Object which is self-similar at all scales of magnification and reduction. Created by duplicating a shape successively according to a set of rules to represent complex imagery including seemly random-shaped things in nature, such as clouds, trees, and mountains.
curves or surfaces generated by some repeated process resulting in self-similarity.
Geometrical entities characterised by basic patterns that are repeated at ever decreasing sizes. They are relevant to any system involving self-similarity repeated on diminished scales (such as a fern's structure) as in the study of chaos. Benoit Mandelbrot was the first to develop and pioneer new methods of mathematics to create fractals with computer programs.
From the Latin, fractus, broken (frangere, to break). A measurement of the degree to which a body takes up space available it; an estimate of its efficiency in using the space it occupies. In more simple terms a fractal is a measure of the irregularity of an object. Mandelbrot uses fractal as a generic term applicable to all mappings of system dynamics in phase space.
Along with raster and vector graphics, a way of defining graphics in a computer. Fractal graphics translate the natural curves of an object into mathematical formulas, from which the image can later be constructed.
(noun) 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. Fractals are generally self-similar and independent of scale.
ever diminishing subdivisions of a basic geometric shape.
