Fractals and Chaos: The Mandelbrot Set and BeyondIt has only been a couple of decades since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot set. That picture, now seeming graphically primitive, has changed our view of the mathematical and physical universe. The properties and circumstances of the discovery of the Mandelbrot Set continue to generate much interest in the research community and beyond. This book contains the hard-to-obtain original papers, many unpublished illustrations dating back to 1979 and extensive documented historical context showing how Mandelbrot helped change our way of looking at the world. |
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algorithm amax Apollonian approximation atom attractor bifurcation boundary bounded Bourbaki C₂ called Cantor dust chaos chaotic circle cluster complex numbers complex plane conjecture construction continuous converge corresponding defined denoted described distribution domain Douady dragon dynamical system example Fatou Fatou-Julia Figure finite fixed point fractal curve fractal dimension fractal geometry Fuchsian function Gaston Julia Gutzwiller Hadamard harmonic measure hence Hölder illustrations infinity intersect interval intrinsic tiling invariant inverse island molecules iteration J-set Julia set Kleinian groups Lattès limit cycle limit points limit set linear lune M-set Mandelbrot set mathematicians mathematics Minkowski measure multifractal measure Myrberg notion observations orbit osculating paper parameter Peano physics Pierre Fatou Poincaré properties quadratic map radius random rational real axis roughness self-inverse set self-similarity self-squared sequence shape Siegel disc structure subradical symmetry tangent theory topic transform unstable fixed point values yield
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