6. USE OF NEWTON – RAPHSON METHOD IN ENGINEERING • In solving non linear equations. • Eg: F : Rk → Rk • To find the zeroes of a function F defined in Banach Space. • To find the zeroes of complex functions. Time domain-synthesis. • In solving flow-mechanic chemistry equations of CO2 storage in saline aquifers.

7. NEWTON RAPHSON CODE (Sin(x))

8. NEWTON – RAPSON (Sin(x))

9. NEWTON RAPHSON CODE(f(z)=z.^3-1)

10. NEWTON RAPHSON(f(z)=z.^3-1)

11. NEWTON RAPSHON CODE (f(z)=z.^3-1)

12. NEWTON RAPSHON((f(z)=z.^3-1))