Fractal Geometry of Nature

  title={Fractal Geometry of Nature},
  author={Benoit B. Mandelbrot},
"...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 

The Postmodern Beauty of Fractals

ABSTRACT Fractal art, one of the significant conjunctions of art, modern mathematics and computer technology, has been the author's primary art medium for the past five years. After presenting an

Fractal geometry in the nucleus

Two recent studies in Science and The EMBO Journal have suggested that chromatin and the nucleoplasmic space surrounding it should be added to the fractal list.

Fractals and image representation

The authors briefly describe the theoretical background of fractal representations and investigate in more detail the validity of such an approach for applications in natural scene portrayal and coding.

A Fractal Comparison of Escher and Koch Tessellations

M.C. Eschers tessellations have captured the imaginations of both artists and mathematicians. Circle Limit III is the most intricate of his tessellations, featuring patterns that repeat at

The notion of dimension in geometry and algebra

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,

“Fractal Architecture”: Late Twentieth Century Connections Between Architecture and Fractal Geometry

Abstract.Michael Ostwald examines the intricate, constantly shifting relationship between architecture and fractal geometry. At times this dependence is diffuse, and modes of theoretical transference

The Nature of Fractal Geometry

Fractals are more than just stunning visual effects – they open up new ways to model nature and allow us to quantify terms like ‘irregular’, ‘rough’ and ‘complicated’, writes mathematician Ian



The Fractal Geometry of Trees and Other Natural Phenomena

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

This paper studies several geometric aspects of the Poisson and Gaussian random fields approximating Burgers k−2 and Kolmogorov $k^{-\frac{5}{3}}$ homogeneous turbulence. In particular, simulated

Lebesgue's theory of integration: Its origins and development

Riemann's theory of integration The development of riemann's ideas: 1870-80 Set theory and the theory of integration The end of the century: A period of transition The creation of modern integration

On certain crinkly curves

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

On growth and form i

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,

Georg Cantor: The Personal Matrix of His Mathematics

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.

Weak convergence to fractional brownian motion and to the rosenblatt process

  • M. Taqqu
  • Art
    Advances in Applied Probability
  • 1975
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


  • J. Gerver
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1969
It is shown that a continuous function which Riemann is said to have believed to be nowhere differentiable is in fact differentiable at certain points.