42 – Fractal Geometry, the Mandelbrot Set, and the Universal in us.

Fractal Geometry is one of the most succinct and revealing scientific theories of the 20th Century. With Fractals, the French mathematician Benoit Mandelbrot overcame the limitations of Classic (Euclidian) Geometry to describe the complexity of irregular shapes in the natural world.

“A Fractal can be defined as ‘A rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,’ a property called self-similarity.” [1]

“The most striking properties of these ‘fractal’ shapes are that their characteristic patterns are found repeatedly at descending and ascending scales, so that their parts, at any scale, are similar in shape to the whole. Mandelbrot illustrates this property of ‘self-similarity’ by breaking a piece out of a cauliflower and pointing out that, by itself, the piece looks just like a small cauliflower. He repeats this demonstration by dividing the part further, taking out another piece, which again looks like a very small cauliflower.” [2] But the most striking examples of self-similarity are found in the reiteration of the most fundamental characteristics of our Universe on every one of its components.

The Mandelbrot Set, a computer-generated program named after Benoit Mandelbrot, was designed to show these repeating patterns at descending and ascending levels of magnification. The set can be seen on YouTube under Mandelbrot Set Zoom. Watch the pattern of the original shape reappear over and over as the program descends deeper and deeper into the set. It is beautiful to watch.

On Post 16 ‘Our Universe is a Hologram’ I wrote about the fact that when a Hologram is broken into pieces, each piece … no matter what size or shape … contains the image of the whole Hologram: ‘Each piece contains the information of the whole’. The Mandelbrot Set is based on this principle, but from a different angle: The Whole is contained in each of its components.

Let’s apply the Mandelbrot Set using some of the fundamental characteristics of our Universe as a Master Model (equilibrium, self-containment, self-generation, self-perpetuation, relative degree of freedom in adaptation) and start a descent into some universal components; a galaxy, a planet, a human being. As we descend into smaller spheres, we begin to see a reiteration of the fundamental characteristics … the blueprint of the Master Model … re-occurring on the components, showing that everything is fundamentally similar, and therefore, interrelated:

  •    As our Universe, our galaxy has obeyed an innate tendency to attain, and sustain, relative states of optimum equilibrium between its energy and mass contents … more mass demands more energy, less energy demands less mass. This is Einstein’s magnificent insight into the nature of reality, e=mc2, which means that no matter how large or small, simple or complex a naturally evolving system might be, its energy and mass contents must remain relatively equivalent.
  •    As our Universe, the Earth has unfolded into a self-contained, self-generating self-perpetuating system while preserving a more or less fundamental configuration.
  •    As our Universe, you and I are endowed with a relative degree of freedom to manipulate and be manipulated by the movement of Evolution.

The Mandelbrot Set is a new insight into the nature of our Universe. When we zoom in repeatedly from one sphere into another …  from dimension to dimension, from galaxy into solar system, from solar system into planet, from planet into human being, and so forth … we find the reiteration of fundamental characteristics.

And because the fundamental characteristics of our Universe … the common blueprint … are reiterated in each and all of its components, including us, the magnificent mystery can be glimpsed at by understanding ourselves.

Share the knowledge.

[1] From Wikipedia

[2] Excerpts from The Web of Life by F. Capra. Highlight mine.

Revised July 2018

Note: New posts are usually published on the 1st and 15th of the month. To subscribe to the Blog, click on the RSS feeder (orange icon) on the left column of the Home page, down below the Archives.

Be Sociable, Share!

96 Responses to “42 – Fractal Geometry, the Mandelbrot Set, and the Universal in us.”

  1. I’m impressed how smooth this text is. it is so well-written.

  2. Chatten says:

    Im grateful for that weblog. Significantly many thanks once again. A lot required.

  3. Hey! Excellent post! Please do tell us when we can see a follow up!

  4. The more I read, the more difficult to stop reading it is.

  5. here says:

    Thanks for the tips you have shared here. Yet another thing I would like to express is that computer memory needs generally rise along with other innovations in the technologies. For instance, whenever new generations of cpus are brought to the market, there is certainly usually a matching increase in the size preferences of both computer system memory as well as hard drive space. This is because the software program operated simply by these cpus will inevitably rise in power to use the new know-how.

  6. seo katalog says:

    I bet you have no idea what I would give to be able to read more such good blogs.

  7. Nürnberg says:

    that your particular experience was so easy to find and how it properly compared to my personal experience.

  8. slanket says:

    Im no pro, but I consider you just made an excellent point. You clearly fully understand what youre talking about, and I can definitely get behind that. Thanks for staying so upfront and so truthful.

  9. I have been reading out many of your stories and i can state pretty clever stuff. I will make sure to bookmark your website.

  10. Thanks for the strategies you have shared here. Also, I believe there are a few factors which keep your automobile insurance premium down. One is, to bear in mind buying motors that are within the good report on car insurance corporations. Cars which can be expensive are definitely more at risk of being stolen. Aside from that insurance policies are also using the value of your truck, so the more pricey it is, then higher the actual premium you have to pay.

  11. You must have spent time to gather this type of content , must of the net is spam.

  12. shared your site in my social networks!

  13. This might not be the ideal place to ask this, but I’m trying to find a pest management company within the pittsburgh area and have no method to find out who is the best. I discovered this business which is actually close to me and wished to see if anybody has any reviews on them. Spectrum Pest Control, 3058 West Liberty Avenue, Dormont, PA 15216 – (412) 446-2802

  14. Is there a way to keep track of blogs like this one?

  15. Your writing is great:)

  16. Do you people have a myspace fan web page? I looked for one on facebook or twitter but could not locate it, I would really like to become a fan!

  17. This is possibly the most detailed content I’ve read on this subject. Phenomenal writing. Continue the detailed work!

  18. Great site, figured out a few new things! Subscribed RSS for later, hope to see more updates like this one.

  19. Hey there! I know this is kind of off topic but I was wondering which blog platform are you using for this website? I’m getting fed up of WordPress because I’ve had problems with hackers and I’m looking at alternatives for another platform. I would be fantastic if you could point me in the direction of a good platform.

  20. Merci pour le post de cet article !!!!

  21. oeuvre d'art says:

    Merci de partager l’ info 😀

  22. You are a very capable individual!

  23. Kopi Luwak says:

    Thanks for posting this, it was very informative and helped me very much

  24. Awesome and an highly interesting post to stumble at on this massive website! Never write some replies only now i couldnt i could not resist ..

  25. Aleen Gimlin says:

    I visited a lot of website but I believe this one has something special in it. “People who lose their parents when young are permanently in love with them.” by Aharon Appelfeld.

  26. Well I definitely liked studying it. This subject procured by you is very helpful for proper planning.

  27. Ethylotest says:

    merci pour le partage !!

  28. Your fashion is so exclusive compared to several others. Thank you for publishing at the time you possess the possibility,Guess I will just make this bookmarked.two

  29. Wow, superb blog layout! How long have you been blogging for? you made blogging look easy. The overall look of your site is wonderful, let alone the content!

  30. Creola Lamp says:

    Totally awesome.

  31. Thanks for sharing this helpful info!

  32. Rene Kalt says:

    Some really superb posts on this web site , thanks for contribution.

  33. ppc services says:

    I truly wanted to make a note to appreciate you for some of the remarkable tricks you are giving at this site. My particularly long internet research has at the end been compensated with brilliant tips to talk about with my classmates and friends. I would repeat that most of us readers actually are unquestionably fortunate to live in a superb website with very many brilliant individuals with great advice. I feel very grateful to have encountered the website page and look forward to some more enjoyable minutes reading here. Thanks a lot once more for all the details.

  34. Stacy Furtaw says:

    I’ve been browsing online more than 3 hours lately, yet I never discovered any fascinating article like yours. It is pretty price sufficient for me. Personally, if all web owners and bloggers made just right content material as you did, the web shall be much more useful than ever before.

  35. 關鍵字 says:

    We simply wished to express thanks regarding putting up this particular data. This particular article happens to be superior, definitely excellent.

  36. Julio Foat says:

    Thanks for your marvelous posting! I genuinely enjoyed reading it, you’re a great author.I will be sure to bookmark your blog and will often come back at some point. I want to encourage you continue your great work, have a nice morning!

  37. About says:

    Epic post, really love your blog, O and have a great Christmas 🙂

  38. he blog was how do i say it… relevant, finally something that helped me. Thanks

  39. I really enjoy reading through on this web site , it holds good articles .

  40. Ronny Vecino says:

    Thanks a lot for sharing this with all people you actually know what you’re speaking about! Bookmarked. Kindly also visit my website =). We could have a hyperlink alternate contract between us!

  41. I conceive other website proprietors should take this web site as an model, very clean and superb user pleasant pattern . “No act of kindness, no matter how small, is ever wasted.” by Aesop.

  42. This is great! How did you learn this stuff?

  43. shared your site in my social networks!

  44. Why didnt I believe about this? I hear specifically what youre saying and Im so happy that I came across your weblog. You genuinely know what youre talking about, and you created me feel like I ought to understand a lot more about this. Thanks for this; Im officially a huge fan of your blog.

  45. Scrapeboard says:

    This really solved my problem, thank you!

  46. Excellent stuff from you, man. Ive read your stuff before and youre just too awesome. I really like what youve got here, adore what youre saying and the way you say it. You make it entertaining and you still manage to keep it smart. I cant wait to read much more from you. This is truly an excellent blog.

  47. It has taken me ages to discover your blog. Thank goodness. This is just the info I was after.

Leave a Reply