Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.

Recensione:

"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 is the fourth volume of Mandelbrot s Selecta, comprising edited reprints of the author s papers. ... One chapter has been written specifically to help the non-expert appreciate the rest of the book. ... accessible to a wide readership. It provides a fascinating insight into the author s journey of seeing and discovering as the early pictures of the Mandelbrot set started to reveal a whole new world. It gives a feeling for his philosophy and approach of experimental mathematics ... ." --Kenneth Falconer, NATURE, Vol. 430, July1, 2004

"Mandelbrot s book is a scientific, philosophic and pictorial treatise at the same time and it is one of the rare specimens of serious mathematics books that can be read and re-read at many different levels. ... The style is what one would call truly Mandelbrotian , a mixture of hard science, often with a personal touch ... . a book that will be as important for the scientific community ... as it will be appealing to a general informed audience." --Ren� L. Schilling, The Mathematical Gazette, March, 2005

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