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So I am trying to find the relationship between fractals and newton's method, and I am trying to use software to generate the fractals pattern. which software can I use to do that and how?

Also i am trying to compare two different types of Newton;s method - the normal one and a new type of newton's method called relax newton's method. The new type maintains a quadratics convergence in most situations, but how can I generate fractals for this new Newton;s method?

Tommy Lassa
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  • Since you probably have access to a browser you could use JavaScript to draw the fractal in a HTML canvas. For Newton's method run it on the points in some subsection of the complex plane. You need to distinguish between the roots that it converges to. These give the colors for the pixels. – Marko Riedel Nov 16 '15 at 23:48
  • Use any C compiler and play with the code in https://commons.wikimedia.org/wiki/File:Newtroot_1_0_0_0_0_m1.png – Lutz Lehmann Nov 17 '15 at 10:17
  • I had to write my own plotter to analyse the structure of bivariate Newton iteration; it can be found here. It should be easily tweakable to handle ordinary univariate functions. – Parcly Taxel Oct 16 '17 at 18:22

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