Mathematics is the study of
change. Mathematics is used throughout the world as an essential tool in many fields, including
medicine, and the
social sciences. It is used for calculation and considered as the most important subject.
Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as
game theory. Mathematicians also engage in
pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
A fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole". The term was coined by
Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured".
A fractal as a
geometric object generally has the following features:
It has a fine structure at arbitrarily small scales.
It is too irregular to be easily described in traditional Euclidean geometric language.
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the
real line (a straight
Euclidean line) is formally self-similar but fails to have other fractal characteristics. Fractals, when zoomed in, will keep showing more and more of itself, and it keeps going for infinity. (Full article...)