FractalsPage 1 of 2
Content
- What are fractals?
- History: Mandelbrot
- Mechanics of fractals
- Apophysis: free fractal generator
- Gallery of free images of fractals
Youtube: Fraktals - Beauty of Mathematics
What are fractals?
The term "fractal" (lat. fractus: broken) describes a mathematical pattern that repeats a certain structure. On a smaller scale, the pattern repeats itself over and over again, with minimum deviance. This principle is not new. In nature, too, there are fractals, for example plants like Romanesco Broccoli or Cauliflower. This principle is even found within snails or ammonite shells.
Cauliflower |
Romanesco Broccoli |
Snails  |
Ammonite shells  |
History
In the 1980s, Benoit Mandelbrot discovered fascinating images by chance while carrying out chaos theory research on an IBM computer. These images developed from a simple mathematical equation, the basic form of which is the so-called Mandelbrot Set.
Mechanics of fractals
In most cases, the Mandelbrot Set fractal serves as a starting point:
When magnifying a section of an image, this section resembles the previous one, yet it is not equal.
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When magnifying even further, another variation comes about.
The variations increase as the image section is further magnified.
Until we´re back at the starting point: the Mandelbrot Set.
Apophysis: free fractal generator
Apophysis is a free program which enables you to construct fractals.
The developer´s homepage can be found here:www.apophysis.org
You can download the program here:
Download
Use of Apophysis - Tutorial
1 - Different variations are available
2 - from left to right: Editor (change Form), gradient (change colour), Adjust (background colour and image balance), mutations (suggests 8 more variations)
3 - 100 randomly constructed fractals
You can save your created fractal by clicking File / Export Flame and specifying the destination on your computer as well as selecting the desired resolution. This opens a window and creates your fractal.
Books about fractals:
 
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