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(21 citation statements)

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“…Additionally, these new definitions of fractal dimension for a fractal structure can be used in empirical applications and they also designed some algorithms to computationally calculate them. For example, the so-called fractal dimension I was applied in the context of the domain of words, which allows us to calculate the fractal dimension of a language generated by a regular expression and even to estimate the complexity of a board game configuration of Othello [15]. But while the box-counting dimension has been widely used in applications (such as disease diagnosis [30], study of earthquakes [20] and analysis of the human retina [22], to name a few), the Hausdorff dimension, which presents the best analytical properties, still results hard to calculate or to estimate in empirical applications.…”

confidence: 99%

“…Additionally, these new definitions of fractal dimension for a fractal structure can be used in empirical applications and they also designed some algorithms to computationally calculate them. For example, the so-called fractal dimension I was applied in the context of the domain of words, which allows us to calculate the fractal dimension of a language generated by a regular expression and even to estimate the complexity of a board game configuration of Othello [15]. But while the box-counting dimension has been widely used in applications (such as disease diagnosis [30], study of earthquakes [20] and analysis of the human retina [22], to name a few), the Hausdorff dimension, which presents the best analytical properties, still results hard to calculate or to estimate in empirical applications.…”

confidence: 99%

“…They have interesting analytical properties and can be calculated with easiness. Further, some interdisciplinary applications of these models have been successfully carried out (see [15,32]). A whole study about fractal dimensions for fractal structures including applications can be found in [16].…”

confidence: 99%

“…In this way, some definitions of fractal dimension for a fractal structure have been already studied in [7][8][9]11] and applied in [10,23], to quote some of them.…”

confidence: 99%

“…In this way, some theoretical results have been shown to generalize the classical models in the context of fractal structures (see, e.g., [13,Theorem 4.15] and [15,Theorem 3.12]). Moreover, we would like to point out that some fractal dimensions for a fractal structure have been already succesfully applied in non-Euclidean contexts, where the box dimension cannot be applied (see, e.g., [18,19]).…”

confidence: 99%