Milos Djukic

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Fractals, Beauty of Complexity (and Chaos)


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


Fractals, Beauty of Complexity (and Chaos)


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.

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.


Fractals, Beauty of Complexity (and Chaos)

The Linux Kernel Graphing Project by Rusty Russel by Visual Complexity


Daniel 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.


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.


Fractals Forever.


All text Copyright 2014 by Milos Djukic - All Rights Reserved


This post was originally published on LinkedIn, May, 2014.


1. Fractal art by Tom Beddard: https://www.fastcodesign.com/1663384/fly-above-a-world-of-fractals-right-in-your-browser-video

2. The Linux Kernel Graphing Project by Rusty Russel: http://fcgp.sourceforge.net/lgp/index.html

3. Tom Beddard Grows Fractals Into Works of Art: https://www.fastcodesign.com/1663070/tom-beddard-grows-fractals-into-works-of-art

3. Insanely deep fractal zoom: http://kottke.org/10/02/insanely-deep-fractal-zoom 

4. Fractal Lab: http://sub.blue/fractal-lab

5. Subblue, Work by Tom Beddard: http://sub.blue/

6. Visual Complexity: http://www.visualcomplexity.com/vc/






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Comments

CityVP Manjit

2 years ago #83

#129
Great idea to refresh this from the beBee honeycomb. Amazing that it was 3 years ago when this was first posted yet I agree it retains its fractal brilliance, the symmetry of excellence keeps getting better with every revival of this buzz.

This is the third time I share this buzz. I miss your great buzzes dear Milos Djukic

great post again!!!!!!!!!!

🐝 Fatima G. Williams

2 years ago #80

#126
I agree this is a beautiful article and can be read a thousand times

Javier 🐝 CR

2 years ago #79

Great read again !

Zacharias 🐝 Voulgaris

2 years ago #78

Fractals are fascinating creatures. However, the self-similarity attribute that often is referred to as their primary characteristic is *not* always the case. Check out this video that explains it better than words could: https://www.youtube.com/watch?v=gB9n2gHsHN4

Fractals forever!

Cyndi wilkins

2 years ago #76

This is one of those buzzes that keeps on giving...We are all fractals in consciousness...all self-similar pieces of the 'whole' ...making up the different aspects of the our beingness...What separates us into 'singularities' is the chaos within the whole. Nice to see this one come around again Milos Djukic;-))

The fractal Milos Djukic- good buzzes keep their value as this one did. One thing that surprised me is the number this buzz has in spite that many readers aren't familiar with complexity and fractals. This shows the value of effective communication and its impact. You are an outstanding example. Fractals forever

Alan Culler

4 years ago #74

Hello @Milos Djukic I enjoyed this post tremendously. "Self-similarity (Fractals) on all scales may be the secret key to understanding the complex phenomena. Self-similarity on rather different scales is another proof of fractal nature of cosmology." It is more than pretty pictures. There seems to be an order in how complex systems break into chaos or emerge from chaos, as evidenced by pictures of fractals, or the Belisof Zhabotinsky reaction https://www.youtube.com/watch?v=3JAqrRnKFHo or the triple spiral design on the curbstone at the 5000 year old megalithic monument tomb at Newgrange in Ireland https://www.dreamstime.com/royalty-free-stock-photos-megalithic-passage-tomb-newgrange-ireland-image19515648 . What is the implication of the fractal nature of cosmology or the orderly emergence from chaos for such complex systems as organizational behaviour or national or international political or economic systems? How extensive is the reach of the quantum world?

Milos Djukic

4 years ago #73

#116
Thank you Solomon. We learn together.

Solomon Jones

4 years ago #72

For now this one is beyond me but I do have the Capacity to learn. Sounds like your an artist though

Gert Scholtz

4 years ago #71

"Fractals are beautiful objects. It is a natural response to the beauty of complexity. Fractal forms and patterns are all around us." - Milos Djukic

Milos Djukic

5 years ago #70

#108
Gerald Hecht🚀 :)

Milos Djukic

5 years ago #69

#106
Thanks Ben roberts.

Milos Djukic

5 years ago #68

Sara Jacobovici, Thank you.

Milos Djukic

5 years ago #67

#101
Franci Eugenia Hoffman, Thanks for the share!

Milos Djukic

5 years ago #66

#101
Franci Eugenia Hoffman, That was our communion and the butterfly effect. Thanks a lot for the endorsement. I greatly appreciate your kindness.

#98
Very impressive Milos Djukic!

Milos Djukic

5 years ago #64

#98
beBee is fractal social network (one and only), therefore I am not surprised :) Thank you all! Cheers, Milos

Milos Djukic

5 years ago #63

#98
Irene Hackett, Thanks for the share!

Milos Djukic

5 years ago #62

#96
Thank you siraj shaik.

Milos Djukic

5 years ago #61

#94
I couldn't agree more with you Ben Pinto.

Milos Djukic

5 years ago #60

cc. Qamar Ali Khan.

🐝 Fatima G. Williams

5 years ago #59

#86
Thank you Paul \. I'm joining that hive right away 💃💃💃 .

🐝 Fatima G. Williams

5 years ago #58

#84
Awww that's an honor 3F- Fractal Fatima Forever I had to type it again 🤗🤗🤗🤗🤗 - I just love the sound of that. Thank you Milos Djukic the world becomes a better place because of people like you.✋✋✋✋✋ Virtual High five

Lisa Gallagher

5 years ago #57

#81
Great idea Paul \ ! When I created my stories hive, that's one of the reasons I added diverse to my description because I also add to it material I want to read but may not be able to right away, even video's that I like.

Milos Djukic

5 years ago #56

#72
Thank you so much for the kind words dear Fatima Williams. I'm honored by your words. 3F - Fractal Fatima Forever :)

Milos Djukic

5 years ago #55

#81
Me too :)

Milos Djukic

5 years ago #54

#78
I couldn't agree more Paul \. Thanks.

🐝 Fatima G. Williams

5 years ago #53

#78
Thanks Paul \ I always email some of the buzzes to myself to read them later at a more relaxed time. So I wont have to go searching 🤔😎😎😎 Thanks for the mail to url option I googled it already 😇😇 But I would love to have the easy email option though ☺☺☺☺

#73
Fatima Williams?

Milos Djukic

5 years ago #51

#71
Thank you .

Milos Djukic

5 years ago #50

#70
I am glad to hear that Antoinette Capasso-Backdahl. Cheers, Milos

Milos Djukic

5 years ago #49

#69
Dear Qamar Ali Khan, Thanks for all you’ve done for me. You always make a difference to my life. ”Gratitude is not only the greatest of virtues, but the parent of all the others.” - Cicero

🐝 Fatima G. Williams

5 years ago #48

Do we not have the option to email buzzes to ourselves.Thank you :)

🐝 Fatima G. Williams

5 years ago #47

Fractals are beautiful objects and you dear Milos Djukic is the human version of Fractal given to us beBees :) Loved looking at the fractal patterns, the beauty and complexity is prodigious.

Qamar Ali Khan

5 years ago #46

You're my favorite writer Milos Djukic! I can travel 10000 miles just to read something from you! I can go anywhere if I come to know that you have published. I can read and re-read your post 100 times to absorb it to make it as a part of my thinking process. This super piece has appeared after such a long wait, but it has compensated my wait and time with the its great quality and superb taste. You're a matchless writer.

Milos Djukic

5 years ago #45

#67
Thanks Aaron Skogen! We learn more when we learn together.

Milos Djukic

5 years ago #44

#65
Thank you dear Joanna Hofman!

Milos Djukic

5 years ago #43

"The Fractal Revolution in Society, Social Media First" long-form post on LinkedIn about beBee importance in the fractal revolution: https://www.linkedin.com/pulse/fractal-revolution-society-social-media-first-milos-djukic?trk=pulse_spock-articles

Milos Djukic

5 years ago #42

#61
Michael Angelo Icarus Yusufidis, I am glad to hear that, Please keep going.. Best, Milos

Milos Djukic

5 years ago #41

#55
Franci Eugenia Hoffman, Thank you. "Remember that you must at all costs remain self-similar..I call it virtual synchronicity or a fractal alignment (I'm not the only one)" - Fractals forever.

Sharing to Science and Math

Sharing in Hurricanes, Tornadoes and Extreme Weather

The more I read about fractals, the more intriguing they become. Fractals forever.

Milos Djukic

5 years ago #37

Some scientific research has clearly indicated that fractal patterns (fingerprints of nature) have also an impact on a stress relief.

Milos Djukic

5 years ago #36

#52
Irene Hackett :)

Milos Djukic

5 years ago #35

#50
You are most welcome dear Aurorasa Sima :)

Milos Djukic

5 years ago #34

#40
Michelle Trenta forever.

Milos Djukic

5 years ago #33

#31
Tag Aurorasa Sima :)

Milos Djukic

5 years ago #32

#30
Your thoughts are very inspired Praveen Raj Gullepalli. Your comment is more like a joy. The written word is the most powerful weapon in the hands of those who strive for truth. You gave us homework and thank you for that. Simply superb comment from fractal mind.

Milos Djukic

5 years ago #31

#32
Thanks Pascal Derrien.

Milos Djukic

5 years ago #30

#34
There is something so essential when it comes to fractals Irene Hackett. It is hard to explain. Beauty and order in disorder, more like an applied chaos. Once again thank you.

Milos Djukic

5 years ago #29

#33
Mamen Delgado, Have a great weekend and please enjoy. Thanks. Kindly, Milos

Milos Djukic

5 years ago #28

#39
Understanding is the key Ivan Campos. Thanks for your comment.

Milos Djukic

5 years ago #27

#36
Oh and this is great news. I am not surprised having in mind who is mom Irene Hackett. "Do not disturb my circles" :) Cheers

Milos Djukic

5 years ago #26

#35
Thank you Frans van Wamel, my friend!

Frans van Wamel

5 years ago #25

You eluded me about fractals a few years ago Milos Djukic. The Universe is indeed a wonderful place. If thoughts patterns are put under the fractal microscope then I can see that the truth does not exist, if perception is not a fact.

Mamen 🐝 Delgado

5 years ago #24

Woww... I keep this Producer to read it during the weekend in a quite moment, if I'm able to find any... 😉 Thanks Milos Djukic for bringing my attention here!!

Pascal Derrien

5 years ago #23

Fascinating :-)

Milos Djukic

5 years ago #22

Thank you Lisa Gallagher!

Milos Djukic

5 years ago #21

#25
A very interesting observation Aurorasa Sima and true.

Milos Djukic

5 years ago #20

#24
Great suggestions Alan Geller! I have chosen: Milos F. Djukic (F. means a Fool) :) Fools and fractals forever :)

Milos Djukic

5 years ago #19

#22
Aurorasa Sima :))) Daniel 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. Too much complexity being bad, I guess, then the chaos prevails :) "Beauty of Complexity (and Chaos)", together?

Milos Djukic

5 years ago #18

#10
Thank you for the kind words debasish majumder.

Milos Djukic

5 years ago #17

#19
I was also thrilled Aurorasa Sima :) And it is real not an art.

Milos Djukic

5 years ago #16

Thank you Ivan Campos! Cheers, Milos

Milos Djukic

5 years ago #15

cc. Qamar Ali Khan.

Milos Djukic

5 years ago #14

1. Fractal art by Tom Beddard: https://www.fastcodesign.com/1663384/fly-above-a-world-of-fractals-right-in-your-browser-video 2. The Linux Kernel Graphing Project by Rusty Russel: http://fcgp.sourceforge.net/lgp/index.html 3. Tom Beddard Grows Fractals Into Works of Art: https://www.fastcodesign.com/1663070/tom-beddard-grows-fractals-into-works-of-art 3. Insanely deep fractal zoom: http://kottke.org/10/02/insanely-deep-fractal-zoom  4. Fractal Lab: http://sub.blue/fractal-lab 5. Subblue, Work by Tom Beddard: http://sub.blue/ 6. Visual Complexity: http://www.visualcomplexity.com/vc/ cc. Margaret Aranda, MD, PhD, Paul \.

Gert Scholtz

5 years ago #13

Milos Djukic Thank you for the link Milos. I appreciate your time to reference further information to this as yet "unfractaled" Bee.

Gert Scholtz

5 years ago #12

Milos Djukic Thank you for the link Milos - I appreciate you taking the time to give more information to this "unfractaled" Bee.

Milos Djukic

5 years ago #11

#11
That's the reason for Linux superiority and possibly penguins, I guess :)

Milos Djukic

5 years ago #10

#11
I am so glad to hear that Gert Scholtz, my friend. For more details please check this paper: Dominik Strzałka, Fractal Properties of Linux Kernel Maps, (2012) Computer Science and Engineering 2(6),:pp. 112-117 (http://article.sapub.org/10.5923.j.computer.20120206.05.html) cc. Phil Friedman The difference between complex and complicated systems is quite subtle: the complicated system is a system that has many interdependent elements, but the dependencies between them are governed by well-known deterministic laws (i.e. such systems are rather simple systems), while in the case of complex systems the dependencies between their components are governed by laws that are not necessary well-known. See the details in [1] [1] F. Grabowski, D. Strzałka, Simple, Complicated and Complex Systems – The Brief Introduction, 2008 Conference On HSI, 1-2 (2008) 576–579.

Gert Scholtz

5 years ago #9

Milos Djukic Finally I am starting, just starting, to understand something about your fascinating fractals. The pattern of the Linux Kernel speaks of the beautiful complexity of fractals. Thank you Milos.

Milos Djukic

5 years ago #8

Thanks Lada Prkic. Fractals forever!

Lada 🏡 Prkic

5 years ago #7

I recently have become fascinated with fractals, partly by reading your posts on LinkedIn. :-) When I think about fractals usually “see” the Mandelbrot set, but there are so many types of fractals we can find in the natural world around us. Thanks for reminding me to some fractal artworks, like "The Great Wave off Kanagawa" and its fractal waves. There is just something mesmerizing about seeing this picture up close. Fractals forever!

Milos Djukic

5 years ago #6

Thank you dear Ali Anani.

Milos Djukic

5 years ago #5

Thanks John White, MBA.

Milos Djukic

5 years ago #4

Thank you Julie Hickman

David B. Grinberg

5 years ago #3

Thank you Milos Djukic for this informative and education primer of fractals. I'm sharing on several hives.

Sara Jacobovici

5 years ago #2

Thanks Milos Djukic for contributing to my discovery and enjoyment.

Lisa Gallagher

5 years ago #1

I was just watching a show tonight and they mentioned fractals, I can't remember what it was in reference to. I need my memory pills but I find this so intriguing even though I'm still learning a lot each time I read. I'm sure the show will come to mind when my head hits the pillow. I love the visuals you provide Milos Djukic, it allows the brain to wander, which is a good thing!

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