Fractals and Chaos

The Mandelbrot Set and Beyond

  • Benoit B. Mandelbrot

Table of contents

  1. Front Matter
    Pages i-8
  2. Quadratic Julia and Mandelbrot Sets

  3. Nonquadratic Rational Dynamics

  4. Iterated Nonlinear Function Systems and the Fractal Limit Sets of Kleinian Groups

  5. Multifractal Invariant Measures

  6. Background and History

    1. Benoit B. Mandelbrot
      Pages 259-267
    2. Benoit B. Mandelbrot
      Pages 268-275
    3. Benoit B. Mandelbrot
      Pages 276-280
  7. Back Matter
    Pages 281-308

About this book



"It is only twenty-three years since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot Set. The graphics were state of the art, though now they may seem primitive. But how that picture has changed our views of the mathematical and physical universe! Fractals, a term coined by Mandelbrot, are now so ubiquitous in the scientific conscience that it is difficult to remember the psychological shock of their arrival. What we see in this book is a glimpse of how Mandelbrot helped change our way of looking at the world. It is not just a book about a particular class of problems, but contains a view on how to approach the mathematical and physical universe. This view is certain not to fade, but to be part of the working philosophy of the next mathematical revolution, wherever it may take us. So read the book, look at the beautiful pictures that continue to fascinate and amaze, and enjoy! " 

From the foreword by Peter W Jones, Yale University

This heavily illustrated book combines hard-to-find early papers by the author with additional chapters that describe the historical background and context. Key topics are quadratic dynamics and its Julia and Mandelbrot sets, nonquadratic dynamics, Kleinian limit sets, and the Minkowski measure.

Benoit B Mandelbrot is Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow Emeritus (Physics) at the IBM T J Watson Research Center. He was awarded the Wolf Prize for Physics in 1993 and the Japan Prize for Science and Technology in 2003.


Apollonian net Cantor Fractal History of Mathematics Invariant Mandelbrot Self-similarity function

Authors and affiliations

  • Benoit B. Mandelbrot
    • 1
    • 2
  1. 1.Mathematics DepartmentYale UniversityNew HavenUSA
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

Bibliographic information