Fun with Fractals

Self-similarity [1] is found in mathematics, nature, and systems, such as stock markets, network traffic, and stress fractures. The whole of a self-similar object is similar to a part of its internal structures.

Imagine, for example, our earth, which is known to be more or less round. If you were to descend to the surface from a satellite view and see that the continents, mountains, cities, and houses were all spheres, the earth would be reflected in smaller, self-similar objects. Of course, this is not the case, so you need to consider other objects on our home planet.

In nature, self-similarity is found, for example, in Romanesco broccoli, in that the global structure of this vegetable is reflected in parts of its edible inflorescence. Fractals [2] give such structures a mathematical basis by describing objects that have self-similarity because the entire object is a copy of its individual parts. Because of self-similarity, a larger object that reflects the structures of the smaller object can always be created.

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