A fractal is a geometric object which is rough or irregular on all scales of length, and therefore appears to be 'broken up' in a radical way.
Fractals of many kinds were originally studied as mathematical objects.
Approximate fractals are easily found in nature.
These objects display self-similar structure over an extended, but finite, scale range.
Examples include clouds, snow flakes, mountains, river networks, cauliflower or broccoli, and systems of blood vessels.
Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm.
This recursive nature is obvious 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. The surface of a mountain can be modeled on a computer by using a fractal: Start with a triangle in 3D space and connect the central points of each side by line segments, resulting in 4 triangles.
The central points are then randomly moved up or down, within a defined range.
The procedure is repeated, decreasing at each iteration the range by half.
The recursive nature of the algorithm guarantees that the whole is statistically similar to each detail.
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