History
The terms fractal dimension and fractal were coined by Mandelbrot in 1975, 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 usual linear terms. The earliest roots of what Mandelbrot synthesized as the fractal dimension have been traced clearly back to writings about undifferentiable, infinitely self-similar functions, which are important in the mathematical definition of fractals, around the time that calculus was discovered in the mid 1600s. There was a lull in the published work on such functions for a time after that, then a renewal starting in the late 1800s with the publishing of mathematical functions and sets that are today called canonical fractals (such as the eponymous works of von Koch, Sierpinski, and Julia), but at the time of their formulation were often considered antithetical mathematical "monsters". These works were accompanied by perhaps the most pivotal point in the development of the concept of a fractal dimension through the work of Hausdorff in the early 1900s who defined a "fractional" dimension that has come to be named after him and is frequently invoked in defining modern fractals.
See Fractal history for more information
Read more about this topic: Fractal Dimension
Famous quotes containing the word history:
“The history of the world is none other than the progress of the consciousness of freedom.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“I believe that in the history of art and of thought there has always been at every living moment of culture a “will to renewal.” This is not the prerogative of the last decade only. All history is nothing but a succession of “crises”Mof rupture, repudiation and resistance.... When there is no “crisis,” there is stagnation, petrification and death. All thought, all art is aggressive.”
—Eugène Ionesco (b. 1912)
“The steps toward the emancipation of women are first intellectual, then industrial, lastly legal and political. Great strides in the first two of these stages already have been made of millions of women who do not yet perceive that it is surely carrying them towards the last.”
—Ellen Battelle Dietrick, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 4, ch. 13, by Susan B. Anthony and Ida Husted Harper (1902)