Fractal

Three common techniques for generating fractals are:

Escape-time fractals — These are defined by a Recurrence Relation at each point in a space (such as the Complex Plane ). Examples of this type are the Mandelbrot Set , Julia Set , the Burning Ship Fractal and the Lyapunov Fractal .

Iterated Function System s — These have a fixed geometric replacement rule. Cantor Set , Sierpinski Carpet , Sierpinski Gasket , Peano Curve , Koch Snowflake , Harter-Heighway Dragon Curve , T-Square , Menger Sponge , are some examples of such fractals.

Random fractals — Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian Motion , Lévy Flight , Fractal Landscapes and the Brownian Tree . The latter yields so-called mass- or dendritic fractals, for example, Diffusion-limited Aggregation or Reaction-limited Aggregation clusters.

CLASSIFICATION OF FRACTALS

Fractals can also be classified according to their self-similarity. There are three types of self-similarity found in fractals:

Exact self-similarity — This is the strongest type of self-similarity; the fractal appears identical at different scales. Fractals defined by iterated function systems often display exact self-similarity.

Quasi-self-similarity — This is a loose form of self-similarity; the fractal appears approximately (but not exactly) identical at different scales. Quasi-self-similar fractals contain small copies of the entire fractal in distorted and degenerate forms. Fractals defined by Recurrence Relation s are usually quasi-self-similar but not exactly self-similar.

Statistical self-similarity — This is the weakest type of self-similarity; the fractal has numerical or statistical measures which are preserved across scales. Most reasonable definitions of "fractal" trivially imply some form of statistical self-similarity. (Fractal dimension itself is a numerical measure which is preserved across scales.) Random fractals are examples of fractals which are statistically self-similar, but neither exactly nor quasi-self-similar.

FRACTALS IN NATURE

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 , Crystal s, Mountain Range s, Lightning , River Networks , Cauliflower or Broccoli , and systems of Blood Vessel s and Pulmonary 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.

In 1999, certain self similar fractal shapes were shown to have a property of "frequency invariance" — the same electromagnetic properties no matter what the frequency — from Maxwell's Equations (see Fractal Antenna ). Hohlfeld,R., and Cohen,N.,"SELF-SIMILARITY AND THE GEOMETRIC REQUIREMENTS FOR FREQUENCY INDEPENDENCE IN ANTENNAE ", Fractals, Vol. 7, No. 1 (1999) 79-84

FRACTALS IN ART

Fractal patterns have been found in the paintings of American artist Jackson Pollock . While Pollock's paintings appear to be composed of chaotic dripping and splattering, computer analysis has found fractal patterns in his work. Richard Taylor, Adam P. Micolich and David Jonas. ''Fractal Expressionism : Can Science Be Used To Further Our Understanding Of Art?''

Fractals are also prevalent in African art and architecture. Circular houses appear in circles of circles, rectangular houses in rectangles of rectangles, and so on. Such scaling patterns can also be found in African textiles, sculpture, and even cornrow hairstyles.. Ron Eglash. ''African Fractals: Modern Computing and Indigenous Design. New Brunswick: Rutgers University Press 1999.''

	CATEGORIES ABOUT FRACTAL

	fractals

	digital revolution

	digital art

	APPAREL
	BABY
	BEAUTY
	BOOKS
	CAR TOYS
	CELL PHONES
	DVD'S
	ELECTRONICS
	GOURMET FOOD
	GROCERIES
	HEALTH & PERSONAL
	HOME & GARDEN
	JEWELRY
	MUSIC
	MUSIC INSTRUMENTS
	OFFICE PRODUCTS
	SOFTWARE
	SPORTING GOODS
	TOOLS & HARDWARE
	TOYS
	VIDEO GAMES
	SHOPPING HOME

	MORE SHOPPING...

Information About

Fractal