The Nova fractal was developed a long time ago by Paul Derbyshire.
The equation that generates the Nova fractal is based on the same procedure as Newton's method for solving equations, with two changes that make an enormous difference. Details are described in the Nova section of the Technical page on convergent fractals.
Some modifications based on a small bug in the initial code to render this fractal are shown below.
As part of the effort to extend the arithmetic code to floatingpoint, with assembly language 64bit division, a few Nova fractal deepzoom images were created.
This is definitely going to get an animation. This fractal is a gift that just keeps on giving, with wonderful new detail emerging constantly at deeper levels of zooming.
This is a set of images exploring the classic cubic Nova fractal. Most of them are rendered at 1000x500 resolution (inspired by the 2:1 aspect ratio of our new laptop), and most have very nice antialiasing, some using up to a 10x10 supersampling grid.

These images show the Nova fractal with the "standard" values of the initial value z_{0}=(1,0) and the relaxation parameter R=(1,0). Two different coloring methods are demonstrated, although the same actual sequence of colors occurs in both. 
This image shows what happens to the standard Nova fractal as z_{0} approaches 0 (for z_{0}=0 the Nova fractal is blank). Compare this to the Nova Bug image below. This is how I first noticed I had a tiny math error in my Nova code. 

Nova Bug  this is due to a bug in my first attempt at writing the code for a Nova fractal. The result is nearly identical to the true Nova fractal except in a small range of parameters. In particular, the bug gave something totally different for z_{0}=0, which inspired me to tweak the original Nova equation to give the result above. 

Modified Nova Fractal at z_{0}=0. This has the modification described in the NovaBug image. It gives something totally different and quite nice when z_{0}=0. 