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The Dimension of Projections of Fractal Percolations [PDF]
Journal of Statistical Physics, 2013 Corrected ...
Károly Simon, Michał Rams
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Fractal Dimension of Backbone of Eden Trees [PDF]
, 1996 We relate the fractal dimension of the backbone, and the spectral dimension of Eden trees to the dynamical exponent z. In two dimensions, it gives fractal dimension of backbone equal to 4/3 and spectral dimension of trees equal to 5/4.
Dhar, D., Manna, S. S.
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AIMS MathematicsThis paper attempts to explore possible box dimension of two added fractal continuous functions with the same dimension. Two interesting and meaningful results are obtained.
Ruhua Zhang , Wei Xiao
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Stage division of urban growth based on logistic model of fractal dimension curves
Results in Physics, 2023 The time series of fractal dimension values of urban form always take on sigmoid curves. The basic model of these curves is logistic function. From the logistic model of fractal dimension curves, we can derive the speed formula and acceleration formula ...
Yanguang Chen
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Understanding the Fractal Dimensions of Urban Forms through Spatial Entropy
Entropy, 2017 The spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it.
Yanguang Chen, Jiejing Wang, Jian Feng
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The Fractal Dimension of Projected Clouds
, 2005 The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a tri-dimensional fractal
Beech M. +9 more
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Fractal Analysis on Asphalt Mixture Using a Two-Dimensional Imaging Technique
Advances in Materials Science and Engineering, 2016 Fractal is a mathematical set that has a fractal dimension which usually exceeds its topological dimension and may be nonintegral. Since the asphalt pavement texture has limitations of randomness and self-similarity, fractal theory has been explored to ...
Yue Hou +3 more
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Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions
, 2018 The fractal dimension of domain walls produced by changing the boundary conditions from periodic to anti-periodic in one spatial direction is studied using both the strong-disorder renormalization group and the greedy algorithm for the Edwards-Anderson ...
Katzgraber, Helmut G. +2 more
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Percolation dimension of fractals
Journal of Mathematical Analysis and Applications, 1990 Abstract“Percolation dimension” is introduced in this note. It characterizes certain fractals and its definition is based on the Hausdorff dimension. It is shown that percolation dimension and “boundary dimension” are in a sense independent from the Hausdorff dimension and, therefore, privide an additional tool for classification of fractals.
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Fractal dimension for fractal structures: A Hausdorff approach
Topology and its Applications, 2012 This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a suitable discretization of the Hausdorff theory of fractal dimension.
Manuel Fernández-Martínez +1 more
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