I'm glad you disagree with the Platonic view of mathmatics.
(Plato was a professional wrestler, who's name translates roughly to "Big
Guy", making him dangerously simmilar to Hulk Hogan! (How's that for an
ad hominum argument?))
On the eyeball fractals, I am reminded of some good advice:
Always keep an open mind, but not so open that your brain falls out.
There are plenty of goofy pop science books on the subject of
fractals and chaos, mostly writen by people who read other goofy pop
science books. Chaos theory, or the little I understand of it, seems to
be the most beautifull, and interesting branch of mathematics that i have
ever seen. But, it's hard, much to hard to get from a dime novel science
book. It is based on non-linear equasions, which are so dificult that
approximation is the accepted way to deal with them, even among advanced
I hope you retain your objectivity while reading on the subject.
there are some good books on the subject, although they treat it only in
a very general way. "Chaos" by James Gliek, is one that doesn't get
bogged down in fantasy. It is mostly, however, about the scientists that
brought chaos theory about, and not so much about the math.
I hope this helps