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Newton Basins

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Visit this site: http://aleph0.clarku.edu/~djoyce/newton/newton.html

Author:David Joyce; Dept. of Mathematics & Computer Science, Clark University
Description: Newton's method for finding solutions to equations leads to some fantastic images when applied to complex functions. This program colors the complex plane according to where an initial guess will eventually take you, and gives each solution a different color so that all the initial guesses that eventually lead you to that solution are colored the same. A Newton basin is just the set of initial guesses that lead to one solution. What's interesting is that Newton basins are fractals - kinds of Julia sets. The site includes background on Newton's method, some examples for a quick idea of the possibilities, and a form that allows you to generate Newton basins for polynomials.

Levels: High School (9-12), College
Languages: English
Resource Types: Graphics, Web Interactive/Java
Math Topics: Imaginary/Complex Numbers, Calculus (Single Variable), Fractals, Numerical Analysis

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