I’m reading a fascinating book by Stratford Caldecott: Beauty for Truth’s Sake. It is about mathematics, the classical curriculum, and Christian theology. One of Caldecott’s main points is that mathematics is an important means of discovering the underlying order and beauty of the universe. I plan to write a more detailed post on the book later, but here is an amazing example of naturally occurring symmetry where you would least expect to find it.
Certain tones create symmetric patterns in sand or salt when it is sprinkled on a plate and the sound vibrates it. These patterns are called Chladni Patterns, named after the 18th century scientist, Ernst Chladni, and they have been known for centuries. Here is a demonstration of how they form when a Mozart aria is being sung:
FracTad's Fractopia 