Box-counting dimensions of generalised fractal nests

Miličić, Siniša

doi:10.1016/j.chaos.2018.05.025

Cited by 9 publications

(4 citation statements)

References 6 publications

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“…One way to calculate the area of the region R limited by the graph of a non-negative function y = f (x) continues in an interval [a, b] and the lines x = a, x = b, and y = 0, is to use the Box Counting Method (BC), [10][11][12][13][14][15] summarized as follows. Algorithm BC is based on filling the space of a set (surface in this case) with a set of objects of the same area or boxes N (δ) as a function of the size δ of the coverings (or boxes).…”

Section: Box Counting Algorithmmentioning

confidence: 99%

New Method to Calculate the Energy and Fractal Dimension of the Daily Electrical Load

2020

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This paper proposes a method to calculate the degree of fluctuation of the daily electrical load-curve using fractal dimension, which is a quantitative estimator of spatial complexity. The conventional methods for forecasting have not studied such a variable, being a new parameter that can be included to characterize the electrical load. The method of fractal dimension also allows us to propose a new numerical method to calculate the integral of a function, using the trapezoid rule, but splitting the curve with fractal segments, to discover other observations, which allows the elevation of new theoretical approaches. The results are compared with the other methods such as the conventional trapezoid rule and the box-counting. It is then a new contribution that expands the universal knowledge on the subject. The case study is the daily electrical load-curve, where the energy demanded corresponds to the area of the [Formula: see text] region bounded by the curve.

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Section: Box Counting Algorithmmentioning

confidence: 99%

New Method to Calculate the Energy and Fractal Dimension of the Daily Electrical Load

2020

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“…For some other examples of "irregular" spiral trajectories and the calculation of their box dimensions and Minkowski content see e.g. [2,18,20,24,27,26]. In this paper we will often speak about a trajectory "near the origin (x, y) = (0, 0)".…”

Section: Introductionmentioning

confidence: 99%

Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations

Huzak

Vlah²,

Žubrinić³

et al. 2023

Applied Mathematics and Computation

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“…There are various algorithms for calculating FD, including the box-counting (BC) algorithm [20], the Katz algorithm [21], and the Higuchi algorithm [22]. The Higuchi and box-counting algorithms have been widely used due to their practical applicabilities and fast speed [23][24][25][26]. In our previous study, a roughness scaling extraction (RSE) algorithm was proposed [27,28], and it has a higher accuracy and anti-noise performance compared with other traditional algorithms.…”

Section: Introductionmentioning

confidence: 99%

Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal

et al. 2022

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Fractal algorithms for signal analysis are developed from geometric fractals and can be used to describe various complex signals in nature. A roughness scaling extraction algorithm with first-order flattening (RSE-f1) was shown in our previous studies to have a high accuracy, strong noise resistance, and a unique capacity to recognize the complexity of non-fractals that are common in signals. In this study, its disadvantage of a long calculation duration was addressed by using a dichotomy-binary strategy. The accelerated RSE-f1 algorithm (A-RSE-f1) retains the three above-mentioned advantages of the original algorithm according to theoretical analysis and artificial signal testing, while its calculation speed is significantly accelerated by 13 fold, which also makes it faster than the typical Higuchi algorithm. Afterwards, the vibration signals of the milling process are analyzed using the A-RSE-f1 algorithm, demonstrating the ability to distinguish different machining statuses (idle, stable, and chatter) effectively. The results of this study demonstrate that the RSE algorithm has been improved to meet the requirements of practical engineering with both a fast speed and a high performance.

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Box-counting dimensions of generalised fractal nests

Cited by 9 publications

References 6 publications

New Method to Calculate the Energy and Fractal Dimension of the Daily Electrical Load

New Method to Calculate the Energy and Fractal Dimension of the Daily Electrical Load

Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations

Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal

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