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From Newton Fractals to Gradient Fractals in Addition to Zhang Fractals
2014 IEEE 17th International Conference on Computational Science and Engineering, 2014The paper employs gradient dynamics (GD), in addition to Zhang dynamics (ZD), to generate new fractals which are quite different from the conventional Newton fractals (NF). The proposed gradient fractals (GF) have three types. Specifically, via appropriate iterative formulas derived in complex domain, the first-type and second-type fractals are ...
Yunong Zhang +4 more
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APPROXIMATION WITH FRACTAL FUNCTIONS BY FRACTAL DIMENSION
Fractals, 2022On the basis of previous studies, we explore the approximation of continuous functions with fractal structure. We first give the calculation of fractal dimension of the linear combination of continuous functions with different Hausdorff dimension. Fractal dimension estimation of the linear combination of continuous functions with the same Hausdorff ...
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2008
Fractals have become increasingly useful tools for the statistical modelling of financial prices. While early research assumed invariance of the return density with the time horizon, new processes have recently been developed to capture nonlinear changes in return dynamics across frequencies.
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Fractals have become increasingly useful tools for the statistical modelling of financial prices. While early research assumed invariance of the return density with the time horizon, new processes have recently been developed to capture nonlinear changes in return dynamics across frequencies.
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IEEE Computer Graphics and Applications, 2005
Cover artist David Works thinks that fractals appeal to an innate sense of aesthetic sensibility and he revels in Apophysis, a freeware fractal flame editor for Windows.
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Cover artist David Works thinks that fractals appeal to an innate sense of aesthetic sensibility and he revels in Apophysis, a freeware fractal flame editor for Windows.
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Fractals and Multi-fractals in Turbulence
1997Turbulent flows refer to situations in which the flow properties at any point vary in a statistically random manner. Fourier analysis shows that wave fluctuations in a range of frequencies and wave numbers are present, the width of the range changing with certain flow parameters like the Reynolds number. (Attempts at characterizing turbulence structure
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IEEE Computer Graphics and Applications, 2005
Fractal artist Terry Wright says the images on his Web site should be viewed in a dark and dimly lit room due to the nature of their textures. "Much of my art uses dark tones and has backlit qualities that do not show up well unless viewed in darkness or ambient light," he explained.
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Fractal artist Terry Wright says the images on his Web site should be viewed in a dark and dimly lit room due to the nature of their textures. "Much of my art uses dark tones and has backlit qualities that do not show up well unless viewed in darkness or ambient light," he explained.
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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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Fractals and Fractal Distributions
2002Scale invariance has attracted scientists from various disciplines since the early 1980’s. B. B. Mandelbrot has been the pioneer on this field; he introduced first ideas in the 1960’s and was the first to write a comprehensive book on scale invariance (Mandelbrot 1982). However, the idea of scale dependence and scale invariance is much older; D.
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Fractals, Multi-Fractals, Psuedo-Fractals and Non-Fractals in Energy Spectral Techniques
EAGE Workshop on Non-Seismic Methods, 2008The demonstration of fractal processes within the earth has been an important step in understanding many processes and the nature of resultant geomorphology. However the complex nature of interplay between many different processes does not lead to simple measures of fractal geometry in practice.
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Fractals and Reactions on Fractals
1989Many of the structures which surround us in nature (mountains, rivers, coastlines, clouds, the vascular system and other biological structures, for example) and systems of scientific interest (aggregates, macromolecules, rough surfaces, “strange” attractors, etc.) cannot be adequately described in terms of the concepts of Euclidean geometry.
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