Mandelbrot Power Ramp

A while back I became interested in how fractals might look when you blend together the same fractal with some parameter varying - as if the fractal was motion-blurring as that parameter changes.

I eventually wrote a little tool called uprMash to help achieve this effect automatically in UltraFractal, but both before and after this I ran a lot of experiments with the mandelbrot fractal as it's "real power" parameter changes.

It is well known that positive integer powers for this fractal give something called the 'multibrot sets' but it seems quite rare to explore non-integer powers or negative values for the real power. I was shown a very interesting example by Alan Tennant that was very detailed, with loads of little 'cuts' everywhere, I'll leave examples of that for a future post, but it piqued my interest in mandelbrot power-ramping and I came up with lots of interesting images based on the idea: