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Newton Raphson fractals

  • To: mathgroup at
  • Subject: [mg26191] Newton Raphson fractals
  • From: "Costas Gavardinas" <el99022 at>
  • Date: Thu, 30 Nov 2000 22:02:09 -0500 (EST)
  • Organization: National Technical University of Athens, Greece
  • Sender: owner-wri-mathgroup at

 I have made a program that computes the complex solutions of a
polynomial equation using the Newton - Raphson method. This program receives
input  a  starting point z0=x0+Iy0 in order to find each solution. This
is repeated for each point of a N by N grid ([-N,N]X[-N,N]). The result is
that for some starting points the method converges to one solution and for
 others  converges to another solution, while for some points the method
diverges. My  question is the following: Is there a way to plot a graph in
which each
 point of the grid will be colored according to whether they lead to
 convergence or divergence and according to the speed of convergence.
Does  anyone know of a way to achieve this by using Mathematica, another
 mathematical package or some other custom program?? Any suggestions
Thank you very much for your help!!

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