Results 11 to 20 of about 10,664 (306)
Manufacturability of Fractal Geometry [PDF]
Materials Science Forum, 2004 Nowadays more and more aesthetic product developments, assemblage and decoration designs are taking aesthetically appealing forms of natural objects such as rough terrain, ripples on lakes, coastline and seafloor topography. They are mathematical definable via fractal geometry theory and emerge to attract a lot of attention.
Yeung, Y.C., Yu, K.M.
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Fractals in Noncommutative Geometry
, 2001 To any spectral triple (A,D,H) a dimension d is associated, in analogy with the Hausdorff dimension for metric spaces. Indeed d is the unique number, if any, such that |D|^-d has non trivial logarithmic Dixmier trace. Moreover, when d is finite non-zero, there always exists a singular trace which is finite nonzero on |D|^-d, giving rise to a ...
GUIDO, DANIELE, ISOLA, TOMMASO
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The Fractal Geometry of the Heart [PDF]
Nature Biotechnology, 1989 Harvey Bialy
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Spectral triples and the geometry of fractals
Journal of Noncommutative Geometry, 2012 We construct spectral triples for the Sierpinski gasket as infinite sums of unbounded Fredholm modules associated with the holes in the gasket and investigate their properties. For each element in the K-homology group we find a representative induced by one of our spectral triples.
Christensen, Erik +2 more
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Geometry, dynamics and fractals [PDF]
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2008 Consider a collection of elastic wires folded according to a given pattern induced by a sequence of fractal plane curves. The folded wires can act as elastic springs. Therefore it is easy to build up a corresponding sequence of simple oscillators composed by the elastic springs clamped at one end and carrying a mass at the opposite end. The oscillation
Bevilacqua, Luiz +2 more
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Fractal geometry of music. [PDF]
Proceedings of the National Academy of Sciences, 1990 Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
A J Hsü, Kenneth J. Hsü
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The Geometry of Fractal Percolation [PDF]
, 2014 A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost every realization of fractal percolation.
Károly Simon, Michał Rams
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Fractal Geometry of Rocks [PDF]
Physical Review Letters, 1999 The analysis of small- and ultra-small-angle neutron scattering data for sedimentary rocks shows that the pore-rock fabric interface is a surface fractal (D{sub s}=2.82) over 3 orders of magnitude of the length scale and 10 orders of magnitude in intensity.
Radlinski, A P +5 more
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Studying the status of fractal geometry in art and its appearance in artwork [PDF]
پیکره, 2015 Euclid was one of the first who attempted to explain natural phenomena in terms of mathematical concepts. His efforts were called Euclidean geometry.
Mahtab Mobini, Nooshin Fatholahi
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Developments in fractal geometry [PDF]
Bulletin of Mathematical Sciences, 2013 Iterated function systems have been at the heart of fractal geometry almost from its origins. The purpose of this expository article is to discuss new research trends that are at the core of the theory of iterated function systems (IFSs). The focus is on geometrically simple systems with finitely many maps, such as affine, projective and Mobius IFSs ...
Barnsley, Michael, vince, Andrew
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