Mixed Fractal Surfaces

It is possible to have a fractal surface which varies in local dimension everywhere. That is to say, on any patch of the surface you can zoom into a rough area (e.g. 2.5D) or zoom into a smooth area (2D). 

Here it is applied to the sphere tree fractal:

and to the non-rotated one:

In both cases the the smaller spheres are disproportionately smaller than in the usual shapes, giving a surface that tends to smooth in the vicinity of each sphere base. 

However, if you zoom in on those smooth surfaces enough you will find a sphere, and if you zoom in on that sphere enough you will find a bud at the top which is just as rough as one of the pictured ones. 

This is much like the Mandelbrot set, which has areas that are locally smooth, in the sense of being a straight thin line as you zoom in further:

But everywhere you can find tiny minibrots.

We can do the same thing with the tree surface fractal:

The surface tends to smooth, however, each smooth dome has child domes that can be just as protruding as the largest ones. So we get a mixed dimensionality. 

Because the mixture of roughnesses is everywhere and at every resolution (rather than separated) these are probably all multifractals, though I've never fully understood the definition of these.