Newton Raphson fractals
- To: mathgroup at smc.vnet.net
- Subject: [mg26191] Newton Raphson fractals
- From: "Costas Gavardinas" <el99022 at mail.ntua.gr>
- Date: Thu, 30 Nov 2000 22:02:09 -0500 (EST)
- Organization: National Technical University of Athens, Greece
- Sender: owner-wri-mathgroup at wolfram.com
I have made a program that computes the complex solutions of a polynomial equation using the Newton - Raphson method. This program receives as input a starting point z0=x0+Iy0 in order to find each solution. This procedure 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 accepted!! Thank you very much for your help!! --