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

In: Fractals and Chaos

Author

Listed:
  • Benoit B. Mandelbrot

    (Yale University, Mathematics Department
    IBM T.J. Watson Research Center)

Abstract

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.

Suggested Citation

  • Benoit B. Mandelbrot, 2004. "Fractal aspects of the iteration of z→λz(1-z) for complex λ and z," Springer Books, in: Fractals and Chaos, chapter 0, pages 37-51, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-4017-2_3
    DOI: 10.1007/978-1-4757-4017-2_3
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