Creating and Modifying Images Using Newton's Method for Solving Equations
Inhaltsverzeichnis
Reference
Stanley Spencer: Creating and Modifying Images Using Newton's Method for Solving Equations. In: Bridges 2010. Pages 183–190
DOI
Abstract
The pictures associated with Newton’s Method of finding the roots of an equation are familiar to mathematicians and non-mathematicians. The main purpose of this paper is to look at ways by which a recognisable image can be produced or modified using the same mathematical process. This paper looks at several ways that an arbitrary pixel image can be iteratively transformed using Newton type algorithms. The standard approach of letting the pixels evolve towards attractors was interesting, but a second approach, one that inverted the process so that attractors became expellers, looks fruitful for creating interesting images. The process was designed to allow equations with up to a hundred roots which created challenges but also opportunities for meaningful outcomes.
Extended Abstract
Bibtex
Used References
[1] Peitgen and Richter, The Beauty of Fractals, ISBN 3-540-15851,-0 Springer, 1986
[2] Hans Lauwerier, Fractals Images of Chaos, ISBN 0-14-014411,-0 Penguin, 1991
[3] David Wells, Curious and Interesting Geometry, ISBN 0-14-011813-6, Penguin, 1991
[4] Chaos Theory, <http://en.wikipedia.org/wiki/chaos_theory>, (Accessed 28.12.2007)
[5] http://www3.babson.edu/Archives/Newton_collection/MS416C.pdf (accessed 01.11.2009)
[6] http://www.polynmiography.com(accessed01.04.2010
Links
Full Text
http://archive.bridgesmathart.org/2010/bridges2010-183.pdf
