Fractal

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See also: Mathematics | Chaos | Complexity

A fractal is a description of the shapes and patterns found in complex structures, chaotic behaviour and dynamic systems. Fractals are self-smiliar at different scales.

There are three types of fractals. Classical or linear fractals such as the Koch Island and Sierpinksi Gasket were the first to be discovered. Then there are non-linear fractals like the Mandlebrot Set and finally are there are random fractals like artwork or the landscape.

Every thing that has radical shape is fractal. Fractal geometry is a more accurate description of the objects that surround us compared to Euclidean geometry.

Euclidean geometry falls apart when the following paradox is considered. If you were to take a map of the British coastline, and with a piece of string measure the depicted coastline, the distance would be X kilometres. If you were to get in a small plane a fly around the coast you would get a measurement greater than from the map. Walking around the coast, taking a measurement by foot and the result would be greater still. Also consider the very difficult possibility of measuring the coastline with a small ruler, and so on. Which count is the best answer?

Fractal Software

  • XaoS - fast, portable, real-time, and interactive fractal zoomer.
  • Deep Zoom - CLI. Generates high precision, highly zoomed, high resolution fractals using the GNU Multiple Precision library. Can zoom far deeper than other zoomers because it does not operate in realtime.
  • ifsplot - an IFS attractor (fractal) plotter. Given an IFS (a set of affine transformations), it generates associated fractal. The libplot library is employed, so any libplot driver is supported (X, eps, PNG, fig, etc.).
  • Ultrafractal - Closed-source

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