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Assignment-1

Assignment-1. Newton Fractals Group N0:7 Reenu Rani Vivek Rathee 56113838 55142176 Ice-3. WHAT IS FRACTAL?. Derived from Latin word Fractus . A shape that appears self-similar on multiple spatial scales.

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Assignment-1

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  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))

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