Order From Chaos
The man who found order in the chaos of the universe, Benoit Mandelbrot, has died.
Mandelbrot, who had joint French and US nationality, developed fractals as a mathematical way of understanding the infinite complexity of nature.
The concept has been used to measure coastlines, clouds and other natural phenomena and had far-reaching effects in physics, biology and astronomy.
His seminal works, Fractals: Form, Chance and Dimension and The Fractal Geometry of Nature, were published in 1977 and 1982. In these, he argued that seemingly random mathematical shapes in fact followed a pattern if broken down into a single repeating shape.
The concept enabled scientists to measure previously immeasurable objects, including the coastline of the British Isles, the geometry of a lung or a cauliflower.
“If you cut one of the florets of a cauliflower, you see the whole cauliflower but smaller,” he explained at the influential Technology Entertainment and Design (TED) conference earlier this year.
“Then you cut again, again, again, and you still get small cauliflowers. So there are some shapes which have this peculiar property, where each part is like the whole, but smaller.”
In the 1960s Mandelbrot, a research fellow with IBM, began a mathematical analysis of electronic “noise” which was sometimes interfering with IBM electronic transmissions, causing errors. Although the nature of these errors was not understood, IBM scientists noted that the blips occurred in clusters; a period of no errors would be followed by a period with many.
Examining these clusters, Mandelbrot noticed that they formed a pattern and that the closer they were examined, the more complex the pattern seemed to become. An hour might pass with no errors, while the next hour might pass with several errors. However, if one of the hours that contained errors was divided into 20-minute sections, there would be 20 minutes with no errors, then 20 minutes with many errors.
On any scale of magnification, Mandelbrot found, the proportion of error-free transmission to error-ridden transmission remained constant. In other words the electronic interference exhibited “self-similarity” at every scale of magnification: each small part, when magnified, reproduced exactly the larger portion.
Mandelbrot began to notice the same phenomenon of “self similarity ” in other fields. For example, when he analysed statistical records of cotton prices, he noticed that, while the daily, monthly and yearly pricing of cotton was random, the curves of daily monthly and yearly price changes were identical.
Of course most of us will remember Manbelbrot for z=z2+c, or :
Cross posted at Newshoggers