Aha, I never got to answer this as I drowned in Torundel comments that I had to answer.
It is true that words and notesa and such are finite, but to me the reason I think of fractals as close to photography is that its endlessness gives it the same lack of control. In a painting I will control a lot of things, almost all of it, while the photographer points his machine towards something and press a button. What happens then looks a lot like reality. Some photographers try to control anything but that often is pretty vain (like when Kurosawa didn't think the look was golden enough on one of the RAN still and had people running around sprouting gold paint on the grass).
Fractals create these little things that is uncontrollable and therefore they also look a lot like reality...