Fractals, Science and Links

Fractals and Science

Fractals

What are fractals?
Fractal is a term which was coined by Benoît Mandelbrot. It refers to a certain group of shapes and objects. Fractals are natural or artificial structures wich offer a high level of scale invariance or self-similarity. Scale invariance relating to fractals means that the scale is not important for the result. Structures which are scale invariant can be observed from different distances but the object always looks the same. Self similarity means that parts of the object are self similar (they contain parts of themself). Self similar structures contain parts which are similar to themselves. It is even possible that the whole structure can be found within the object (i.e. Mandelbrot Set). Because of these two attributes very complex structures can be reduced to simple rules when they are recognized as fractals.
Examples for natural fractales are:                                                         Examples for artificial fractals are:


Fern                                                                                                               Sierpinski triangle

Romanesco broccoli                                                                                   Koch snowflake
 

 

After understanding the beauty of fractals you will always try to find fractal structures in your environment. And you will find them. Fractals are more than just a mathematical theory to describe certain things. Fractals are the answer to so many different questions.​
Before he died, I tried to contact Benoit Mandelbrot to see if he had any contact with Dali. I had become convinced that not only would Dali utilize fractals heavily in his work were he alive, but he may have done so already. At a later time I'll write an article on why I feel this.
As said above, fractals are everywhere. Every breath you take sends air into the fractal network of your lungs, every pump of your heart (which in itself is fractal) sends life through the fractal network of your viens. There are mystical as well as practical qualities in fractals, and I will continue to explore these concepts.
While there are many kinds of fractals and many programs to generate fractals, I thought I'd provide links to several of what I consider the best. Most are free, so download them and get immersed in the visual qualities of fractal making. I don't believe that the world at large is ready to call a fractal art, but do believe, that utilizing fractals in the right compositions, can be immortal.