Nevertheless, I can say this much about fractals. They are both infinitely detailed and infinitely beautiful. All are pleasing to the senses. Nature follows mathematical rules, and we are of nature. Thus, it's not surprising that there are examples of purely mathematical constructs, like fractals, that we find beautiful no matter what our skill at math may be.
Mathematics can also describe chaotic behavior and structures.
Sometimes chaos can be pleasing to the senses, but it often isn't. Euclidean geometry, the geometry we all learned about in school, describes simple objects. The Greeks found such things divine, and thought the real world to be somehow less so because its structure could not be as easily described as, say, a circle. Our heads aren't spheres, trees aren't cylinders, and flowers aren't circles. The real world isn't less perfect because of this, it's more so.