12 - Unknown
13 - Crystals 1
14 - Triangulation
15 - Crystals 2
16 - The End of All Things
17 - Crystal Cluster
18 - Cosmic Strings
19 - Ice
20 - Bent Time
00 - The Collision
01 - Spacial Distortion
02 - The Nebula
03 - Dark Matter
04 - Cosmic Entity
05 - Shells
06 - The Globe
07 - Cosmic Rose
08 - The Vortex
09 - Space-Time Continuum
10 - Bio-Technology
11 - Thought
Thorinair's Fractals blog has been created!
What is a fractal?
A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole", a property called self-similarity. Roots of mathematical interest on fractals can be traced back to the late 19th Century; however, the term "fractal" was coined by BenoƮt Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.
A fractal often 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.
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, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns. 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.