I love the description given by the BBC for their documentary “The Secret Life of Chaos” (which you can watch here).
As I have written a few articles about fractals, chaos and controls lately, I have added links internal to this blog to the text.

“Chaos theory has a bad name, conjuring up images of unpredictable weather, economic crashes and science gone wrong. But there is a fascinating and hidden side to Chaos, one that scientists are only now beginning to understand. It turns out that chaos theory answers a question that mankind has asked for millennia - how did we get here?

In this documentary, Professor Jim Al-Khalili sets out to uncover one of the great mysteries of science -

• how does a universe that starts off as dust end up with intelligent life?
• How does order emerge from disorder?

It’s a mindbending, counterintuitive and for many people a deeply troubling idea. But Professor Al-Khalili reveals the science behind much of beauty and structure in the natural world and discovers that far from it being magic or an act of God, it is in fact an intrinsic part of the laws of physics.

Amazingly, it turns out that the mathematics of chaos can explain how and why the universe creates exquisite order and pattern. The natural world is full of awe-inspiring examples of the way nature transforms simplicity into complexity. From trees to clouds to humans - after watching this film you’ll never be able to look at the world in the same way again.”

Notice that this introduction can be sum up by “Chaos vs God” or “Chaotical Design vs Intelligent Design”. However, anyway, one question remains: who created the laws of physics? Or how were created these laws of Physics, if you prefer ;-)

I have often privately said that James Gleick’s Chaos book gives clearer answers than the Bible about our world. Now is the time to say it publicly!

Enjoy the documentary!

The BBC aired on Thursday, January 14th an excellent documentary about Chaos, Fractals and Nature. You can watch it right here thanks to YouTube. If you are in UK you can also watch it on the BBC website at this address.

I am glad the BBC helps making these subjects popular and fashionnable more than 20 years after James Gleick’s Chaos book.

Part 1

All parts follow.

Thx Pixgeeks for reminding me of this nice Google logo involving fractals.

It was in memoriam to Gaston Julia’s Birthday.

In case I need to precise, the fractals you see on the logo are called Julia sets because the French mathematician Gaston Julia described them first. However, most of my readers already know that, right? ;-)

To say something only initiated people can understand: “The Mandelbrot set contains all Julia sets”. (That is why the fractal on the left is actually the Mandelbrot set.)

You can check all google logos here.

Mandelbulb by Daniel White

As we are still at the beginning of the holiday season, maybe you haven’t bought all your gifts yet. In that case, here are a few lifechanging books you can offer to your loved ones.
By lifechanging, I mean you will never look at the world in the same way after reading one of these books. There is even a good chance you will find the world a lot more simple after your reading because these books give you keys to the behaviour of nature and mankind.

Have you ever heard of simplexity ?

Some systems are a lot simpler than they look like. For instance, let’s consider the shape of a tree. It looks complex, especially if you compare it with a straight line. However, if you have read Mandelbrot or heard of fractals, you know that all you need to draw a tree is a 2 lines pattern, which you repeat a big number of times introducing at each step some light randomness. You can model pretty easily this tree shape. At least you can generate at your will tree shapes. That is typically the way used in computer graphics to generate natural virtual 3D scenes. However, this does not mean you can predict the accurate shape of a tree from its seed.

Let us draw the Mandelbrot set with OFC. The point is to make a new example of use of OFC and it is also to have some fun with the so interesting fractal theory. To see how fashionable it is, read this post: Good news from the combat against the crisis. This post is highly inspired from this nice French page about the Mandelbrot set. I am using the algorithm given there.

  def index_mandelbrot_fractal
    # from http://perso.numericable.fr/~haasjn/haasjn/AlgoMandel.txt 
    @graph = open_flash_chart_object(500,500,"/test_it/graph_code_Mandelbrot_fractal")     
  end

  def graph_code_Mandelbrot_fractal
    #    Algorithm to draw Mandelbrot's fractal 
    #    
    #    variables a,b,x,y,xmin,ymax,cx,cy,width,step:real
    #              i,j,nx,ny,n:int
    #              r: table
    #        
    #    cx,cy    coordinates of the image center in the complex plane
    #    xmin     image left limit 
    #    ymax     image upper limit
    #    width    image width in the complex plane
    #    nx       image horizontal resolution 
    #    ny       image vertical resolution
    #    nmax     maximum number of loops to compute the convergence of the complex sequence
    #    step     step between 2 points 
    #    r        table containing the result for each point
    #
    #    in the loop 
    #    i,j  indices of the point 
    #    a,b  point coordinates
    #    x,y  values of the complex sequence
    #    x1   next value of x 
    #    n    indice of the complex sequence
    # 
    #    Algorithm beginning 
    #    cx,cy,width,nx,ny,nmax are given at start 
    cx = 0
    cy = 0
    width = 4.to_f
    nx = 100.to_f
    ny = 100.to_f
    nmax = 250.to_f

    xmin = cx-width/2
    ymax = cy+width/2*ny/nx
    step  = width/nx

    # Preparation of the chart
    chart = OpenFlashChart.new
    title = Title.new("Mandelbrot set")
    chart.set_title(title)
    r = Array.new # results 

    # The loop asks : does the point (a,b) belong to the Mandelbrot set ? 
    # The bigger n, the more probable the point belongs to  the set 
    for j in 0..ny-1
      b=ymax-j*step       
      for i in 0..nx-1
        a=i*step+xmin
        x=0
        y=0 
        n=0
        #  while x*x+y*y<4 and n<=nmax
        while x*x+y*y<4 && n<=nmax
          x1=x*x-y*y+a
          y=2*x*y+b
          x=x1
          n=n+1
        end

        # Adding the point to the chart
        # Needs to associate a color according to n 
        # that is according to the time needed to converge
        amplif = 1
        c = (16.0.+n/nmax*(255.0-16.0)*amplif).to_int
        c = [255,c].min
        col_gray = (255-c).to_int.to_s(16).to_s
        col =  "#"+col_gray+col_gray+col_gray
        scatter = Scatter.new(col, 2);
        scatter.set_values([ScatterValue.new(a,b)])
        chart.add_element( scatter )

        # if you want to store the result 
        r.push([a,b,n,c])
      end #i
    end #j

    x_axis = XAxis.new
    x_axis.set_range(xmin,-xmin)
    chart.x_axis = x_axis

    y_axis = YAxis.new
    y_axis.set_range( -ymax, ymax )
    chart.y_axis = y_axis
    render :text => chart.to_s      
  end

<script type="text/javascript" src="/javascripts/swfobject.js"></script>
<%= @graph %>

He is from a minority. He is American, lives in the US but has a dual culture. He studied in the best universities. He is one of the smartest guys on Earth. He had many awards for his outstanding work along his long and brilliant career. He has always fought received ideas. He is not afraid of complexity but knows to recognize simplicity in the middle of intricated systems that most people consider as infinitely complex. He is not afraid of telling people when they are wrong. He is not afraid of telling them what to do. He does not hesitate to fight alone against the majority but definitely prefers to be with the majority. If listened to earlier, many casualties would have been avoided. He wants to change the world and he has a plan.
No, I am not speaking about Barack Obama. Let me continue. He is Franco-American. He studied aeronautics. He deserves a Nobel prize in all categories: economy, physics, medecine (biology), chemistry, and even litterature and peace, because his work helped describing and understanding the geometry of nature. His work can indeed be applied to stock market, natural borders, lungs description, fluid mechanics, animal population evolution, clouds. He wrote many inspiring books. If more listened to the world would be way more peaceful because better understood and less submitted to crisis.
Yes, I am speaking about Benoit Mandelbrot and the good news is: his work on finance is slowly being recognized by the media and by economists.

Listen to Mandelbrot and global warming, crisis and wars will just be bad memories. OK I am exaggerating, but I am not sure how much ;-).

PS If you know which conferences Mandelbrot is going to attend this year, please let me know in the comments because he is definitely the celebrity I would love most to meet.

In my 2009 wishes, I wished that people better understand the world. For this purpose, I suggested they read The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward by Benoit Mandelbrot.
Actually, for one year and a half we have been inside this growing up crisis I have been appalled by the small number of articles in the media about Mandelbrot’s work on Finance and more generally by the small number of articles about chaos theory and economy. Indeed more than ten years ago, Mandelbrot explained why the finance world was walking on its head. To make it short, it is because financial theory fundamental principles are wrong and over-optimistic. These principles state that the hazard involved in the market theory is regular enough to be smoothed by the big numbers law. This hazard is “benign”. Basically, with the standard theory, crisis can’t happen. So yes, you must be dreaming, there is no crisis, unless you listen to Mandelbrot that tells you that the hazard is actually “savage” and potentially leading to a collapse of the market: a crash.

So where is the good news ?

I wish you all an excellent year 2009 filled with happiness in your private life as well as in your professional life.
Besides that, I wish you to better understand the world we all live in. For this purpose, here are some subjects that deserve all your attention and about which I will blog soon.

• Control Systems
• Economy
• Fractals
• Chaos Theory
• Statistics
• Polls

This beginning of the new year will be very busy around here. Indeed, I am going to make a major update for ThinkoSphere.com with the new design and I will start a blogging series about Control Systems. Later on I will blog about the fractal theory applied to finance because it is today the best theory explaining the crisis that I have found so far. I am currently reading the book “fractals, hazard and finance” from Benoit Mandelbrot*, father of the fractal theory. This book is amazing, it is ten years old but it looks like it was written 2 days ago, after the crisis.

Moreover, I also wish you to be better understood by your company, by your mayor, by your government. I wish you more democracy in your environment. This starts by giving more your opinion when you are polled. So I wish you more polls and finally I wish you to find your interest in ThinkoSphere.com.

* I am actually speaking about “fractale, hasard et finance” a book in French. Its equivalent in English is The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward. This is probably the best quality and best quality/price ratio book about finance you can buy nowadays!