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The proof is self-evident (and self-similar!)

Beauty is truth, truth beauty.

This page outlines the aesthetics of the metaculture philosophy.

Fractals encapsulate the essence of what humans find beautiful--symmetry, complexity, color, and pattern, because they reveal an essential underlying truth about the order of the universe, as well as the order of our neurons.

There are a number of articles articulating this point well:

While the study of aesthetics is a cornerstone topic in philosophy and a necessary component of a complete philosophical system, it is admittedly the least interesting, well-developed, or groundbreaking aspect of metaculture at the time of this writing. But it does fit very nicely into the holistic picture of the fractal universe and mind.

And if you can't see the subjective beauty of a fractal just by looking at it, this wiki is not going to be able to explain it to you.

Aesthetics - What Good Is It?

Intro to Aesthetics - Philosophy Tube

A Trip to Infinity Mandelbrot Fractal Zoom

Infinity Liquid Mandelbrot Zoom

11 Dimensions Mandelbrot Fractal Zoom

Morrissey - To Me You Are a Work of Art