Fractal aspects of the iteration of z→λz(1-z) for complex λ and z

  • Benoit B. Mandelbrot


Chapter foreword concerning the illustrations, especially the “missing specks” of Figure 1 (2003). As described in Chapter C1, this paper boasts many “firsts” and was instrumental in reviving the theory of iteration. The many new observations it contains concern the set in the μ-plane for which A. Douady and J.H. Hubbard soon proposed the term “Mandelbrot set.” Each observation was stated as a mathematical conjecture or became the source of one. Thus, the figures in this paper played a fundamental historical role.


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Copyright information

© Benoit B. Mandelbrot 2004

Authors and Affiliations

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

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