Fractal Geometry of Nature

@inproceedings{Mandelbrot1984FractalGO,
  title={Fractal Geometry of Nature},
  author={Benoit B. Mandelbrot},
  year={1984}
}
"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature 
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25,558 Citations
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25,558 Citations

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This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative…

The Influence of Benoît B. Mandelbrot on mathematics

Introduction We begin this article, which deals largely with Benoît B. Mandelbrot’s contributions to and influence upon mathematics, with a quotation from the introduction to Fractals: Form, Chance,…

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References

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Before we can tackle some specific new technical tidbits, which this paper hopes to contribute to the study of the geometry of plants, we must deal with the first term in the title. You are not…

Prelude to dimension theory: The geometrical investigations of Bernard Bolzano

AbstractThis paper treats Bernard Bolzano's (1781–1848) investigations into a fundamental problem of geometry: the problem of adequately defining the concepts of line (or curve), surface, solid, and…

On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars

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Introduction. In any field of geometric investigation the curves fall roughly into two classes, constituted respectively of the curves ordinarily investigated and of the other curves; these unusual…

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THIS book, at once substantial and stately, is to the credit of British science and an achievement for its distinguished author to be proud of. It is like one of Darwin's books, well-considered,…

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If one were to consult only the published record of his research, the factors influencing his discovery, development, and subsequent defense of set theory and the transfinite numbers would remain obscure, and one could only hope for a partial view of what Cantor accomplished.

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The invention relates to apparatus for the wet-treatment of textile materials particularly in endless web or rope form whether as yarn or made-up. Wet-treatment liquid, particularly dye liquor is…

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