Animated Newton fractals

[lkmitch]

Here are a couple of animations of Newton's method fractals that I did.  Both use quartic polynomials as the underlying function to be solved, and in both, the roots of the function move around during the animation.  In the first, the roots move around on four different circles and the colors reflect the angle of the solution.  In the second, the roots move around on four different rose curves and the zebra-striped coloring reflects the number of iterations needed for convergence.  Both are better viewed in high quality.

<a href="http://www.youtube.com/v/eBI9_WR28OQ&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/eBI9_WR28OQ&rel=1&fs=1&hd=1</a>
<a href="http://www.youtube.com/v/qvUnptfCNTQ&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/qvUnptfCNTQ&rel=1&fs=1&hd=1</a>

Kerry

[Dinkydau]

I really liked the second one 

[HPDZ]

This is a pretty cool idea.

I would suggest moving the roots on more visually obvious trajectories so one can really appreciate how the boundaries change as the roots move around, especially when you get to multiple degenerate roots.

And a bit more slowly...