Friday, April 25, 2008

Friday beautiful science

Today's Friday beautiful science was inspired by the obituary of Edward Lorenz:

In discovering “deterministic chaos,” Dr. Lorenz established a principle that “profoundly influenced a wide range of basic sciences and brought about one of the most dramatic changes in mankind’s view of nature since Sir Isaac Newton,” said a committee that awarded him the 1991 Kyoto Prize for basic sciences.

Dr. Lorenz is best known for the notion of the “butterfly effect,” the idea that a small disturbance like the flapping of a butterfly’s wings can induce enormous consequences.

As recounted in the book “Chaos” by James Gleick, Dr. Lorenz’s accidental discovery of chaos came in the winter of 1961. Dr. Lorenz was running simulations of weather using a simple computer model. One day, he wanted to repeat one of the simulations for a longer time, but instead of repeating the whole simulation, he started the second run in the middle, typing in numbers from the first run for the initial conditions.

The computer program was the same, so the weather patterns of the second run should have exactly followed those of the first. Instead, the two weather trajectories quickly diverged on completely separate paths.

At first, he thought the computer was malfunctioning. Then he realized that he had not entered the initial conditions exactly. The computer stored numbers to an accuracy of six decimal places, like 0.506127, while, to save space, the printout of results shortened the numbers to three decimal places, 0.506. When typing in the new conditions, Dr. Lorenz had entered the rounded-off numbers, and even this small discrepancy, of less than 0.1 percent, completely changed the end result.
The photo above is a demonstration of chaos theory. It's a Mandelbrot set, that is seen to contain the same patterns at large and small magnification. You can zoom and explore a Mandelbrot set here. For more on Chaos Theory (written for non-mathematicians), see:



Duncan Wilson said...

Hey, I see you comment on Abbie's blog, ERV a lot. It's disappeared, though, do you know where it went to?

On topic, I got nothing, save that fractals are cool looking.

The Factician said...

She's moved. Explained here:

David Amulet said...

Beautiful indeed.

On a related note, I think Mandelbrot Set would be a great name for a band.