Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.
What is a fractal?
B. Mandelbrot: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.
WHAT IS A FRACTAL .. IN NATURE WE FOUND THEM EVERYWHERE
A DOT HAS A FRACTAL DIMESION OF 0 , A LINE 1 A PLANE DIMENSION 2 AND A SPHERE DIMENSION 3 ..BUT THERE ARE OTHER BODIES ..
WHAT IS A DIMESION OF BUCH OF GRAINS OF SAND ..
IT HAS TO > 0 & & < 2 . Based on a lot TOPOGRAPHY mathematics and some own theorems .The fractal theory allows to calculate dimesions of complicated geometrical bodies .. Now it is possible to write the equation of these VERY COMPLICATED SHAPES.. To everybody's surprise some of those equation are very simple .. And are iterative equations .. The coordinates of point Pn dependes in turn od point Pn-1 ..and so forth ..
Some of the shapes thus descrived and determined .. Are of a COMPLEXITY that appears to be QUASI CAHOTIC ..But they are not ALL THE UNIVERSE appears to be DETERMINISTIC .. the famous BUTTERFLY THEOREM ,, one BUTERFLY in china can be RESPONSABLE FOR A CYCLON IN AMERCA .. ALL THE UNIVERSE IS CONNECTED .NOW .!
Fractals are related with Chaotic nature of the systems. You can also search "chaotic" keyword. In simulation programs it is possible to build a chaotic oscillator to see fractals.
1. A fractal has statistical self-similarity at all resolutions and is generated by an infinitely recursive process. In reality, those fractals generated by finite processes may exhibit no visible change in detail after some stage so are adequate approximations. So, for computer graphics we can extend the definition to include anything that has a substantial measure of exact or statistical self-similarity. ...
2. A self-similar structure whose geometrical and topographical features are recapitulated in miniature on finer and finer scales.
3. An irregular geometric object that is self-similar to its substructure at any level of refinement. The fractal dimension is a measure of the irregularity of the boundary of the object. Clouds have been shown to exhibit fractal characteristics with cloud perimeters having fractal dimension of about 1.35. ..
4. an algorithm, or shape, characterized by self-similarity and produced by recursive sub-division; more generally the branch of mathematics named and explored by Benoit Mandelbrot
5.a complex geometric figure whose small-scale and large-scale structures resemble one another. Fractals represent mathematical equations and may be used for illustrating the regular features of complex objects and patterns
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.
