Mandelbrot set variable power render

[Dinkydau]

The idea is this: add a new real axis, let's say P, to the complex plane and let p there be the power in the formula of the mandelbrot set. You then get a 3d-shape that shows the transition of the set between the powers. At p=2 the standard mandelbrot set would be a slice of this shape. I hope this is a clear enough description. Has anyone ever tried to render that?

Another idea: what would the graph look like of a function indicating the area of the set for variable power p?