Results 231 to 240 of about 16,389 (269)
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A MATRIX METHOD FOR APPROXIMATING FRACTAL MEASURES
International Journal of Bifurcation and Chaos, 1992Let X be a bounded subset of Rn and let A be the Lebesgue measure on X. Let {X:τ1,…, τN} be an iterated function system (IFS) with attractor S. We associate probabilities p1,…, pN with τ1,…, τN, respectively. Let M(X) be the space of Borel probability measures on X, and let M: M(X)→M(X) be the Markov operator associated with the IFS and its ...
Boyarsky, A., Lou, Y. S.
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Fractal Measure and Microscopic Modeling of Osseointegration
The International Journal of Periodontics & Restorative Dentistry, 2015In this study, the process of osseointegration on titanium implant surfaces with different physicochemical treatments subjected to a simulated corporal fluid submersion was evaluated using the concept of fractal dimension. It was found that different treatments led to rather different calcium phosphate crystal growth patterns, with fractal dimension ...
Leonardo Cavalcanti Bezerra, Santos +5 more
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Packing Measure and Dimension of Random Fractals
Journal of Theoretical Probability, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berlinkov, Artemi, Mauldin, R. Daniel
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Electromagnetic scattering measurements on a fractal surface
IEEE International IEEE International IEEE International Geoscience and Remote Sensing Symposium, 2004. IGARSS '04. Proceedings. 2004, 2004In this paper we present a procedure devoted to validate innovative theories on the electromagnetic scattering from natural surfaces, using fractal functions for the surface description. A fractal surface has been built as a superposition of cardboard and aluminium layers, according with a computer design based on the Weierstrass-Mandelbrot (WM ...
RUELLO, GIUSEPPE +6 more
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Comparison of fractal measures
Science in China Series A, 2005In this paper, the relationship between thes-dimensional Hausdorff measures and theg-measures in Rd is discussed, whereg is a gauge function which is equivalent to ts and 0
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Fractals in Nature Growing and Measuring Random Fractals
1994On the following two pages are several pictures of scraggly structures. What do they have in common? Answer the following questions and be prepared to discuss them. (1) How are these objects similar to each other in appearance? In what ways do these objects look different? (2) There are many ways to rank objects.
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Hausdorff measure of fractal-Sierpinski carpet
Approximation Theory and its Applications, 2000The authors obtain an upper bound for the Hausdorff measure of the Sierpiński carpet by considering a special cover of this space. The (strict) upper bound which they find is \(1.091\).
Chen, Fangyue, Xie, Tingfan
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Deterministic fractals and fractal measures
2011This is a survey paper on the general theory of fractals and fractal measures containing several proofs and exercises. It has the style of Lecture Notes and is suitable for a short introduction on this subject. The paper is concentrated on questions which have not been completely worked out in the main reference books of this subject as are \textit{K ...
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Generalizations of the Hausdorff dimension of fractal measures
Physics Letters A, 1985zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Geometric Measures for Fractals
2010In this survey article, we review the concept of fractal curvatures and fractal curvature measures and discuss some of the results known for self-similar sets. We emphasize in particular the close relations to the Minkowski content.
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