(I think my original post on this wound up only going to the sender of the message to which I was replying. But the reply could as easily have been to several of these messages.)
While there's nothing wrong with having some fun with fractals, it may be a mistake to ascribe too much relevance to them.
Yakov Khurgin, in his book "Did you say mathematics?" -- translated from the Russian by George Yankovsky and available quite cheaply through Mir Publishers of Moscow -- cites the remarkable (and now long-forgotten) studies of the shapes of leaves done by mathematicians from Descartes (the jasmine curve x^3 + y^3 = 3axy) to German mathematicians of the 19th century (with full-volume treatises on "The Analytical Shapes of Leaves").
Something similar may be happening with fractal images. There is a vague descriptive power to them (though the model is approximate -- after all, rivers and arteries and cauliflower only branch finitely often, and the nature of the largest branches is qualitatively different than that of the smallest ones), but that is not the same as actually modelling something to the extent of capturing some useful information or process.
None of which is to say fractals can't be pretty and raise some interesting mathematical questions -- or that there aren't some substantial models that use them (anyone actually know of one?). But they are not essential to one's mathematical education in the way that, say, most of the standard curriculum is. I know plenty of mathematicians who know nothing about fractals; but all of them understand high school algebra.