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Self-similarity (Fractals) on all scales may be the secret key to understanding the complex phenomena. Self-similarity on rather different scale is another proof of fractal nature of cosmology.

Multiscale modeling of physical phenomena and matter-materials response on different length scale represent powerful tool in modeling. This approach presents a breakthrough in the phenomenological analysis of complex phenomena. The fractal nature of the fracture process and the geometry of a crack are well described in the literature. For fractal geometry in physics, I suggest you to study the  “Hofstadter’s butterfly” – mathematical object describing the behaviour of electrons in a magnetic field.

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Fractals are beautiful objects. It is a natural response to the beauty of complexity. Fractal forms and patterns are all around us. Salvador Dali was one of the pioneers in the use of fractals in art (“Visage of War”, 1940). Also look up the painting: ” The Great Wave off Kanagawa”, 1829–32 by Katsushika Hokusai and you will see one of the greatest fractal art examples (suggested by Mr. Les Moore, dear LinkedIn member).

D. E. Berlyne pointed out in his book “Aesthetics and psychobiology” (1971) that perceptions of beauty increase linearly with visual complexity, until an optimum level is reached and then decrease. Some scientific research has clearly indicated that fractal patterns (fingerprints of nature) have also an impact on a stress relief. Microscopy is an ideal research tool for sure. I see them more by microscope, but also in everyday life. Discover and enjoy.

I have recently published post on LinkedIn – “Fractals & Microstructural Disorder”, about research of the great mathematician Prof. Benoît B. Mandelbrot (20 November 1924 – 14 October 2010), founder of Fractal Geometry and pioneer of Complex Systems Mathematics:

“Fractals & Microstructural Disorder” – LinkedIn post by Milos Djukic:
http://www.linkedin.com/today/post/article/20140408234122-248021126-fractals-microstructural-disorder?trk=prof-post

“Prof. Mandelbrot paved the way for the attainment of fundamental results such as the definition of the role of microstructural disorder and the scale effects on the fracture energy of materials”.


Indeed, after many years, Prof. Mandelbrot valuable work and fractals are still alive. The near future will show us what is the impact of these extraordinary findings.

(Photo: Julia set (indigo).png and Hofstadters butterflu.png by wikimedia.org)

All text Copyright © 2014 by Milos Djukic – All Rights Reserved

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