Fractal dimension is a quantitative property of a set of points in an n-dimensional space that measures the extent to which the points fill a subspace as the number of points becomes very large. From:Encyclopedia of Physical Science and Technology (Third Edition),2003 ...
The fractal dimension of human sperm flagellar curves is used to look up for features pointing to hyperactivation movement. The original 2D fractal dimension formula is directly extended to calculate its 3D counterpart, by means of the Katz Fractal Dimension formula. For each spermatozoon a time-...
Other methodologies use the concept of Levy stable fractional motions to describe the evolution of a stock’s price, taking volatility into account (Kim et al.2019; Panas2001). Several studies have demonstrated that the fractal dimension is not the inverse of the self-similarity index (Fernández...
fractal dimension serves as a practical tool for quantifying the complexity and self-similarity of fractal objects. It has been used to analyze financial data, predict market trends, identify patterns, and test the impact of interest rates,exchange rates, andinflationon stock-market performance. Fina...
Geometrical fractal patterns of different scaling behaviours are generally determined by the fractal dimension D, which quantifies the change in the geometrical details of the fractal relative to the change in the scales7. One of the widely studied geometrical fractal shapes that can be introduced ...
当然,不可能无限期地将r减少到0。因此,τq的估计是由log Mr曲线的斜率,q作为log r的函数给出的。 Figure 3.9: τq On the basis of τq, it is possible to define the generalized dimensions Dq: 根据τq,可以定义广义尺寸Dq: Figure 3.10: Dimension spectrum Dq维数谱Dq...
Fix the dimension d⩾1. With the notation of Proposition B.2, we have ββ!∑1⩽|αα|⩽n(−d)−|αα||αα|!∑s=1n∑ps(ββ,αα)∏j=1s(|ℓℓj|!(12|ℓℓj|))|kkj|(kkj!)(ℓℓj!)|kkj|=2(n+1)!(12n+1). Proof of Lemma B.3 Define the following...
predominant determinant in heterogeneous resonant media. In fact, the scaling profile ofLCcircuits with inductanceLand capacitanceCrelies more on the form of the lattice array rather than the lattice dimension17,18. This is because the impedance across two opposite farthest sites varies due to the ...
修改Koch曲线岛迭代二叉树临界嵌套层次分维测定The iterative two-fork tree of perimeter and area on a modified Koch curve island is acquired,and from this, the formulae for calculating perimeter and area is obtained.It shows that the theoretical value of fractal dimension could be acquired from ...
light intensity distribution. This is achieved by dividing the system into small boxes of varying sizel. We then determine the minimum number of boxesN(l) needed to cover the system for each sizeland evaluate the fractal dimensionDfusing the power-law scaling\(N(l) \sim l^{ - D_f}\)...