I believe fractals can be incredibly beautiful, and I believe our sense of what is beautiful has evolved by identifying the things we see in nature. Fractals are a great format for expression in nature for their simplicity of encoding: an algorithm which encodes for a self similar object saves a lot of bits by only expressing the general shape and where to attach little replicas, thus not requiring to pinpoint where every last carbon atom goes.
But I think it's wrong to say that fractals exist in nature. It's similarly wrong to say that a circle exists in nature. A circle is a mathematical abstraction, and as such, I don't think it can exist in a fuzzy quantum-mechanical world such as our own. Likewise, a fractal is a mathematical abstraction, and if you examine a shell or a leaf or whatever natural example of a fractal you can hold, you will see the fractal nature of it breaks down at some point.
So in some ways, mathematics captures the essence of the beauty we see in the real world, in a richer way than nature herself can express!
http://www.skytopia.com/project/fractal/mandelbulb.html
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