"Now it's a very long time since I did fractal geometry..." Yep, same here I'm afraid. But A Pollock at the fundamental level is just atoms, which I would think is just another countable set. Still, research has been done into the fractal nature of his paintings. Apparently as he matured the HD dimension increased.
I'm thinking of real phenomena exhibiting a 'partial' fractal nature. I think you are thinking in the pure maths realm.
BTW I still don't like his paintings generally. Manet and Holbein are more my thing, or Morandi on certain occasions.
I've been working in a public facing creative arts role for a while now and my appreciation of the likes of Pollock has become somewhat more favourable over that time.
Hadn't heard of Morandi, not sure his stuff means much to me, however I like this photographic interpretation of his work - http://static.dezeen.com/uploads/2009/06/dc03_ins.jpg (to sell a dinner service). Thanks for the pointer.
Has anyone managed to compute the value of the Hausdorff-Besicovitch dimension?