Fractals: Hunting the Hidden Dimension

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Fractals: Hunting the Hidden DimensionMysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature. You may not know it, but fractals, like the air you breathe, are all around you.

Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart.

In this film, we takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry.

For centuries, fractal-like irregular shapes were considered beyond the boundaries of mathematical understanding. Now, mathematicians have finally begun mapping this uncharted territory.

Their remarkable findings are deepening our understanding of nature and stimulating a new wave of scientific, medical, and artistic innovation stretching from the ecology of the rain forest to fashion design.

The documentary highlights a host of filmmakers, fashion designers, physicians, and researchers who are using fractal geometry to innovate and inspire. Also check out Fractals: The Colors of Infinity.

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Comments and User Reviews

  • Jason

    I have seen this documentary before elsewhere, but felt the need to comment here on how fascinating and relevant this documentary is to our understanding of the relationship between math and our natural world. A must see documentary!

  • Anthony

    very nice shows explicitly the practical application of what initially seems an obscure branch of mathematics showing in fact that fractals are mathematics!

  • Anthony

    Perhaps the problem describing nature is in fact that it doesn't have a zero on the end!!!

  • Epicurean_Logic

    Once I had a dream, and this is it:

    One of the most fundamental and geometrically mesmerising observations that can be made about fractals is the self-similarity exhibited by these fractional dimensional objects. In fact, self-similarity is the main way of deciding whether an object can be described by fractal geometry or not. Is the cloud describable by fractals? Look at the overall shape, then at smaller part of the cloud. Does the smaller part resemble the whole. Yes? Then look at an even smaller sub-area of cloud. Does it resemble the larger part? Yes? Does this process exhibit self-similarity at smaller and smaller scales? Yes? Result: you are looking at a fractal structure.

    Another powerful property of fractals is that they are described by very simple equations, (repeated) iterated thousands and millions of times and that these simple steps produce impossibly complex structures from a basic repeated pattern. So called complexity from simplicity. Now, this is a very appealing and desirable method for mother nature to operate on. Complexity from simplicity. Keep this is mind for what follows:

    Interlude 1: There are no straight lines and circles in nature and these are the fundamental building blocks of classical math. Not that this bothers the mathematician. Why should it? Math is context free and does not operate within the confines of the real world. It requires and lives within the ideal arena of the mind. In contrast to this, nature works exclusively in fractals!

    Nature encodes structure using repetition (iterated equations) and generates fractal structures. Does nature physically solve equations at each stage of the process? It seems more likely that iteration is just the method that we use to describe this constant repetitive process. What is the process that nature uses to solve these equations? What is it that mother nature does over and over again to create complex self-similar fractal structures? These structures range from the human lungs, to clouds, to trees and through to galaxies and beyond.

    I say that mother nature is fundamentally repetitive in her basic methods; she does the same thing over and over again without regard or intelligence for the outcome or aesthetics of her activities. And yet, fractal mathematics has demonstrated that this simple repetitive mathematical banging of the drum can create immensely complex structure's, like the M-set, a complete C.G.I. planet in Star Trek 2: the wrath of Khan and computer generated volcanic lava flow. Let us not even consider the unfathomable and inevitable possibility that there are interactions between more than one repetitive process!

    Interlude 2: Could it be possible that causal determinism re-surfaces in science in the form of fractals? I hope so. If only to avoid the indefinite nature of statistical methods. I claim that determinism exists on a level that is far to complex for the human mind to ever penetrate and it is my dream that fractal geometry will be the science of the 21st or 22nd century that will bring it back to where it belongs; the fore-front of human knowledge.

    In conclusion: It is useful for mother nature to operate in a way that is simple to execute and that has complex ranging outcomes. The result's of unremarkable repetition manifest in the complex and amazing structures that we humans call fractals.

  • http://princejaka.wordpress.com princeton

    @Epicurean_Logic

    Nice!

  • googoo

    i love it when the whole world can be reduce into a formula , the more design the better

  • Achems Razor

    @Epicurean_Logic:

    Good blog, and makes sense, wish that I could write as well.

  • Another viewer

    Great!

  • Dedman

    Fascinating....and beautiful. Yet, I'm having difficulty actually 'seeing' repeating patterns in the things around me! When I look at a leaf, I see SIMILAR patterns, but not mirror or exact repetition. Or a mountain. Or a rock.
    Is it my limited understanding of higher mathematics that prevents me from observing this phenomena?

  • Waldo

    @ Dedman

    No, it's not you. The patterns you see in nature always slightly change everytime they are manifested. Now back off a little further and see if you can find a pattern in those slight differences and how they are manifested. If you can you are one of the few, humans usually have issues with pattern recognition once this many variables are in play. But the patterns are there all the same, mathematics is just the easiest way of discovering them.

    Think of the beat pattern of your favorite song, it ends on what we call the down beat. Usually this beat falls at the end of each measure and then the pattern starts over. Now think of a tree as that song, except every time the pattern starts over just one or two extra beats are added. The result is that you can't pick out the exact beat of the tree, it seems random and without rhyme or reason. In reality it is the same pattern with slight variations added in a rhythmic fashion so that the variations themselves have a pattern. The difference is like listening to some simple song in standard 4/4 time, and then listening to Tool or some other rhythmically advanced band. The patterns are much harder to pick out in a Tool song versus say "home on the range" or "Amazing Grace", but they are still there. Enjoy, fractals are the most beautiful and awe inspiring of all mathematical constructs. Thankyou, Mister Mandelbrot.

  • Anna

    @Waldo: the downbeat is actually beat 1 of the bar/measure. The last beat (the 4th beat in 4/4 time) is the upbeat. Some songs start on the upbeat, some on the downbeat, but 1 is always the strongest beat in any time signature, even irregular ones. "Schism" changes time signature/meter 40 times :)

  • Reasons Voice

    When dealing with plant life the recurrent patterns of long term growth (such as limbs on trees) can be correlated to the solar year. The callendar is the written expression of a natural pattern confirmed by science. Fractas applied to nature is just a step further in recognising the true depth of patterns in nature.
    Today we have things such as this to show us those patterns. Where in the past, more nature bound cultures had an inherent knowledge of them. Hunters and forragers could read the patterns of nature as a means of survival. Such as counting the nodes in stalks of grass to asses the availability of water in an area. We as a modern society have drifted far from these recognitions and fractals help us to reestablish a connection to them.

  • Waldo

    @ Anna

    I'll take your word for it, I play guitar by ear. Tool is my favorite band to listen to because of their irregular timing and crazy bass riffs. I have just set up a studio in my bed room and stopped playing with the bar bands I was running with, so I could work on my own stuff. Thanks for the heads up, playing by ear sometimes puts you at a disadvantage, and then at other times its perfect.

    I am trying to learn to read music and understand the timing notations and so forth. I play mostly jazz, I know thats odd for a Tool fan but I love playing the stuff. Thanks again for the heads up, down beat starts 4/4 and upbeat ends the measure- got it! Now where is the kick drum on standard 4/4 timing? I would imagine on two and four, correct? And the up beat is on the "and" correct? Snare on one and three (down beats). Let me know if this is right.

  • Achems Razor

    @Waldo:

    Since I play the drums, the basic beat is as follows: 4/4 timing.

    High hat on 1, 2, 3, and 4

    Bass drum on 1 and 3.... Snare on 2 and 4...

    Cymbals 8, or 16th notes. And then any types of configurations.

    This beat can apply for rock, blues, country, funk and pop. Jazz is usually played with brushes etc:

  • Reasons Voice

    @Waldo; Nothing strange about loving Tool and Jazz. They are different in style yes but both fundamentally about musical perfection. In that way they are similar to classical music. If you have never heard it I strongly recommend the symphonic rendition tool album. It only furthers ones appreciation of Tool to hear their music played with the complexity of a full symphony orchestra.

  • Tom

    Excellent documentary! Another example of intelligent design.

  • Waldo

    @ Reasons Voice

    Yeah, I have the string Tool thingy. But, its not a full orchestra, just a few violins and a cello. Maybe we are talking about two different things.

    @ Achem

    Thanks for the lay out, I was almost right. I can actually play drums fairly well if you sit behind them and say- "Just play". But, if you say now tell me what timing that was or what drum fell on what part of the count, I have no idea. Same with guitar, I can hold my own with anyone- well almost anyone. I am not looking to cut heads with Steve Via yet, not much for shredding any way. Now if you want to hear some good jazz, say Django Reinhardt or Joe Pass- I'm your guy. I love playing Stevie Ray Vaghn and Hendrix stuff as well, but blues gets old after a while. Its great to listen to, but to easy to play. I can even play alot of classical stuff by ear. You would think since I can play it I could read it with no issues, but it just doesn't come natural to me. Thats really starting to slow me down now that I have my studio set up and need to lay out click tracks and use different softwares, I will get it though.

    O.k. I am way off topic so, sorry guys. I will shut up now.

  • Achems Razor

    @Waldo:

    I suppose music is like fractals in a way, so many different variations that can stem from one note, or one beat, that can lead to a full blown orchestra.

    I also play steel guitar, have a double neck 16 string solid body electric gold top les paul gibson, circa. the 1950's.
    Actually can read piano music on that.

  • brown

    People i think we find a tool to measure the whole universe.

    What if, and only what if these fractals is the door to the secret code we so long has been searching for. The code of everything and the door to the architect itself. Would that be something extraordinary to accomplish?

    I can imagine that if these are is in nature itself bounded natural phenomena that occurs in every structure, than everything would be possible to achieve in a fragment of roughness.

    For instance a mindreaders. That sounds now pure fictions, but thinks for it a minute, a mind is something that is apart of these complex structure that can be expressed as an fractals. Fractals can be reversed tuned to an applications of machine, ...if it plays the same rules that nature itself. Mind also communicate with waves, waves can be expressed by fractals.

    Now use these knowledge wisely

    cheers ;)

  • Anonymous

    Interesting and informative docco, more interesting as a list of applied fractal uses than history.

    I'd be interested in the applications of increasingly fine resolution/detail fractal applications - as the film showed, the original applications (and reporting of) appeared to relate to fairly coarse fractals.

  • rhea

    Wonderful documentary. All of life is geometric -- all of life is fractal. Of course! Now I see it everywhere. Awesome. How simple and how smart.

  • yaj

    This demonstrates how math truly is the language of God. Great documentary! If you really want to understand nature and the natural world, this is a must see.

  • http://www.facebook.com/TheShinyObject Paul Michaelson

    Speaking as a drum machine artist I can say that patterns are broken up just like that for example 4 8 12 24 34 ect.. and though 4 o to eight my contain many broken up variations of the same number seqence.

  • http://www.facebook.com/TheShinyObject Paul Michaelson

    Until the variations are not audible to the human ear.

  • Guest

    Yes true, as long as a person follows the consistence beat of the high-hat, can impose many different variations. At least is how I do it.

  • http://twitter.com/Sean13dna Sean Bradley

    God=nature

  • http://www.facebook.com/abroazhar Abro Azhar

    God=nature = Sophism
    where God and His creation is not 'Two' Things, but they are one, so in this sense 'we' are also God, as we are part of nature.
    While Abrahamic Religions strictly says: God and His Creation are Two Separate Things.

  • http://www.facebook.com/people/Steven-Matthew-Ryan/806126574 Steven Matthew Ryan

    The old Mandlebrot set again, seems as glorious as ever , viewing a zoom in of a 3d fractal set
    for me anyway concretes a theory about scale that I've had for many years
    apply it to the universe and it makes more sense.
    We exsist on a scale and view the universe at that fixed size.
    Exsisting on a larger or smaller scale size, the view maybe different with similar physics.
    For one this dark matter and dark energy scientists go on about maybe the void that
    encompasses and seperates matter'
    just as the negative space separates the fantastic infinite spiralling fractal.
    Like a ratio if you will, change that ratio by too much and you get event horizons
    like supanova and black holes...
    I don't know but it's food for thought.

  • http://pulse.yahoo.com/_CWXVJGGWG4XPNF2NPQFXBUASPU Cody Welch

    Physicians? Er, physicists.

  • sknb

    This is one of the documentaries that changed my life. It changed my way of looking at the world and started a now - 3 year fascination with fractals.

  • sknb

    Well said, sir. Well said.

  • Dennis Reese

    only makes sense i watch this/found this a few days after my first few DMT experiences..

  • sknb

    While I agree with you strongly that much of common western religion seems to stress the division of God from his creations ------

    Jewish Mysticism (Kabbalah) is rooted in the idea that everything- man, God, the universe, is all ONE. I am not as familiar with Sufism, but have been told there are similar concepts there as well.

    It is interesting to me also that these mystic traditions are often in conlflict with the religious hierarchy and mainstream.

    Excellent point though.

  • Guest

    Good doc. I wonder if a fractal pattern could be found in the flow of thoughts. It seems like it has only been applied to physiological (biological)structure.
    az

  • RathnashikamaniBijja

    Fractals are the mystery of creation. There is and endless wonder in their infinite patterns.

  • ecoguide

    Humans are the 'fractal' thoughts of the Universe. If you can see the latest photos taken from space by Hubble & Chandra of the edges of our universe, you might notice that the images resemble the neuron 'network' of the human brain. Millions upon billions of galaxies forming intricate 'fractal' networks that look so much like our neuron cells, axons, synapses, etc. An uncanny mirror image I would say of our brain. Maybe we are only thoughts in the mind of our Creator...

  • madscirat

    Great doc. Learned some things I did not know about the history of fractals. Last part was a bit funny. I'm sure the impoverished people of South America will be heartened to know that Western scientists have determined exactly how much land they need to set aside to clean up our pollutants.

  • sknb

    Every couple of months I feel the need to watch this doc and comment on how it changed my life and my perception of the world around me.

  • http://profiles.google.com/ihorbert Isaiah Horbert

    I'm curious as to whether there are any fractal relationships with respect to social interaction. This is interesting -kinda boring- but interesting.

  • DigiWongaDude

    A hallucinogen...'ooo pretty pictures' kinda defeats the intended message though.

  • Isaiah James

    Awesome, just awesome!

  • Cosmo

    our creator..?

  • ffeldon

    THANK YOU for allowing this to be viewed by the public, for free. I'm a math professor. In my Liberal Arts Math class we study fractals. This video is a required assignment. Feedback from students is great. I appreciate all your work to make this documentary film available!