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I think the topological dimension of cantor dust is 0, it is made from 0 dimensional points/dust. Its fractal dimension is about 0.63.
The Mandelbrot set is the set of interior points. They fill an area, and just like a disk, if you bring it twice as close it fills 4* as many pixels. Its topological dimension is 2, and its fractal dimension is 2. So the 'set' isn't fractal by Mandelbrot's 1975 definition.
The border of the set is a line, which is 1 dimensional, but if you bring it twice as close it fills 4* the pixels to draw the border, so its fractal dimension is 2, larger than its topological dimension, so a fractal. This is why Wikipedia is careful to say "the boundary of which forms a fractal."

But that's being fussy, everyone knows it as a fractal

Well, I can't help with What is a "fractal"?  Too many definitions out there...

But I can babble with the best of them about What is "art"?

There is no criteria which can be used as a blanket statement to define whether anything is "Art" or not.

Art is an Intent and an Act of Creating Something. Not a finished item.

It is a Process, not a material object.

It is a Thing To Do, not a Thing.

It is a Verb, not a Noun!

Sometimes the finished product is not the point at all, but merely the by-product of the Art.

There is certainly a danger that this idea infected me when I read "The Beauty of Fractals" back in my school days. But I have no conscious memory of such a quote in that book. The book did profoundly impress me, though, and was a big part of the reason why I chose to study mathematics, and do that at the University of Bremen. Funnily enough, I then proceeded to never meet Professors Peitgen or Richter during all of my education.

I don't regret the path I have taken, though. And I did get to meet some some of the " fractal celebrities" eventually.