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Enhancing Computational Thinking with Spreadsheet and Fractal Geometry: Part 2 Root-finding using Newton Method and Creation of Newton Fractals

by K. P. Soman, Manu Unni V.g, Praveen Krishnan, V. Sowmya
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 55 - Number 14
Year of Publication: 2012
Authors: K. P. Soman, Manu Unni V.g, Praveen Krishnan, V. Sowmya
10.5120/8821-2742

K. P. Soman, Manu Unni V.g, Praveen Krishnan, V. Sowmya . Enhancing Computational Thinking with Spreadsheet and Fractal Geometry: Part 2 Root-finding using Newton Method and Creation of Newton Fractals. International Journal of Computer Applications. 55, 14 ( October 2012), 9-15. DOI=10.5120/8821-2742

@article{ 10.5120/8821-2742,
author = { K. P. Soman, Manu Unni V.g, Praveen Krishnan, V. Sowmya },
title = { Enhancing Computational Thinking with Spreadsheet and Fractal Geometry: Part 2 Root-finding using Newton Method and Creation of Newton Fractals },
journal = { International Journal of Computer Applications },
issue_date = { October 2012 },
volume = { 55 },
number = { 14 },
month = { October },
year = { 2012 },
issn = { 0975-8887 },
pages = { 9-15 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume55/number14/8821-2742/ },
doi = { 10.5120/8821-2742 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:57:12.004845+05:30
%A K. P. Soman
%A Manu Unni V.g
%A Praveen Krishnan
%A V. Sowmya
%T Enhancing Computational Thinking with Spreadsheet and Fractal Geometry: Part 2 Root-finding using Newton Method and Creation of Newton Fractals
%J International Journal of Computer Applications
%@ 0975-8887
%V 55
%N 14
%P 9-15
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This article shows how Newton's iterative methods for finding root of a polynomial equation can be used to create fractals in spreadsheets. Newton's method has served as one of the most fruitful paradigms in the development of complex iteration theory. The process of iteration is impossible to carry out by hand but extremely easy to carry out with a computer. By doing such experiments students get a feeling that they have the power to explore the uncharted wilderness of the dynamics of Newton's method. It gives mathematics an experimental component. It also illustrates a symbiotic relationship between technology and mathematics [1]. Technology can be used to develop our intuition, and mathematics is used to prove that our intuition is correct. The article explores Innovative use of Microsoft Excel's What-if Analysis tool to do automation of repeated computation. The method employed can also be used for Neural Network training and data clustering [9] in Excel. A wide variety of fractals can be created by using different polynomial equations [2-7].

References
  1. Freitas, J. O. ,Ramos, S. , "Computer Experiments with Newton's Method", 2003
  2. http://hal. inria. fr/docs/00/05/43/27/PDF/co37th2. pdf. Accessed 5 August 2012
  3. Tatham, S. , "Fractals derived from Newton-Raphson". http://www. chiark. greenend. org. uk/ ~sgtatham/ newton/. Accessed 5 August 2012
  4. Bourke, P. , "Gallery of fractals created using the Newton Raphson method", http://paulbourke. net/fractals/newtonraphson/ (Accessed 5 August 2012)
  5. Barnsley,M. F. , Devaney,R. L. , Mandelbrot,B. B. , Peitgen,H. O. , Saupe,D. , Voss,R. F. , Heinz-Otto Peitgen, DietmarSaupe, "The science of Fractal Images", Springer-Verlag, 1988
  6. Barnsley,M. , "Fractals Everywhere", Academic Press Inc, 1988
  7. Falconer,K. , "Fractal Geometry: Mathematical Foundations and Applications",Wiley, 2003
  8. Peitgen,H. , Juergens,H. , and Saupe,D. , "Fractals for the Classroom",Springer-Verlag, New York, 1992
  9. Mumford,D. , Caroline Series David Wright , "Indra's Pearls: The Vision of Felix Klein" , Cambridge University Press, 2002
  10. Aravind, H. , Rajgopal, C. and Soman,K. P. , "A Simple Approach to Clustering in Excel", International Journal of Computer Applications 11(7):19–25, December 2010.
Index Terms

Computer Science
Information Sciences

Keywords

Fractal Newton method Spreadsheet Fractal geometry

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