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Fractals can be most simply defined as images that can be divided into parts, each of which is similar to the original object. Fractals are said to possess infinite detail, and some of them have a self-similar structure that occurs at different scales, or levels of magnification. In many cases, a fractal can be generated by a repeating pattern, in a typically recursive or iterative process. The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus or "broken". Before Mandelbrot coined his term, the common name for such structures (the Koch snowflake, for example) was monster curve.
Fractals of many kinds were originally studied as mathematical objects. Fractal geometry is the branch of mathematics which studies the properties and behavior of fractals.
Because a true fractal possesses infinite granularity, no natural object can be a fractal. However, natural objects can display fractal-like properties across a limited range of scales.
"Approximate fractals are easily found in nature. These objects display complex structure over an extended, but finite, scale range. These naturally occurring fractals (like clouds, snowflakes, mountains, river networks, and systems of blood vessels) have both lower and upper cut-offs, but they are separated by several orders of magnitude. Trees and ferns are fractal in nature and can be modeled on a computer using a recursive algorithm. This recursive nature is clear in these examples -- a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature." Hunting the Hidden Dimension Nova PBS WPMB-Maryland. 10/28/2008
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