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Introduction

This page allows you to explore the Generalised Newton Fractal for polynomials with real coefficients up to order 9. Patterns are generated by picking a starting point and iterating until it converges on a root or we run out of iterations. The potential starting points are combinations of a seed (Sx,Sy) and a constant I'm calling alpha (Ax, Ay). So for any polynomial we could construct a 4−dimensional pattern Sx x Sy x Ax x Ay. As we are limited to a 2−D screen we construct patters by keeping two of these parameters constant and varying the other two. Currently we have two modes, keeping the seed constant and varying alpha or keeping alpha constant and varying the seed. There are four other potential slices that could be obtained by varying one 'S' and one 'A' which I may add at a later date. I have implemented these options in the similar 4−D Mandelbrot explorer page.

An animation mode allows you to explore a 3rd dimension by varying some of the parameters, including the terms in the polynomial.

Some videos generated using this page can be seen here.

My earlier Newton Raphson pages can be accessed from here.

If you only want to solve polynomials, rather than draw pictures, visit the polynomials page.

Interactive Section


  Equation:

Animation:       Iteration 0 of

Instructions

I haven't written these yet. For now, operating this control is similar to the WebGL Mandelbrot.

For more information about the Netron Raphson fractal see the Newton Raphson page.

Other pages

 

(c) John Whitehouse 2010 - 2018