The Mandelbrot Set & Fractal Geometry

Hi Friends,

Have you ever heard of Benoit Mandelbrot and his research within Fractal Geometry? Benoit was born in Poland and he did some amazing work developing new mathematics letting us explore the “hidden dimensions of fractal geometry”.

Fractal Geometry

 

“Fractals” are objects that display self-similarity at various scales. If we magnify a fractal we shall find small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. All though the Mandelbrot set is infinitely complex we can created them based on very simple mathematics.

The most famous fractal is called “The Mandelbrot set” which was generated by computers at IBM where Benoit was working at the time.

 

fractals, ibm fractals, mandelbrot set, monument mandelbrot, statue fractals,

Fractals can be found all around us in the Universe. A good example of fractals would be looking at a pictures of our solar system and then looking at a picture of an atom. Just as the sun circles around our 2-dimensional flat planet on a large scale, we can see almost the same pattern if we magnify this picture and study individual atoms which we shall find circling around the negatively charged electrons.

heart, fractals heart,

These fractals resemble a human heart.

 

shell fractals, seashell geometry,

These fractals resemble a seashell

 

core, suns core, sun geometry,

These fractals resemble our star

 

cyclone, fractals hidden in nature,

These fractals resemble an cyclone on earth

 

broccoli fractals,

These fractals resemble Broccoli

 

lsd patern, lsd hallucinations,

These fractals resemble my living room floor last weekend

 

peacock, fracals peacock

These fractals resemble a peacock

 

fractal flowers,

These fractals resemble spring flowers

 

 

Arthur C Clarke made the bold claim that fractal geometry was one of the most revolutionary discoveries within the field of mathematics all though at that time it was questioned if the discovery of fractals would ever have real world applications. Today fractal geometry is being used for Animations, Virtual Reality, Bio Medicine, Invisibility Cloaks, Therapy, Neuro-Linguistic Programing, Cold Fusion & Telecommunications.

 

 

 

 

  I love watching fractal geometry patterns after a hard day in the laboratory as a way to relax and float away into a different state of mind where I can explore my inner consciousness. Watching these animations seems(?) to open us up to new ideas and expands our creative abilities.  

 

 

 

The concept of fractals made a huge impact on my life and the way I observe the world around me when I was first presented to them. As this is a very open subject poorly understood and open for debate I would love for to hear what others have to say about the importance and meaning of Fractal Geometry.

 

Truth is always open for debate!

 

 

 

 

 

8 Responses to “The Mandelbrot Set & Fractal Geometry”

  1. curbina says:

    I see fractal patterns in the way rain and water streams erode the landscape. In the way that tree branches grow. In the way that blood vessels irrigate the organs. Nature is full of fractal patterns. I thing that the Universe, seen from a good enough distance, is a fractal pattern in itself.

    Fractal erosion pattern in Chile’s Valle de la Luna.
    http://i1.treknature.com/photos/8986/valle_de_la_luna.jpg

  2. Yes. Fractals DO represent life and all it’s constituant parts…

  3. Yeah I’d say that’s pretty much how the livingroom floor looked! :) It’s also interesting to ponder why ancient astrologers had this notion of “as above so below”.. Is that not describing a fractal universe if anything?

  4. Michael Anderson says:

    Ancient astrologers were morons. Yes: morons. Superstitious morons who lived in fantasy worlds populated by demons and gods and spirits. The universe is not “a fractal”, but fractals possess properties that enable visual representations of them to resemble natural forms – which I think has more to do with the way our visual cortices work than the way the universe works. We seek “beauty” (a cultural construct if there ever was) and symmetry. and fractals give us that. I think one of our commenters here regarding the living room floor might have been making a reference to abuse of hallucinogenic drugs, which often present a fractal-ish view of reality that, again, has to do with the nature of the human visual cortex, especially when stimulated in certain ways (cf. phosphenes). I note BTW that several of the images in this post are not of fractals, but of e.g. an actual hurricane, an actual peacock, etc, which I must admit seems odd; was this a deliberate attempt to deceive, or a mistake? And cold fusion is a complete and utter hoax that has never worked under impartial test conditions, so really – are yo just another nutjob, on the Net, or?…

  5. Dr. Bob, I enjoyed your fractal vids! Here is one I am betting you have not seen yet or you would have posted it by now. The entire 7 minutes is great, but from 4:00 minutes on…you will be absolutely hypnotized by something that I am betting you have not seen yet in the world of fractal imagery. The only way I can describe it is “a fractal square-dance” (again, the part beginning at 4:00, where the video link below, will start you.). I have seen quite a few good 2D animations, and a handful of good 3D ones. This one definitely gets the fractal Oscar if you ask me. And I know what you are talking about when you say you like to relax and decompress after a long day at work by watching fractals. Careful, this one WILL likely detach you from reality: https://www.youtube.com/watch?feature=player_detailpage&v=nCfJCUnsn4A#t=240

    And I guarantee that after watching it that you’ll start it over. Fractal Lover’s HEAVEN! heh heh
    ~SDRanger

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