Work In Progress!

Generating Fractals

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Several phenomena exist in nature which cannot be quantitatively solved , but the qualitative nature of non linear dynamics enables to get quite a precise idea of the pattern followed. Nature in particular , is quite an enigma. Much of its creations are highly symmetric , and exhibit a fractal nature. Trees for instance, have a particular spreading pattern. Zooming in on the leaves, we are able to observe a similar branching of the veins.

 Barnsley’s Fern

Barnsley’s fern is A splendid example of how randomly chosen functions can be used to iterate a point in order to obtain a beautiful fern-like pattern which is also a fractal. Thus, Non – linear dynamics appears to be the language of nature.

The constants used by the mathematician Michael Barnsley can be modified suitably to produce patterns resembling different species of fern.

Barnsley fern

The Barnsley Fern is a fractal named after the British mathematician Michael Barnsley . The zoomed in portion confirms its multifractal nature

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An actual fern

Source Code for generating the fern


 

Julia Set

The Julia tree which assumes equal angles at each branch. The program , like most fractal programs , has been ridiculously simple to write , and yet produces spectacular results. Such is the beauty of Non linear dynamics .

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Source Code for the Julia tree

 

Sierpinski Triangle

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Source Code for the Sierpinski Triangle

 

 

Mandelbrot Set

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Source Code for the Mandelbrot set


 

A homemade fractal

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