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

Benoit B. Mandelbrot
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Benoit B. Mandelbrot: Yale University, Mathematics Department

Chapter C3 in Fractals and Chaos, 2004, pp 37-51 from Springer

Abstract: 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.

Keywords: Fractal Dimension; YORK Academy; Strange Attractor; Kleinian Group; Fractal Attractor (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-1-4757-4017-2_3

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