Difference between revisions of "Field:Fractals"

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:'''Strange attractors'''  {{Hide|
 
:'''Strange attractors'''  {{Hide|
 
::Fractals that are considered strange attractors are generated from a set of functions called attractor maps or systems. These systems are chaotic, because the functions map points in a seemingly random order. These points are actually not completely random and are in fact evolving towards a structure that can eventually be seen as the form of the attractor.
 
::Fractals that are considered strange attractors are generated from a set of functions called attractor maps or systems. These systems are chaotic, because the functions map points in a seemingly random order. These points are actually not completely random and are in fact evolving towards a structure that can eventually be seen as the form of the attractor.
::*Examples include: [[Lorenz Attractor]], [[Henon Attractor]], [[Cantor Dust]] , and [[Rossler Attractor]].
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::*Examples include: [[Lorenz Attractor]], [[Henon Attractor]], [[Cantor Set]] , and [[Rossler Attractor]].
 
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Revision as of 11:00, 3 June 2009


Fractals

NorwayCoastline.png

A fractal is often defined as a geometry shape that is self-similarity, or whose magnified parts look like a smaller copy of the whole. It was coined by Benoit Mandelbolt in 1975 from the latin term fractus meaning "fragmented" or "irregular".

This concept can be explained in a commonly used nature analogy involving the coastline of an island :

 Suppose you wanted to measure the total perimeter of an island. You could begin by roughly estimating
 the perimeter of the island by measuring the border of the island from a high vantage point like an
 airplane and using miles as units. Next, to be more accurate, you could walk along the island's borders
 and measure around its various coves and bays using a measuring tape. Then, if you wanted to be really
 accurate, you could carefully measurearound every single protruding rock and detail of the island with
 a yardstick or even a foot-long ruler.

Clearly, the perimeter of the island would grow as you decrease the size of your measuring device and increase the accuracy of your measurements. Also, the island would more or less like similar (in terms of becoming more and more jagged and complex) as you continued to decrease your measuring device.


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