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The Fatou and Julia stories. The inexhaustible function z squared plus c. Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets. Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs. Mandelbrot 1 2 1. Fractals, a term coined by Mandelbrot, are now so ubiquitous in the scientific conscience that it is difficult to remember the psychological shock of their arrival. What we see in this book is a glimpse of how Mandelbrot helped change our way of looking at the world.

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    This view is certain not to fade, but to be part of the working philosophy of the next mathematical revolution, wherever it may take us. IBM T. Front Matter Pages i Certain Julia sets include smooth components. Mathematical analysis while in the wilderness.

    Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments. Cantor and Fatou dusts; self-squared dragons.

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    The inexhaustible function z squared plus c.

    Key topics are quadratic dynamics and its Julia and Mandelbrot sets, nonquadratic dynamics, Kleinian limit sets, and the Minkowski measure. Back Matter Pages Two nonquadratic rational maps devised from Weierstrass doubling formulas. Front Matter Pages i Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski. IBM T.

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    What we see in this book is a glimpse of how Mandelbrot helped change our way of looking at the world.

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    IBM T. L Frame and K Mitchell. Front Matter Pages i Key topics are quadratic dynamics and its Julia and Mandelbrot sets, nonquadratic dynamics, Kleinian limit sets, and the Minkowski measure.

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    Cantor and Fatou dusts; self-squared dragons.

    Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets. Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs. Advertisement Hide. This view is certain not to fade, but to be part of the working philosophy of the next mathematical revolution, wherever it may take us. This heavily illustrated book combines hard-to-find early papers by the author with additional chapters that describe the historical background and context.

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    The inexhaustible function z squared plus c. Key topics are quadratic dynamics and its Julia and Mandelbrot sets, nonquadratic dynamics, Kleinian limit sets, and the Minkowski measure. Two nonquadratic rational maps devised from Weierstrass doubling formulas.

    So read the book, look at the beautiful pictures that continue to fascinate and amaze, and enjoy! Introduction to papers on chaos in nonquadratic dynamics: rational functions devised from doubling formulas.

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    The inexhaustible function z squared plus c. Mathematical analysis while in the wilderness. This view is certain not to fade, but to be part of the working philosophy of the next mathematical revolution, wherever it may take us.

    It is not just a book about a particular class of problems, but contains a view on how to approach the mathematical and physical universe.

    Acknowledgments related to quadratic dynamics.

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    1. Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments.