Mandelbrot set with z->z^n where n is fractional

Here is a view of the Mandelbrot set that I have not seen before. The typical Mandelbrot set iterates with z->z^2. I have experimented with mapping z->z^n where n is a fractional number. For example, the following image is a screen-shot of the Mandelbrot set where z->z^2.05. The basic images for the Mandelbrot sets were created with a C++ program. The C++ program creates the PNG images by using the library PNGWriter. Source code Tar file source.tar

Movies: Animated GIF images

Here is a link to an animated gif which demonstrates the different sets created for z->z^n where 0.1<=n<=9.0:

Range: 0.1<=n<=9.0 Size: 1.5MB Animation: Mandelbrot 0.1-9.0 Individual frames: Individual frames

Here is probably my favorite part of the series. This is a link to an animated gif which demonstrates the different sets created for z->z^n where 1.50<=n<=2.10. This animation works from 1.50..2.10 and then 2.10..1.50 before it loops.

Range: 1.50<=n<=2.10 Size: 700KB Animation: Mandelbrot 1.50-2.10 Individual frames: Individual frames

Here is a link to an animated gif which demonstrates the different sets created for z->z^n where 1.00<=n<=8.00:

Range: 1.00<=n<=8.00 Size: 3.8MB Animation: Mandelbrot 1.00-8.00 Individual frames: Individual frames