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MessagePosté le: Mer 28 Sep - 13:11 (2016)    Sujet du message: Space Filling Curves Pdf Free Répondre en citant

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Space Filling Curves Pdf Free

v t e Fractals Characteristics Fractal dimensions Assouad Box-counting Correlation Hausdorff Packing Topological Recursion Self-similarity Iterated function system Barnsley fern Cantor set Dragon curve Koch snowflake Menger sponge Sierpinski carpet Sierpinski triangle Space-filling curve T-square Strange attractor Multifractal system L-system Space-filling curve Escape-time fractals Burning Ship fractal Julia set Filled Lyapunov fractal Mandelbrot set Nova fractal Random fractals Brownian motion Brownian tree Diffusion-limited aggregation Fractal landscape Lvy flight Percolation theory Self-avoiding walk People Georg Cantor Felix Hausdorff Gaston Julia Helge von Koch Paul Lvy Aleksandr Lyapunov Benoit Mandelbrot Lewis Fry Richardson Wacaw Sierpiski Other "How Long Is the Coast of Britain?" Coastline paradox List of fractals by Hausdorff dimension The Beauty of Fractals (1986 book) . B. (The restriction of the Cantor function to the Cantor set is an example of such a function.) From it, we get a continuous function H {displaystyle scriptstyle H} from the topological product C C {displaystyle scriptstyle {mathcal {C}};times ;{mathcal {C}}} onto the entire unit square [ 0 , 1 ] [ 0 , 1 ] {displaystyle scriptstyle [0,,1];times ;[0,,1]} by setting. McKenna, Douglas M. Java applets:. If a curve is not injective, then one can find two intersecting subcurves of the curve, each obtained by considering the images of two disjoint segments from the curve's domain (the unit line segment). A curve (with endpoints) is a continuous function whose domain is the unit interval [0,1].

But the graphical construction was perfectly clear to himhe made an ornamental tiling showing a picture of the curve in his home in Turin. One might be tempted to think that the meaning of curves intersecting is that they necessarily cross each other, like the intersection point of two non-parallel lines, from one side to the other. Therefore, Peano's space-filling curve was found to be highly counterintuitive. The analytic form of the Hilbert curve, however, is more complicated than Peano's. Six iterations of the Hilbert curve construction, whose limiting space-filling curve was devised by mathematician David Hilbert. (Here the sphere is the sphere at infinity of hyperbolic 3-space.). At that time (the beginning of the foundation of general topology), graphical arguments were still included in proofs, yet were becoming a hindrance to understanding often counterintuitive results. Sometimes, the curve is identified with the range or image of the function (the set of all possible values of the function), instead of the function itself. {displaystyle H(x,y)=(h(x),h(y)).,} . There are many natural examples of space-filling, or rather sphere-filling, curves in the theory of doubly degenerate Kleinian groups.

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