Fractals, what are they?

Question

Are they the very definition of infinte space?

Answer 1

Don't know but you should be able to find the answer the same way I would, by searching the internet.

Answer 2

A line has one dimension, a surface has two and a solid object has three. But Imagine an equilateral triangle. Rub out the middle third of each side and replace it with two equal lines the same length as the section you rubbed out, so you've got a shape a bit like a star of David. Then repeat the process so you've got a shape a bit like a snowflake. Keep repeating the process indefinitely and the length of the snowflake curve grows without limit. It's got some other interesting properties. For instance, you can't draw a tangent to it. This is a fractal. It's number of dimensions is a fraction between 1 and 2. There are plenty of other examples of fractals. Google the images of a Sierpinski gasket, the Mandelbrot Set and Julia sets. Some space-filling curves are fractals with dimension slightly less than 2. In other words, even though they are lines, they're more like a surface than a line. Fractals have at least one practical application. A thin film of conductor deposited on an insulating surface in a shape rather like a snowflake curve makes a very small broadband aerial.

Answer 3

Fractal, in mathematics, a geometric shape that is complex and detailed in structure at any level of magnification. Often fractals are self-similar—that is, they have the property that each small portion of the fractal can be viewed as a reduced-scale replica of the whole. One example of a fractal is the “snowflake” curve constructed by taking an equilateral triangle and repeatedly erecting smaller equilateral triangles on the middle third of the progressively smaller sides. Theoretically, the result would be a figure of finite area but with a perimeter of infinite length, consisting of an infinite number of vertices. In mathematical terms, such a curve cannot be differentiated (see Calculus). Many such self-repeating figures can be constructed, and since they first appeared in the 19th century they have been considered as merely bizarre.

A turning point in the study of fractals came with the discovery of fractal geometry by the Polish-born French mathematician Benoit B. Mandelbrot in the 1970s. Mandelbrot adopted a much more abstract definition of dimension than that used in Euclidean geometry, stating that the dimension of a fractal must be used as an exponent when measuring its size. The result is that a fractal cannot be treated as existing strictly in one, two, or any other whole-number dimensions. Instead, it must be handled mathematically as though it has some fractional dimension. The “snowflake” curve of fractals has a dimension of 1.2618.

Fractal geometry is not simply an abstract development. A coastline, if measured down to its least irregularity, would tend toward infinite length just as does the “snowflake” curve. Mandelbrot has suggested that mountains, clouds, aggregates, galaxy clusters, and other natural phenomena are similarly fractal in nature, and fractal geometry's application in the sciences has become a rapidly expanding field. In addition, the beauty of fractals has made them a key element in computer graphics.

Fractals have also been used to compress still and video images on computers. In 1987, English-born mathematician Dr. Michael F. Barnsley discovered the Fractal TransformTM which automatically detects fractal codes in real-world images (digitized photographs). The discovery spawned fractal image compression, used in a variety of multimedia and other image-based computer applications.

Answer 4

fractals are graphical representations of specific mathematical equations that use imaginary numbers (y'know, the square root of negative one). they have a property called "self-similarity" which means that if you look into the pattern deep enough (or copy the pattern enough times), the result will look exactly like what you started with. each repeating of the pattern is called an iteration. do a google search for "mandelbrot set," and you will get a good idea of what these look like. fractals also have the unique characteristic of an infinite volume contained within an infinite boundry all of which fits in a finite plane. weird stuff.

Answer 5

One type of fractal, the Hilbert curve, does in fact define infinite space by filling it up completely! This function is continuous everywhere but nowhere differentiable.

Answer 6

lost on the infinite space thing, no clue

they are Mandelbrot or Julia sets mostly

its using some simple math formulas and inputs to make really nice pictures, they involve tings with smaller and smaller versions making some really col effects

fractals occur in nature too

Answer 7

It has something to do with space...