There are two kinds of symmetry, repetition and recursion. Recursion means repetition in subelements, like the pattern of veins in a leaf.
Symmetry is unfashionable in some fields now, in reaction to excesses in the past.
Architects started consciously making buildings asymmetric in Victorian times and by the 1920s asymmetry was an explicit premise of modernist architecture. Even these buildings only tended to be asymmetric about major axes, though; there were hundreds of minor symmetries.
The danger of symmetry, and repetition especially, is that it can be used as a substitute for thought.
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"Making money is art and working is art and good business is the best art." ~ Andy Warhol
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