Tuesday, June 14, 2011

Fractal eXtreme: The Complex Newton Set

I'm excited about the next few posts because the fractals are getting really interesting and beautiful, and so much more fun to blog about. You'll now see a few perfect examples of why I got so into this fractal art thing in the first place. Also, after posting the next three (or so) posts, I'm going to really start making my own artistic pieces, as well as make some changes to this blog in order to showcase my future creations :)

But for this post, let me stick to the title: The Complex Newton Set. As you can see here, upon loading the default, it looks very similar to the Classic Newton:

 The Complex Newton Set
But it has two more "spokes", and thus all the smaller self-similar iterations are different as well. Ok, cool, but now, what's nice about the Complex Newton is that you can change it's exponent. It can be either any real number (essentially, the shape cycles between having many more spokes to being a very slow-loading circle/eye-shaped thingy... ) or any complex number (much more interesting, as can be seen here):

 Complex Newton x: 1.25 y: -7

 Complex Newton x: 3.35 y: -1.45

 Complex Newton x: 8.4 y: 0.75
Unfortunately, zooming into these monsters doesn't yield anything too exciting... Only more self-similar shapes. But still, very pretty right? :) And with some time and creative effort, truly original works of art can be got.

Next up, The Auto Quadratic Set :)