Fractal 012009A1 By LBGrover

Fractal 012009A1 By LB Grover

Fierce Red Fractal

Defining Fractals
While mathematicians possess many complicated computational methods to define a true fractal, they are really not that simple to comprehend (as opposed to many other complex mathematical ideas). A fractal is a complex shape which, when viewed in finer and finer detail, shows itself to be constructed of ever smaller parts, similar to the original.

Sound complicated?

Another

Fractals were started in the 1900's (early) before computers were available no generators as well they were done by hand and eye using geometry and math. Can't someone be good at math and geometry enough not to have to depend on a generator? What can you tell me about the history of fractals?

Fractals have their roots in 19th century mathematics. In Jean Perrin, Les Atoms, and William Fellers' book Introduction To Probability, they discussed both real and simulated Brownian motion (a natural phenomenon which is chaotic in nature).

In 1918 both Fatou and Julia worked on what we would think of as the more standard types of fractals.

One of the most inspiring works however seems to have been Poincaré's Vorlesungen uber die Theorie der Automorphen Funktoren published in 1897 which contained many influential illustrations. His drawings of hyperbolic tesselations were embellished by M.C. Escher and made into a form of art which itself could be argued to be closely related to fractals.

Some of the modern interest in fractals among the general public comes from the computer-assisted work of the IBM fractal project and 20th century mathematicians like Benoit Mandelbrot after whom the Mandelbrot set is named. Pictures of this set are quite fascinating and show surprising features at every level of detail. Until the introduction of the computer, very little from this area of mathematics was in the form of graphics. IBM's fractal project added the pictures to what is inherently an incredibly visual field of mathematics. This added dimension of the field in turn gave rise to new discoveries and incarnations of fractals such as mountains and clouds.




Also
fractal often has the following features:[3]

It has a fine structure at arbitrarily small scales.
It is too irregular to be easily described in traditional Euclidean geometric language.
It is self-similar (at least approximately or stochastically).
It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
It has a simple and recursive definition.
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; for instance, it is regular enough to be described in Euclidean terms.

Images of fractals can be created using fractal generating software. Images produced by such software are normally referred to as being fractals even if they do not have the above characteristics, as it is possible to zoom into a region of the image that does not exhibit any fractal properties.


Food for thought