Category Archives: General

While looking for information on the fractal nature of the internet, I came across an article by Dr. Martin J. Fischer and Dr. Thomas B. Fowler, at:

http://www.cis.uab.edu/courses/cs725/2009-Summer.d/Fractals-HeavyTails-HaOut.pdf

It contained this graph:

Before the complexities of the internet were fully understood, people would model internet traffic the same way they modeled telecommunications traffic:  with Poisson Distributions.  This graph compares the measured amount of internet traffic with voice traffic modeled using Poisson Distributions.  As one zooms in on a certain interval in both graphs, the voice traffic eventually becomes level and uniform.  The internet traffic, on the other hand, does not, and retains the same random fluctuations.

From what I could gather from the article, the internet possesses complex network layers, which exhibit random bursts of activity that cannot be dampened.  The telecommunication traffic, on the other hand, is not as complex; it does not contain layers of networks, and is capable of having its “burstiness” dampened and smoothed out.  This is why the Poisson Distribution can be used to model telecommunications, but not internet traffic.

Ecological Patterns in Coral Reefs

As covered in this week’s reading, a number of natural ecological patterns can be seen in coral reef ecosystems.   The video below gives a brief overview of coral reefs and their dynamics.  It does not specifically address the different spacial patterns that occur, but it shows a wide variety of coral reef footage that does display the different patterns that emerge.  The reading for this week mentioned some types of patterns that can occur in coral reefs, such as regularly spaced coral plates and reef islands that form.  The coral naturally exhibits individual growth symmetry and pattern, which then lead to larger growth patterns once other outside factors become involved.  These factors can include the flow path of water, the available nutrients of an ecosystem and its distribution, and the dispersion of other organisms that directly influence the coral.  These types of small scale and large scale patterns, and some of their influences, can be seen in the following video after the first 25 seconds or so.

Mandelbrot

Not to be morbid on the eve of our paper submission, but did anyone else see this? I thought it was relevant…
(I’m not sure why the link isn’t showing up but click the “Published..” below)

Course Description

From the self-assembly of viruses into beautiful (and deadly!) structures, to the chaos of global climate cycles or the clumpiness of galaxies in the universe, it’s clear that the rules of nature can create both order and disorder. What causes systems to tend towards order or chaos, even though we know that entropy is always increasing? What’s the difference between random and chaotic behavior? How are catastrophes like earthquakes and traffic jams triggered? In a seminar setting, we will look at such examples from across the sciences and engineering. Along the way, we’ll use a variety of approaches: reading and discussion, examining the natural world, conducting laboratory and computer experiments, and writing about our explorations. Sometimes we’ll use mathematics, and at other times pictures and words, in our attempt to understand how these phenomena emerge.

Lorenz attractorMandelbrot setzebra

fractal cauliflowertraffic jamcapsid virus


Example: Shaken Cornstarch Patterns

Below is a sample “video hunt” entry which illustrates a few main themes of the seminar.  A few things to note:

  • Each entry should have a descriptive title and be marked with the appropriate “Media Hunt #X” category.
  • Each entry is created from the same WordPress account name so that you receive credit for your work.
  • The text below contains information about the source of the video, what the video depicts,  and what relation the video has to the seminar. Entries should be a minimum of a paragraph in length, but a great video may deserve more discussion!
  • A very interesting still image can be used in place of a video.
  • You can use the “Add  Image” button above to make an image appear within your entry. For images already present online, you just need to copy the URL.

In addition, please feel free to comment on each other’s entries using the “Comment” button.

Some sources for videos/images:


Sample entry

This movie created by Robert Deegan shows the dynamics of container of a cornstarch-water mixture being vibrated at various frequencies. Initally, the mixture behaves like a liquid. However, once energy is injected into the system through vibrations, complicated patterns develop. While these patterns appear spatially and temporally chaotic, there is also a large degree of order in the system: the spacing between the stripes is quite constant.

Remarkably, if the surface is disturbed by a puff of air, a permanent hole in the fluid can develop. If the mixture is very strongly shaken, this initial hole can become unstable and develop tall protrusions. This is an example of a small disturbance growing into a much bigger effect, a common phenomenon in nonlinear and nonequilibrium systems.

There is also a Humorous Remix available on YouTube which is fun to watch.