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

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.