Newton's Basin
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- | The colors in a Newton's Basin usually correspond to each individual root of the equation, and can be used to infer where each root is located. Each color region reflects the set of | + | The colors in a Newton's Basin usually correspond to each individual root of the equation, and can be used to infer where each root is located. Each color region reflects the set of coordinates whose x-values, after undergoing iteration with the equation describing the fractal, will eventually get closer and closer to the value of the root. |
The animation emphasizes the roots in a Newton's Basin, whose equation clearly has three roots. The image featured on this page is also a Newton's Basin with three roots. | The animation emphasizes the roots in a Newton's Basin, whose equation clearly has three roots. The image featured on this page is also a Newton's Basin with three roots. |
Revision as of 13:34, 5 June 2009
- Newton's Basin is a visual representation of Newton's Method, which is a procedure for estimating the root of a function.
Newton's Basin |
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Basic Description
This image is one of many examples of Newton's Basin or Newton's Fractal. Newton's Basin is based on a calculus concept called Newton's Method, a procedure Newton developed to estimate a root of an equation.
The colors in a Newton's Basin usually correspond to each individual root of the equation, and can be used to infer where each root is located. Each color region reflects the set of coordinates whose x-values, after undergoing iteration with the equation describing the fractal, will eventually get closer and closer to the value of the root.
The animation emphasizes the roots in a Newton's Basin, whose equation clearly has three roots. The image featured on this page is also a Newton's Basin with three roots.
A More Mathematical Explanation
- Note: understanding of this explanation requires: *Calculus
The featured image on this page is a visual representation of Newton's Method for calculus expanded i [...]
The featured image on this page is a visual representation of Newton's Method for calculus expanded into the complex plane. To read a brief explanation on this method, read the following section entitled Newton's Method.
Newton's Method
Newton's Basin
Teaching Materials
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Related Links
Additional Resources
- http://www.chiark.greenend.org.uk/~sgtatham/newton/ for further mathematical explanation
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