The idea of fractals is one of those key concepts about the nature of the universe that is mind-blowing, but we don't really know what to do about it. Fractals are infinitely complex, self-repeating patterns found in nature and mathematics. One of the reasons they're important is because they demonstrate that seemingly random dynamic behavior is actually orderly. Chaos is not about disorder, it's about symmetry. The beating of a heart, the shape of a coastline, the flow of rivers, neural firing, etc. exhibit this behavior. Fractals can be visually gleaned in the extravagant creations of the natural world.
Sometimes I like to look at these fractal patterns and remind myself that they're the outward showing of something that is more fundamental. The flow of ocean breezes, the configuration of stars, and the formation of thought. In the small and in the large, its properties border on the mystic and have been equated to the hallucinatory world created by certain neurochemicals. Spiritual explorers are known to be drawn to these fractal shapes because it reminds them of experiences that they've had on those altered states.
It surprises me that this concept of nature as a fractal is not more salient in popular culture and classic culture. They're clearly there all around us and inside us. Yet, they remain so elusive, unknowable, and mysterious.
Self-similarity in action at different levels of magnification
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