A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.
The object need not exhibit exactly the same structure at all scales, but
the same "type" of structures must appear on all scales. A plot of the
quantity on a log-log graph versus scale then gives a straight line, whose slope
is said to be the fractal dimension.
The prototypical example for a fractal is the length of a coastline measured with
different length rulers. The shorter
the ruler, the longer the length measured,
a paradox known as the coastline paradox.
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