Fractals are patterns generated
mathematically thru simple and recursive algorithms, where a pattern
is usually generated iteratively, replicating itself but in a smaller version.
These geometric patterns are usually fragmented and rough, but usually aesthetic
looking, and appears like an artistic work. The geometry of nature, such
as patterns of coastlines, land relief or
mountain ranges, are usually closely related to
geometry of fractals. Other natural objects that approximate fractals to a degree include clouds,
lightning bolts, and snow flakes. Therefore, fractals provide a method to describe
The term "Fractals" was coined by Benoît Mandelbrot
in 1975, who made extensive studies on Fractals. It came from the Latin
word "fractus" meaning "broken" or "fractured."
Fractal shapes are too irregular to be easily described in traditional Euclidean
geometric language. A fractal exhibits a fine structure at arbitrarily
small scales. Fractals are often considered to be infinitely complex, and
exhibits a property called self-similarity where they appear similar at all
scales or levels of magnification.
One of the well-known fractal set of points is the
Mandelbrot Set discovered by Mandelbrot.
More Mathematical Recreations