Thursday, April 17, 2008

Edward N. Lorenz, a Meteorologist and a Father of Chaos Theory, Dies at 90 - New York Times 

This morning driving to work I saw the most amazing cloud formation which if I have a chance I will post pics of.

Then later I saw that meteorologist Edward Lorenz had died:

Edward N. Lorenz, a Meteorologist and a Father of Chaos Theory, Dies at 90 - New York Times

Here is more on Lorenz from Wikipedia:

"The Lorenz attractor is a 3-dimensional structure corresponding to the long-term behavior of a chaotic flow, noted for its butterfly shape. The map shows how the state of a dynamical system (the three variables of a three-dimensional system) evolves over time in a complex, non-repeating pattern.

The attractor itself, and the equations from which it is derived, were introduced by Edward Lorenz in 1963, who derived it from the simplified equations of convection rolls arising in the equations of the atmosphere.

From a technical standpoint, the system is nonlinear, three-dimensional and deterministic. In 2001 it was proven by Warwick Tucker that for a certain set of parameters the system exhibits chaotic behavior and displays what is today called a strange attractor. The strange attractor in this case is a fractal of Hausdorff dimension between 2 and 3. Grassberger (1983) has estimated the Hausdorff dimension to be 2.06 ± 0.01 and the correlation dimension to be 2.05 ± 0.01.

The system arises in lasers, dynamos, and specific waterwheels [1].

The equations that govern the Lorenz attractor are:

\frac{dx}{dt} = \sigma (y - x)
\frac{dy}{dt} = x (\rho - z) - y
\frac{dz}{dt} = xy - \beta z
where σ is called the Prandtl number and ρ is called the Rayleigh number. All σ, ρ, β > 0, but usually σ = 10, β = 8/3 and ρ is varied. The system exhibits chaotic behavior for ρ = 28 but displays knotted periodic orbits for other values of ρ. For example, with ρ = 99.96 it becomes a T(3,2) torus knot."

If I have a chance I will post a pic of a plotted trajectory of a Lorenz system.

I was noticing this amazing cloud wall, with a leading frontal shelf anterior to a section of somewhat regular columns of puffy mammatus cloud trailing behind. The cloud line was distinct in a relatively cloud free morning sunrise. I saw the cloud once on the interstate south of Indianapolis, finally parking my car just west of it at work (32 MILES NORTH OF HOME). What strikes me most about formations, such as this one, is orderliness of it, the whole cloud punctuated with periodic features. This was not an amorphous mist. This cloud was order out of chaos.

"Chaos and fractals are related. For instance the Lorenz attractor describes the weather which is a chaotic phenomenon; but within the chaos of the weather there is an underlying order described by the Lorenz attractor which is fractal in its self-similarity at any scale. The same is true for clouds. They are also formed by chaotic processes, but at the same time clouds are fractal in that they are the same at all scales."

-- from a web page of Dr. Sijpkes, referencing James Gleick's book "Chaso: the making of a new science" which talks a lot about Lorenz. http://www.arch.mcgill.ca/prof/sijpkes/philo2003/diagram/intro.html

My friend, PFG, an applications developer, wrote:
"I just checked this guy's wikipedia page last week. I didn't know anybody else knew who he was. I read the article he wrote in the Journal of Atmospheric Sciences in 1963 back in 1987 at Bracken Library. I couldn't believe they had it. (Deterministic nonperiodic flow. Journal of Atmospheric Sciences. Vol.20 : 130—141 link [8]. ) This article was the foundation of Chaos Theory. I used his equations on my TI-99/4A to plot the Lorenz attractor. He and Douglas Hofstadter made me want to study computer science."

If you read the wiki or the NY Times article on Mr. Lorenz you will see he was still active until recently writing and getting outdoors. I only hope I am so lucky.

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