ResearchChannel - The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin and Return

One of the next books I would like to get is Benoit Mandelbrot's The (Mis)Behavior of Markets.

Mandelbrot invented fractal geometry, a groundbreaking way of describing the natural world that far surpassed euclidian geometry in its ability to describe the rough and asymetrical forms found there. This "new" book published in 2006 applies the same theories to describing the stock market. Reminds me a lot of the premise behind the movie Pi.

Here is a video of Mandelbrot talking about his book published by the Microsoft Corporation on the Research Channel.

ResearchChannel - The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin and Return

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Chaoscope

Lately I have been having some fun with a new fractal program called Chaoscope. The nice thing about this program is that it allows you to view your fractal images in 3D, rotate them and change the colors till you find the something really amazing. You can also watch animations. Here are a couple of images I created.

Relevant Media: Nova: Fractals

Nova did nice show on fractals which aired on October 28th. A while back I posted a link to Arthur C. Clarks show on the same topic. It was good, but there was too much emphasis on the fact that the colors used to highlight the features of the fractal look like an LSD trip. This documentary lacks the trippy music (which is a plus), however, the commercial does not. It was posted on youtube.




Another problem with Clark's documentary was, that it didn't cover as many of the practical uses and insights. Part of that may just have to do with progress over the last couple of decades, but some things were just overlooked, like how Benoit Mandelbrot discovered why IBM was having problems sending digital information over phone lines. Or how the first practical application of fractals was in the digital animation of mountain ranges. You can get further information about fractals, and watch the full episode online at Nova Online.

Comments: Chaos Theory and Music

About two years ago I read a blurb about Diana Dabby and how she used chaotic progressions of classical music, to produce new and interesting variations on those themes. Until now I had never heard the music itself. It was that blurb that got me interested in fractal music. Here are two video clips from Steven Strogatz visual presentation on Chaos Theory (the other parts are on YouTube, but this is by far my favorite).

Part 1


Part 2

Relevant Media: Fractals - Arthur C. Clark: The Colors of Infinity

Unlike traditional Euclidian geometry, fractal objects have the ability to describe the natural world. The jagged contours of a coastline or a mountain range, the etherial shape of clouds, the branching of trees, the crystaline patterns of a snoflake. Fractals have been refered to as the geometry of God. Today, fractals are used for image compression as well as for creating realistic digital landscapes. Below is an episode of Arthur C. Clark Presents, called Fractals the Colors of Infinity .



While I enjoyed the video, I did not like the soundtrack too much. Producers of the show probably thought the swirling colors looked like an LSD trip, but if you listen to the show you realize that the colors are used to highlight different parts of the pattern that would not be evident in an unchanging monochromatic scheme.

I recently used one of the techniques demonstrated in the video to prepare a slide for my powerpoint presentation How We Got The Bible. The principal of self-similarity means that any part of a natural is approximately similar to another part of itself. This should allow you to fill in a missing portion of a photo depicting a natural landscape in a way that does not appear artificial. Below is a picture of two people in front of the caves where the Gospel of Judas was discovered. For my presentation, I did not want the people in the image, so I used photoshop to edit them out. I did this by useing a the magic eraser to delete them, and taking a sample from the nearby rocks to fill in the empty space where they stood. The casual observer would probably not notice anything unusual about the photo; but you can see a pattern in the rock which is repeated three times. I could have done several things to disguise this. like inverting and reversing the image each time, or taking samples from other places, but I'm not trying to be a Rembrandt here, and you get my point.

Before















After

Fractal Art: Galaxy / Fractal Music: Ghosties

Unlike the smooth lines and curves of traditional geometry, fractals are able to more accurately represent the patterns in nature.

Listen to Ghosties

Fractal Music: Captivity / Fractal Art: Jacob's Ladder

Captivity


This midi piece is called captivity. It has an ominous tone that concludes with on a bright note - possibly signaling an unexpeted liberation.

Jacob's Ladder


I named this fractal image, Jacob's ladder due to its spiral off into infinity and the apparent motion along its spiral.