Saturday, August 7, 2010

July 21 - Benoit Mandelbrot: Fractals and the art of roughness‏

Dear Friends,

Be Well.


At TED2010, mathematics legend Benoit Mandelbrot develops
a theme he first discussed at TED in 1984 -- the extreme
complexity of roughness, and the way that fractal math can
find order within patterns that seem unknowably complicated.


Benoit Mandelbrot: Fractals and the art of roughness

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    2 days ago: need to limit nature to numbers; thus defining an equation to constant. I do say brilliant.

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    Jul 25 2010: I like that he sounds like Mr. Adelberg from Home Movies.

    PS - Cool Maths.

  • Jul 26 2010: What a youthful voice!

  • Jul 8 2010: The complexity comes from the simple rules.If the rule is repeated and repeated again without end,what will happen?will it be a open form that change all the time,or is it a closed form that will be quite regular after evolving for sometime.
    I thinks there are two problems here? One is how the system will evolve,will it be open-form or closed-form? and if at some stage the evolution is influenced by other factores, how would the system looks like? ;the other is how can we get to know the simple rules by analysing the complicated objects.

    • Jul 8 2010: i agree with u, kang fan, but the concept is mind blowing! is the an end at all??!!

    • Jul 8 2010: I have a background in philosophy but I am realizing an interest in mathematics and the philosophy of science. So forgive me if I sound like a total newb, but I grasp ideas better when I find a connection between the esoteric and the practical--this to me is philosophy. Is there anywhere I can look for research into the practical applications of fractals and the two problems you mentioned above. Even a point in the right direction to material that will open the world of fractals to me would help as well. I know I could just jump into the material myself but I always like a little direction first.

      • Jul 12 2010:


      • Jul 23 2010: Petrol Molotov have given something good.In fact everyting i know and think about begins with the bbc video. (No directions here but a little experience). Instead of using the words "fractals" only,we can use "development" and "computation" .If we look closer inside them ,there are some common characters.they tell the same things--how the system will evolve given some certain rules which could be simple or not. The "development" is a biological term ,it describes how complexity comes from the simple.We all come from a simple fertilizered egg and that is where the development begins. If you have played the "Life game",you would also wonder "what if the rules are 3D-related,will it reach a certain closed form ?"of course it will,we humans are similar ,right?that is the result of closed-form thing,so i think we wil get some ideas by studying how the organisms develop .On the other aspect,computation is also related to fractals ,stephen wolfram and his contribution are fatastic

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        Jul 26 2010: @ William Moreno- If you are interested in learning more about fractals (the history, practical applications, etc.) I suggest checking out a fantastic web site at There are hundreds of documentaries there, all free to watch. If you check under the math/science category you'll see a couple of docs on fractals, both of which are very good. Hope this helps!

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    Jul 25 2010: I will explore this with interest because it justifies my belief that chaos is order with options.

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    Jul 22 2010: For me as a non-mathematician this is really fascinating to watch, even though I do not get most the concepts he is talking about. It is just inspiring to see to which kind of problems one can dedicate ones whole life to. How different the view is we take on earth, life andeverything!

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    Jul 22 2010: I don't really see the point of his talk that much. I mean, he breezes through a bunch of concepts and images without really opening them up at all. If you didn't know what they were before, you're none the wiser. If you've already read about them, you can just go "hey, there's that probability distribution function graph!". Anyway, I love the man and his work.

  • Jul 20 2010: Even though I was a tad baffled at times, this was a great video. Thank you so much for providing this to us.

  • Jul 18 2010: I used fractals to design 3 theater stages, well one is with tessellations, if you are interested to see how different geometries can be used in theater stage designer please have a look, the document is in Spanish but the images of the results are there. I am so excited to see this TED conference i have researched an read a lot of this fabulous bright man.
    Here are the single pics without the research:

    • Jul 19 2010: Hello... seeing your work was inspiring... i've used some basic "math ideas" for lighting and performing... The beauty of simmetry and roughness of these incredibly appealing concepts can be detected in so many "simple examples" in performed arts concerning no only space, in one hand, but also time in the other. Take a look of a "simple" performance of Samuel Beckett's "Quad"... both space and time are affected via the endless repetition of an action (and by the music or background sound too)!!! GreETINGS

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    Jul 15 2010: what a wonderful experience, to watch and more importantly listen to this remarkable intellect as he joyfully shares some of his personal history, his perspectives, and of course his remarkable ability to mathematically quantify patterns and shapes that began as imaginary numbers and equations, and have made understanding of our natural world possible. His message of simple rules, repeated over and over speaks volumes to all who dare to describe some of the universe's greatest mysteries. Thank you sir!

  • Jul 15 2010: Roughness in the world is very beautiful,and I enjoy the amazing talk.
    Fractals are absolutely fascinating.
    Mandelbrot's thoery,Fractal,shows us a more complicateed but simple idea to understand the real world.

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    Jul 14 2010: Before I heard of this work, I was drawn to photographing patterns in nature and human designs like architecture, streets, networks, etc.

    Once i (relatively) understood the nature of Mandelbrot's fractals, I could imagine higher and higher in the natural spectrums of repetition.

    Dr. Mandelbrot, your work lead me to imagining a creator/creative source out of the infinite, I hope that is not an offense because I think of it as a huge compliment. I didn't see the creator the way I imagined one, when I was an atheist. I saw it as something extraordinarily small, dense, powerful. The truest meaning of being created in the image of god, I could imagine to be a fractal manner of magnitude.

    The whole way we see the world over the next decades will be partly because of what you made us see; that which you named for us ("us" being the humans that is).

    Thank you for seeing what I have come to call God - and come to feel a belonging to, a leaf of the vine of an All being.

  • Jul 12 2010: the NOVA special on fractals is pretty awesome.

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    Jul 12 2010: Wonderful talk from a truly great man. Thanks TED!

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    Jul 6 2010: For more information about the 3D Fractal Geometry see:

    • Jul 6 2010: check this out: -do rat's have cauliflower's for brains, or is it worse than that?

  • Jul 8 2010: You know a subject is interesting when 50% of the comments are links to more on the topic...
    (and the other half are of people quoting the talk.)

    brilliant speaker, fascinating subject. I very much enjoyed it.

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      Jul 12 2010: You know the talk is interesting when 50% or more of the comments are actually about the talk :o)

  • Jul 11 2010: Guys like Benoit Mandelbrot helping us to overcome our blindness to the most obvious. Great Talk.

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    Jul 11 2010: This simple and beautiful complexity has been barely incorporated into our scientific understanding of space. But worry not: just like Gödel's incompleteness reasoning (which should have changed the entire technological development), so are Mandelbrot's fractals yet to be exploited in our technological advancement.

    There is almost zero appreciation by the scientific community about these "hardest" problems. Understandable, who wants to deal unhuman complexity after all, right? But the problem is that unfortunately, today, science is enslaved to serve economics and consumerism; and consumers could not care less if the product is elegantly designed or if it is a breakthrough in human thought: the product should work, and that's all. The management, reliability, and financial departments of companies are interested into delivering the product as fast as possible as early as possible to the consumers. Scientists oblige.

    So who is going to investigate all that richness, all that beauty?

  • Jul 10 2010: Simple is the real rule.

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    Jul 7 2010: "Simple rules which are repeated, without end".


    • Jul 7 2010: Sounds like a Dungeons and Dragons campaign!

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      Jul 9 2010: So, insanity isn't really that insane?
      Insanity: doing the same thing over and over again and expecting different results.
      Nope, it's just persistence.

  • Jul 8 2010: in turn influence political decisions. Political decisions, however, are also likely to be ethical decisions--enter metaphysics....blah, blah, blah. See what I'm sayin'? I guess this would be the philosophy of science. Any suggestions on where to look for ethical considerations of Mandelbrot's work? Anybody?

    • Jul 8 2010: Consider this: The branches of a tree, a lightning strike or the the map of your nervous system all have the same geometry. All are fractal and all exhibit the phi ratio.

      Everywhere in nature we see the same patterns repeating at different scales. The atom (as we picture it) appears to resemble the solar system, which resembles the galaxy and so on. To understand the fractal interrelationship of all thins is to understand our own fractal interconnectedness. Nothing can be thought to be truly separate from anything else.

      The fractal structure of nature can help us understand the way in which we are interconnected. This inherent oneness (alluded to in many mystical traditions) has many ethical implications.

      • Jul 8 2010: Thank you Mr. Hey for your very thoughtful and helpful response. It is exciting to consider the possibilities of this field. I have just finished a course on Baruch Spinoza's Ethics and have been considering what it means to think of everything as nature--"Deus, sive Natura." At the heart of my questioning is whether we can be lead to ethical truths by pure geometric (mathematical) proofs, or whether everything is really ruled by analysis and begins with a query into the causes of what is sensible (i.e. the sensible world) and only then culminating into principles. I find myself questioning what it means to be able to move from first principles to the world of phenomena without the need for analysis. I may be beating a dead horse, but oh well. Thank you for listening.

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          Jul 8 2010: Russel and Whitehead tried to map out universal truths in their Principia Mathematica. Then Kurt Gödel came along with a proof that turned their effort on its ear. It works like this: Imagine a way to create a unique number for any equation. It doesn't matter how that number is created; merely that every equation has only one unique number describing it. Next, imagine an equation that contains the number describing itself. So, what happens? Every time you evaluate the equation the number changes! So, no complete set of immutable rules. Completeness gives way to iteration, where each observation changes the observed.

          What Benoit Mandelbrot has done is to explore iterative spaces. The result has yielded previously unknown spaces of incredible beauty.

          Where could this lead for ethics? What if ethics are also iterative spaces? Where each new generation yields a new truth?

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          Jul 9 2010: About iteration and ethics, you should see the Iterated Prisoner's Dilemma, for example.

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    Jul 9 2010: I love this guy, humble, childlike, facinating... What I wouldn't give to discuss his ideas with him.

    How could we preserve his essence, his mind, his heart? What a sense of calm, joy, silliness, and benevolence... God does good work!

  • Jul 7 2010: I had the at most respect for Prof. Mandelbrot ever since I was enlightened of his endeavors. I was literally AMAZED to see the Fractal pattern in a Brownian motion, because I have studied the statistical aspect and density function generation based on turbulent fluid flows and shocked to see that it can all be an instantaneous snapshot of fluid in motion or turbulence could actually have a repeating pattern. I'll really look forward to the further taking of this matter, as the chaotic quantum world could actually be invaded as such, and the long lived fantasies of Einstein, Bohr and so many brilliant minds, who invested their lives up on, becoming true; the formation of Unified Field Theory.

    • Jul 9 2010: "shocked to see that it can all be an instantaneous snapshot of fluid in motion or turbulence could actually have a repeating pattern"

      so what you're saying is that turbulance in fluid flows can be somewhat adequately modeled at different resolutions without precise equipment? That would be amazing!

  • Dan F (+49)

    Jul 7 2010: This guy is a national treasure. Is it not amazing how ongoing academic achievements have brought about the study of fractals in learning of the complexity of our primitive natural history and the physical world? Mind boggling! Who knows, if there are extra dimensions in space, will the study of fractal aid in that search?

    • Jul 9 2010: perhaps the strings in string theory are really just koch snowflakes and peano curves? interesting idea...

  • Jul 8 2010: It seems counterintuitive to see roughness as the opposite of regularity, even more so to consider that the roughest, or most irregular, phenomena are controlled by the simplest or most elegant of rules. It only becomes reasonable to me when I consider that the simplest rules are the least constricting and offer the widest range of complexity. So one can say that to complex problems there are often simple guidelines if not answers. Sounds like a jurisprudence. However, what I find interesting about Mandelbrot's discussion is this break from, one can say, the math of phenomena of the natural world and conceptual math of an abstract realm . I wonder in what ways this break must echo Cartesian difficulties with methodology and metaphysics. (any suggestions where to look?) >>Mandelbrot was able to find a point of connection between the esoteric and the practical, which most likely has it's most profound impact in its ability to influence readings of economic and sociological data, which in

    • Jul 9 2010: Stephen Wolfram's "A new kind of Science" looks at cellular automata and attempts to codify exactly what rules will produce "random" behavior, which rules produce "ordered" behavior, and comes up with some seriously surprising findings... a rule set that seems robust may end up dying out, while a rule set that seems really boring may suddenly explode into all sorts of interesting patterns after a few thousand iterations.

  • Jul 8 2010: Indians r mostly Famous in Particle Usage of Curvy Fractals in their daily Life.If U observe Indian Home,U will see lot of Non-Linear/Curvy Fractals around the Floor,roof,Sofa, on Bed sheets,etc at Entrance of Home(espcially at Festivals)called Muggu in Telugu:Literally translates-Drawings with colourful chalk powders

    THIS IS MY OWN THOUGHT & I DEDICATE IT TO Benoit MANDELBROT.Wish he will use it first.
    One thing I can say:If Fractals r divided into, Non-Linear/Curvy Fractal & Linear Fract'.
    The Cultures which are mostly towards the world of Curvy Fractals,will be tending towards the Natural Co-existence with Less Human made/machines.
    & The Cultures mostly towards World of Linear Fractals -be mostly tending towards the Industrialisation & co-existence with more Human made/Machines.
    Both Curvy & Linear Fractals have its place,since I believe If The EARTH Appreciates the Curvy Fractal system, in-contrary,rest Universe to reach- it Appreciates the Linear Fractal; We have to Balance it.

  • Jul 8 2010: I love the beauty of the mandlebrot set but don't see why people are trying to attribute any ethical values to it [see some comments]. to me it just shows the neutrality of nature and it's, and possibly the universe's underlying patterns , no more no less

    • This post has been removed by the author.

  • Jul 8 2010: Some Fractal theories:
    -> The smallest Particle (smaller than Atom Particles) which is having a definite shape - make all the substance in this Universe -The Fractal theory as the Principle :Could be true :No one can argue Until they knw about the Smalest Particle.
    Thoughts on Fractal Measurement: I Think one can measure Fractal on 2D & Human made Stuff &The Distance Universe (since it still a 2D for us). Like from the Screen of a Computer or a Painting etc. That too if he just think about the object on its surface which is Visible to naked Eye. (if one goes a layer deep into the object, It will be a totally different story).
    And I believe no One could Fractal Measure Natural objects &Landscapes in real. Two persons could feel same measurement of Fractal ONLY If they stand flawlessly in a same Micro Point & same Micro Angle towards the real natural object (that obvsly & pratcaly will not happen) There are, 360^§° ways to fractal measure a Natural Object surface

  • Jul 8 2010: Prof Benoit Mandelbrot is doing a Great work. I wld like 2 tell my Own Histry with Fractals.
    When I was Tenager -In my Home -have a Big Mirror -which has some very tiny Rusty spots inside it (which could not be seen even from a foot away from eye).
    I use to Play with those spots, like keeping one of My Eye open and very close to the Spot (attaching my face to Mirror) nothing except the Tiny Spot -enlarged and expanded -covers all my Eye:I use 2 see Same kind of Fractal Fig with the Equation Z --> Z^2+C: Which Prof has shown.I use to thought that I Invented something (could be useful to Fractal researchers), and will be a scientist later.
    I also use to have some Circle playable Kits: like mathematical Instruments - Protractors and Circles with all size of holes scattered over it, and all these have outer perimeter as Gearing/Saw like surface at its end. So when Two circles of the same kind are used 2 draw fig's,moving like Gears.A combination of amazing Fractals will Occur. G8 1.

  • Jul 8 2010: The Mandelbrot Set song by Jonathan Coulton:

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How to Digitally Record/Video a UFO sighting:

Como registar digitalmente ou gravar um vídeo de um avistamento de um UFO:

Stabilize the camera on a tripod. If there is no tripod, then set it on top of a stable, flat surface. If that is not possible lean against a wall to stabilize your body and prevent the camera from filming in a shaky, unsteady manner.

Estabilize a camera com um tripé. Se não tiver um tripé, então coloque-a em cima de uma superfície estável. Se não for possível, então encoste-se a uma parede para estabilizar o corpo e evitar que a camera registe de maneira tremida e instável.

Provide visual reference points for comparison. This includes the horizon, treetops, lampposts, houses, and geographical landmarks (i.e., Horsetooth Reservoir, Mt. Adams, etc.) Provide this in the video whenever is appropriate and doesn’t detract from what your focus is, the UFO.

Forneça pontos visuais de referência para comparação. Isso inclui o horizonte, cimo das árvores, postes de iluminação, pontos de referência geográficos (como o Reservatório de Horsetooth, Mone Adams, etc) Forneça esses pontos no vídeo sempre que for apropriado e não se distraia do que é o seu foco, o UFO/a Nave.

Narrate your videotape. Provide details of the date, time, location, and direction (N,S,E,W) you are looking in. Provide your observations on the weather, including approximate temperature, windspeed, any visible cloud cover or noticeable weather anomalies or events. Narrate on the shape, size, color, movements, approximate altitude of the UFO, etc and what it appears to be doing. Also include any unusual physical, psychological or emotional sensations you might have. Narrate any visual reference points on camera so they correlate with what the viewer will see, and thereby will be better able to understand.

Faça a narração do vídeo. Forneça pormenores sobre a data, hora, local e direcção (Norte, Sul, Este, Oeste) que está a observar. Faça observações sobre as condições atmosféricas, incluindo a temperatura aproximada, velocidade do vento, quantidade de nuvens, anomalias ou acontecimentos meteorológicos evidentes. Descreva a forma, o tamanho, a cor, os movimentos, a altitude aproximada onde se encontra o UFO/nave, etc e o que aparenta estar a fazer. Inclua também quaisquer aspectos pouco habituais de sensações físicas, psicológicas ou emocionais que possa ter. Faça a narração de todos os pontos de referência visual que o espectador irá ver e que, deste modo, será capaz de compreender melhor.

Be persistent and consistent. Return to the scene to videotape and record at this same location. If you have been successful once, the UFO sightings may be occurring in this region regularly, perhaps for specific reasons unknown, and you may be successful again. You may also wish to return to the same location at a different time of day (daylight hours) for better orientation and reference. Film just a minute or two under “normal” circumstances for comparison. Write down what you remember immediately after. As soon as you are done recording the experience/event, immediately write down your impressions, memories, thoughts, emotions, etc. so it is on the record in writing. If there were other witnesses, have them independently record their own impressions, thoughts, etc. Include in this exercise any drawings, sketches, or diagrams. Make sure you date and sign your documentation.

Seja persistente e não contraditório. Volte ao local da cena e registe o mesmo local. Se foi bem sucedido uma vez, pode ser que nessa região ocorram avistamentos de UFOs/naves com regularidade, talvez por razões específicas desconhecidas, e talvez possa ser novamente bem sucedido. Pode também desejar voltar ao mesmo lugar a horas diferentes do dia (durante as horas de luz)para ter uma orientação e referência melhor. Filme apenas um ,inuto ou dois em circunstâncias “normais” para ter um termo de comparação. Escreva tudo o que viu imediatamente após o acontecimento. Logo após ter feito o registo da experiência/acontecimento, escreva imediatamente as impressões, memórias, pensamentos, emoções, etc para que fiquem registadas por escrito. Se houver outras testemunhas, peça-lhes para registar independentemente as suas próprias impressões, pensamentos, etc. Inclua quaisquer desenhos, esbolos, diagramas. Certifique-se que data e assina o seu documento/testemunho.

Always be prepared. Have a digital camera or better yet a video camera with you, charged and ready to go, at all times. Make sure you know how to use your camera (and your cell phone video/photo camera) quickly and properly. These events can occur suddenly, unexpectedly, and often quite randomly, so you will need to be prepared.

Esteja sempre preparado, Tenha sempre uma camera digital, melhor ainda, uma camera vídeo consigo, carregada e pronta a usar sempre que necessário. Certifique-se que sabe como lidar com a sua camera (ou com o seu celular/camera fotográfica) rápida e adequadamente. Esses acontecimentos podem acontecer súbita e inesperadamente e, por vezes, acidentalmente, por isso, necessita estar preparado.

Look up. Be prepared. Report. Share.

Olhe para cima, Esteja preparado, Relate, Partilhe.



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