Fractals: The Colors of Infinity

Fractals: The Colors of Infinity

1994, Science  -   47 Comments
Ratings: 8.93/10 from 122 users.

The Mandelbrot set - someone has called it the thumb-print of God - is one of the most beautiful and remarkable discoveries in the entire history of mathematics.

With Arthur C. Clarke as narrator and interviews with a number of notable mathematicians, including BenoƮt Mandelbrot, this program graphically illustrates how simple formulas can lead to complicated results: it explains the set, what it means, its internal consistency, and the revolutions in thought resulting from its discovery. Asked if the real universe goes on forever, Stephen Hawking defines its limit of smallness; the Mandelbrot set, on the other hand, may go on forever.

The invention of the silicon chip in the 1970's created a revolution in computers and communication and hence transformed our way of life. We are now seeing another revolution which is going to change our view of the universe and give us a better understanding of its' working.

This film will explore the fractal universe and on our voyage of discovery, we will be helped by: Professor Ian Stewart of the Mathematics Institute, University of Warwick, an author of over 100 published scientific works; Dr. Michael Barnsley, former professor of mathematics at Georgia Institute of Technology who received a 2.5 million dollar government grant in 1991 to develop a fractal image compression systems.

Directed by: Nigel Lesmoir-Gordon

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47 Comments / User Reviews

  1. Adam R Togstad

    The crazy idea to me is that it makes it infinite. Infinite mind, law of attraction, and my general art sense say that this is exactly how you become one within yourself. its the parallel universe coming into picture.

  2. PF Fan

    The music is Pink Floyd. It's leftovers from the Division Bell which was originally supposed to be a double album. Much of that music became "The Endless River". Listen to "Calling" from that album:

  3. Tink

    Who does the music? Sounds like Pink Floyd. Anybody know,, and what album? Thanks!

  4. T.O.T.

    Extraordinarily special. I looking more in to this.

  5. Brian Sinclair

    I can't stop thinking about this now...

  6. mahsa


  7. TheRealMax

    Gosh, anthropomorphically. Are we reasonable or unreasonable.
    Get real people.

    Sorry, I do not discount the relevance of feedback in systems. But resorting to heaps of 'woo woo' adds very little to the conversation.

    Lets not get carried away.

    1. Ryan Weaver

      This has intense relevance to like 34945 things in my life. It might be that you are ignorant of relevant things, or just lack the right perception to understand why Fractals are important. Remember when you were a child and you KNEW that scientists would just keep looking for the smallest thing because eventually you'll just find more small things? I think there is some intuition and genuine truth to a childs mind in that respect. Keep in mind that the same observation can be inverse. It is no coincidence that we can now define Infinity with mathematics. But please, follow history like 99.9% of most people, and justify your cognitive dissonance with an opposing OPINION rather than thought.

  8. Rammstein Fanatisch Fur Immer

    Its true, how far does space really go? Does it have an end at some point? Unfortunately we do not have the kind of technology to prove what lies beyond space. Take an ant for example, WE are fractals in their eyes or even smaller. A molecule in itself is fractal, you look closer and it has more details to it than what we can see. A jelly fish, tentacles could be precieved as fractals, its rich design and texture, like the barbs with venom. I was smoking a cigarette and stared at the trees and saw fractals its pretty cool to see the world in a different aspect.

  9. Helen Plourde-McSweeny

    I feel like I already knew this and am so grateful for scientists who can lay claim with facts and representative shared data.

  10. Adam LaRocco

    welp, forgot to take my acid for this one lol

  11. youngtom

    I have noticed that if i go into an open area say a clearing in the woods and i start spinning in the center of the opening, with my eyes open and looking straight out to the surrounding area. what i see appers to be a fractal spinning .

  12. Michael Hoevenaar

    We are just one big holographic fractal.

  13. JohnJameson

    Its all a question of scale. One day someone will see it in 3 then finally 4

  14. Winston Smith

    i don't understand what it is beyond a fancy continuous spiral

    1. Oldest Modus

      a fractal infinite continuous spiral.

    2. William Fraser

      It proves that in an infinity or diversity of chaos all expanding from a simple formulae, hidden in this mind blowing complexity, there is order. There is method in the maddness (chaos).

    3. Rammstein Fanatisch Fur Immer

      just like joker said but not exactly you turn everything in and on itself and you basically disrupt the natural order and everything become..."chaos"

    4. William Fraser

      It also gives us humans an glimps into infinity even if it is only in an abstract mathemetical world. Although fractural geometry is evident in all aspects of design in the universe.

  15. Waqas Malik

    Fractals, the way I see it, gives fine resolutin between the fate we have and the destiny we make. They tells us how our choices and choices of time can co-exist.

  16. dr_funkenstein666


  17. toddy

    wished i had some phsychedlics when watching oh well. The music was not no way close to American rock much more similiar to Pink Floyd( old floyd that is). You can understand why the phsychedelic community embrased the beauty of fractuals art form, the idea of infinity in the designs. There was a thing i remember hearing that if you want to understand the universe or the language of God it is to try to understand mathematics as well as you can. So kids do good in math in school.

  18. Aw Heck

    Natural forms look like computer generated images of Mandelbrot sets -- the interviewees then claim that natural forms are produced by a process (not specified) which is supposedly analogous to a computer programme. Ludicrous. Absolutely ridiculous. Did they leave logic at home today? That's like saying that because a ball and the moon look similar they were produced by the same process. Some posters claim to like the computer generated images and American rock background music. I find both trite and boring. Yawn.

    1. Ansar11

      If the ball was made of rock and orbited the Earth, then maybe that would be a good analogy. If you look at DNA and how cells operate based on their DNA you will see it is almost exactly like code.

      Any programmer who studies how DNA works will immediately recognize the similarities. DNA looks like OOP code, even down to having comments and functions. There is a set in DNA that represents /* and */ in c++ or java, anything in between the two commands never gets used.

    2. Robin Forward

      Look into genetics mate, it is quite similar to a computer program (maybe not analogous though). The genotype codes for the phenotype. The structure of phenotype is formed from fractals.

      Also computer generated images are made to look like natural forms by the use of fractals not the other way around.

  19. digital rot


  20. Patka4400

    [QUOTE]Iv taken trips a few times to experiment,
    I swear this Is all that you can see,
    all you want to do Is lie down and close your eyes after a strong dose, and Its like a live spectacle, colours swirling and dancing around, exactly like this doc.

    It Is a profound experience.[/QUOTE]

    I know exactly what you mean. Since I'm an epileptic and have had brain damage (LOL, similar to Nikola Tesla, my hero), I see that stuff all the time when my eyes are closed, without consuming trips (especially when I'm sleep deprived). The colors and shapes in my case are very similar to the fractal patterns in the movie, but infinitely more complex in multiple dimensions and at multiple places at the same time and at multiple times at the same place (it's kind of difficult to explain). And I wasn't aware that they were fractal patterns until college (math student).

    Makes me wonder if Mandelbrot was using psychedelics or had brain damage. :P

    Anyhow, thanks Vlatko for this beautiful documentary. Never can have enough mathematics :D

  21. Coyote03

    infinite complexity from one simple formula, very cool! I believe this technology is what powers Adobe Photoshop's Content Aware Fill, amazing!!!

    From the beginning I was thinking to myself 'if this isn't David Gilmour, then someone sure as hell is ripping him off' good to know he did the music for this film, definitely added to the feel!

  22. Enki

    Fascinating documentary. I find most things in life seem to be embedded in simplicity. I believe it's our preconceived perceptions that can often make things appear complex.

  23. Motherchi

    Now consider this about what we do know of life. The only thing constant is change. Nothing ever just...stops. The only reason why anyone would think that of black holes is because no one has been through one to the other side. We thought there was no such thing as atoms either because we could not 'see' atoms. Everything in life continues....I saw fractals when I was 4...this theory is nothing new to me. I used to draw them as a child. Love all these videos.

  24. Evan

    Never underestimate how short life is.

  25. Kizzie

    screw the math

    1. Aaron_of_Portsmouth

      In case you didn't know, the math is what makes it possible to create and explain the beautiful patterns. The physical universe is suffused with mathematics. Are you saying that you should "screw" yourself?

  26. Kizzie

    Sometimes I think life is not meant to be figured out because it is so simple.Just BELIEVE, and ENJOY your life but also LEARN from it.

  27. silkop

    One interesting question that this documentary throws up (implicitly) is the concept of "complexity". Is the Mandelbrot set complex? How do we measure "complexity" of a thing? Is a seemingly "complex" thing generated by a simple formula actually complex? What the heck are we even talking about? This question very much also applies to "complexity" in the mouth of creationists and of *gasp* Richard Dawkins.

    I think the underlying intuitions goes pretty much toward "oh gosh, if we wanted to describe this thing in such-and-such way, then it would take so-and-so many bits of information; the more bits, the more complex". But then we discover the simple generating process and suddenly we can describe the same thing with just a couple of bits. It's not only the case for fractals. Take for example the number PI. Suppose you want to send someone the first 10^9 decimal digits of PI. How many bits of information do you need? It all depends on whether you know the you are dealing with PI (the recipe for PI, the generating process or algorithm).

    I suppose that to describe any real thing in detail actually *does* require tons of information. Unlike for hypothetical "entities" such as PI or the Mandelbrot set, it is not sufficient to provide a generating self-referencing recipe, a mathematician's wet dream. Instead, you have to provide the generating blueprint AND all the "external inputs" that perturbed the blueprint's execution over the entire time during which the thing to be described "existed". However, unlocking just the blueprint might make a greater difference than sampling the "external inputs" alone. So yes, there is some potential for interesting applications and new discoveries, but I wouldn't be so optimistic and so amazed about it as the commenters in this documentary.

    I liked the comparison made in this doc between the QM probabilistic fairy tale vs. the consistent, deterministic yet unpredictable (because practically too fine-grained) world. I definitely prefer the latter model myself.

  28. silkop

    Infinity, existence, my ass. This video nicely illustrates my grudge with mathematicians. Matematical infinity and existence does not correspond to what any sane person understands as existence in the empirical sense. What they call "infinity" is just repetition of a generating process with a finite (and indeed very compact) description. Mandelbrot set's "infinity" is just about as amazing, mystical and real as the infinity of this computer program:

    for (;;) { print "dumb\n"; }

    1. Aaron_of_Portsmouth

      Wow---that's quite a chip you have on your shoulders. I can have a lumberjack remove that for you.

  29. Triad

    @ V

    The term Scientific Deism Is new to me.
    Does this mean you would not call yourself an Ateist?

    @ Chadzuka
    Perhaps Galileo was more Intelligent.
    I think the reason he was popularised so much was not because of whether he was special or not, but because of the phenominal contribution he made to science.

  30. V

    Triad. Scientific Deism - the belief in the existence of an infinite intelligence is very different from superstitious organized religion based upon confusing ancient texts. Logic often conflicts with faith and emotion. Faith is not hope or trust, it is foolish and fatalistic. It is a childish reaction to fear and restricts people from making their own decisions. Faith is paired with fate, and destiny. All three words evoke a sense of helplessness - and the lack of choice. If one has faith that means one cannot be free. There is no such thing as absolute certainty.

    All law is created by humans to make sense of the universe. Some are arbitrary while others hit closer to home by describing in quantitative terms aspects of the universe that have few exceptions. Fractals are unique in that they predict some of those exceptions.

    1. Harry Spencer

      So you are absolutely certain there is no such thing as absolute certainty. Hmmm. Interesting!

  31. Triad

    I bet he really did take some shrooms.
    Come on Arthur..

    Imagine that documentary Is 16 years old!! Is he still alive?

    Iv taken trips a few times to experiment,
    I swear this Is all that you can see,
    all you want to do Is lie down and close your eyes after a strong dose, and Its like a live spectacle, colours swirling and dancing around, exactly like this doc.

    It Is a profound experience.

    I understand now why no amount of, or lack of science,
    can persuade someone that believes In God.

    All I can say after It Is there Is soooo much we do not understand... Thats all.

  32. Yavanna

    Watched this twice today. Wonderful if only for the trippy graphics and music :)

  33. lou

    If only Albert Einstein had todays technology to fnish his work.

  34. sang

    2 thumbs up

  35. josh

    truely good documentry the music is also extreamly good.

  36. Vinod

    Thanks for this knowledge full documentary..

  37. Vinod

    I believe the number doesn't disappear rather tends towards negative infinity.