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Their favorite example of a fractal is the discrete self-similar snowflake, which can be constructed by repeatedly inserting a tiny triangular wedge between two half-circles that touch each other at an angle of 109.5 degrees (i.e., the neo-Pythagorean theorem).[32] The only way to clear up this contradiction is to admit that "fractal" and "smooth" are one and the same, and that the former (fractal) is therefore the smoothest (that is, the less-compressible) of all: the snowflake curve[33].
Discovering fractals was not limited to mathematicians. By the end of the 19th Century, industrialists from all over France had begun showing larger and more complex creations as a marketing ploy. This marketing strategy was called the Levy flight of design .
However, the name fractal is first widely applied in the context of a 1982 paper by Benoit Mandelbrot, who defined the word[37] and used it to describe a class of objects that display scale-invariant behavior over all or a large part of their range. These objects are characterized by the property that if you zoom in sufficiently on any part, no matter how small, you can again reproduce the whole object. While statements like extquotedblleft a ball of light has dimension three extquotedblright and statements like extquotedblright A one-dimensional ring has no dimension extquotedblright characterize one type of fractals, real-world fractals are defined in a more rigorous way, requiring more than that. Mandelbrot's paper draws its impetus, in part, from the observation that birds' feather shapes are visually striking because of the self-similar patterns in them. Evolutionary biologists interpret bird wing patterns to be the result of natural selection, with the strongest bird wings being selected for and retained, and weaker wings being weeded out or recycled. According to Mandelbrot, children and animals are said to "self-organize" when they discover or exhibit fractal patterns in their play.
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