Fractals and Chaos The Mandelbrot Set and Beyond / by Benoit Mandelbrot.

"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...

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Bibliographic Details
Main Author: Mandelbrot, Benoit. (Author,
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: New York, NY : Springer New York : Imprint: Springer, 2004.
Edition:1st ed. 2004.
Series:Springer eBook Collection.
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • List of Chapters
  • C1 Introduction to papers on quadratic dynamics: a progression from seeing to discovering (2003)
  • C2 Acknowledgments related to quadratic dynamics (2003)
  • C3 Fractal aspects of the iteration of z ? ? z (1-z) for complex A and z (M1980n)
  • C4 Cantor and Fatou dusts; self-squared dragons (M 1982F)
  • C5 The complex quadratic map and its M-set (M1983p)
  • C6 Bifurcation points and the “n squared” approximation and conjecture (M1985g), illustrated by M.L Frame and K Mitchell
  • C7 The “normalized radical” of the M-set (M1985g)
  • C8 The boundary of the M-set is of dimension 2 (M1985g)
  • C9 Certain Julia sets include smooth components (M1985g)
  • C10 Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs (M1985g)
  • C11 Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets (M1985n)
  • C12 Introduction to chaos in nonquadratic dynamics: rational functions devised from doubling formulas (2003)
  • C13 The map z ? ? (z + 1/z) and roughening of chaos from linear to planar (computer-assisted homage to K Hokusai) (M1984k)
  • C14 Two nonquadratic rational maps, devised from Weierstrass doubling formulas (1979–2003)
  • C15 Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments (2003)
  • C16 Self-inverse fractals, Apollonian nets, and soap (M 1982F)
  • C17 Symmetry by dilation or reduction, fractals, roughness (M2002w)
  • C18 Self-inverse fractals osculated by sigma-discs and limit sets of inversion (“Kleinian”) groups (M1983m)
  • C19 Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski (2003)
  • C20 Invariant multifractal measures in chaotic Hamiltonian systems and related structures (Gutzwiller & M 1988)
  • C21 The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems (M1993s)
  • C22 Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991)
  • C23 The inexhaustible function z squared plus c (1982–2003)
  • C24 The Fatou and Julia stories (2003)
  • C25 Mathematical analysis while in the wilderness (2003)
  • Cumulative Bibliography.