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Self-Affine Fractals and Fractal Dimension
Physica Scripta, 1985Evaluating a fractal curve's approximate length by walking a compass defines a compass exponent. Long ago, I showed that for a self-similar curve (e.g., a model of coastline), the compass exponent coincides with all the other forms of the fractal dimension, e.g., the similarity, box or mass dimensions. Now walk a compass along a self-affine curve, such
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A Unified Approach to Fractal Dimensions
International Journal of Cognitive Informatics and Natural Intelligence, 2005Many scientific chapters treat the diversity of fractal dimensions as mere variations on either the same theme or a single definition. There is a need for a unified approach to fractal dimensions for there are fundamental differences between their definitions.
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1996
Each stage of the generation process for a fractal curve adds more length to the curve. A fractal curve generated through an infinite number of steps will have infinite length. It was demonstrated in Chapter 2 that the length of different fractal curves grows from one generation stage to the next at different rates.
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Each stage of the generation process for a fractal curve adds more length to the curve. A fractal curve generated through an infinite number of steps will have infinite length. It was demonstrated in Chapter 2 that the length of different fractal curves grows from one generation stage to the next at different rates.
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Fractal dimension of semiconducting fractal sensors [PDF]
2004 14th International Crimean Conference "Microwave and Telecommunication Technology" (IEEE Cat. No.04EX843), 2004 Metal oxides are used for analysis of gas in the air in nano-dispersion semiconducting sensors developed in recent years. The fractal dimension of such a semiconductor sufficiently influences the character of the electrical conductivity and hence the sensitivity and operating speed of the sensor.
A.A. Tolstaya +3 more
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Function Norms and Fractal Dimension
SIAM Journal on Mathematical Analysis, 1997The author defines function seminorms to measure irregularity of functions. For a bounded measurable function \(f:D\subset\mathbb{R}^N\to\mathbb{R}\) and \(\alpha>0\) the \((\alpha)\)-seminorm is \[ L^\alpha(f;D)= \Biggl({1\over\text{Vol}_N(D)} \int_D |f(x)|^\alpha dx\Biggr)^{1/\alpha}, \] \(\text{Vol}_N(D)\) is the Lebesgue measure of \(D\). This will
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Fractal Dimensions as Chaos Indicators
Celestial Mechanics and Dynamical Astronomy, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1993
Publisher Summary This chapter describes fractal dimensions. Fractal dimensions are various numbers associated with fractals, which can be used to compare them. Fractal dimensions provide an objective means for comparing fractals. Fractal dimensions are important because they can be defined in connection with real-world data, and they can be measured ...
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Publisher Summary This chapter describes fractal dimensions. Fractal dimensions are various numbers associated with fractals, which can be used to compare them. Fractal dimensions provide an objective means for comparing fractals. Fractal dimensions are important because they can be defined in connection with real-world data, and they can be measured ...
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A fractal approach to dynamic inference and distribution analysis
Frontiers in Physiology, 2013Marieke M J W Van Rooij, John G Holden
exaly