Search results
Results from the WOW.Com Content Network
Benoit B. Mandelbrot [a] [b] (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life".
In geometric measure theory such a smooth curve as the circle that can be approximated by small straight segments with a definite limit is termed a rectifiable curve. [7] Benoit Mandelbrot showed that D is independent of ε.
The Mandelbrot set is widely considered the most popular fractal, [44] [45] and has been referenced several times in popular culture. The Jonathan Coulton song "Mandelbrot Set" is a tribute to both the fractal itself and to the man it is named after, Benoit Mandelbrot. [46]
The seven states of randomness in probability theory, fractals and risk analysis are extensions of the concept of randomness as modeled by the normal distribution. These seven states were first introduced by Benoît Mandelbrot in his 1997 book Fractals and Scaling in Finance, which applied fractal analysis to the study of risk and randomness. [1]
The terms fractal dimension and fractal were coined by Mandelbrot in 1975, [16] about a decade after he published his paper on self-similarity in the coastline of Britain. . Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in ...
In probability theory and statistics, the Zipf–Mandelbrot law is a discrete probability distribution.Also known as the Pareto–Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf, who suggested a simpler distribution called Zipf's law, and the mathematician Benoit Mandelbrot, who subsequently generalized it.
Chaos: Making a New Science was the first popular book about chaos theory. It describes the Mandelbrot set, Julia sets, and Lorenz attractors without using complicated mathematics. It portrays the efforts of dozens of scientists whose separate work contributed to the developing field.
In the first chapter, the Black Swan theory is first discussed in relation to Taleb's coming of age in the Levant. The author then elucidates his approach to historical analysis. He describes history as opaque, essentially a black box of cause and effect. One sees events go in and events go out, but one has no way of determining which produced ...