In the present paper, we try to estimate the fractal dimensions of the linear combination of continuous functions with different fractal dimensions. Initially, a general method to calculate the lower and the upper Box dimension of the sum of two cont...
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. In contrast, fractal paramet...
Recent work has shown that more research is needed in applying fractal analysis to multi-resolution remote sensing data for landscape characterization. The purpose of this study was to closely examine the impacts that spatial and spectral resolutions...
In this research, fractal properties of a cell wall in growing cotton fibers were studied. It was found that dependences of specific pore volume (P) and apparent density (ρ) on the scale factor, F = H/h, can be expressed by power-law equations: P...
This paper investigated the surface length of roads from both horizontal and vertical perspectives using the theory of fractal dimension of surfaces and curves. Three progressive experiments were conducted. The first demonstrated the magnitude of the...
Branching patterns are ubiquitous in nature; consequently, over the years many researchers have tried to characterize the complexity of their structures. Due to their hierarchical nature and resemblance to fractal trees, they are often thought to hav...
Zeolite Y and Ti-containing zeolite Y (1%, 2% and 5% TiO2) were synthesized by a hydrothermal seed-assisted method. In order to evidence the evolution of morphology, structure, and fractal dimensions during the zeolitization process at certain time i...
The fractal dimension is a key parameter in quantifying the morphology of aerosol aggregates, which is necessary to understand their radiative impact. Here we used Transmission Electron Microscopy (TEM) images to determine 2D fractal dimensions using...
To study the effects of rock models with different fractal dimensions on their mechanical properties and fracture behavior, three representative numerical rock models, including the digital texture model, the Voronoi polygon model, and the Weibull di...
In this research, the fractal structure of beads of different sizes obtained by the spray-drying of aqueous dispersions of microcrystalline cellulose (MCC) was studied. These beads were formed as a result of the aggregation of rod-shaped cellulose na...
Accurate classification of plant disease by farming robot cameras can increase crop yield and reduce unnecessary agricultural chemicals, which is a fundamental task in the field of sustainable and precision agriculture. However, until now, disease cl...
Fractal theory of particle size distribution (PSD) is a widely used approach in soil science. However, fractal studies on sandstone PSDs are scarce in sedimentology and geology. Taking littoral sandstones in the Carboniferous Donghetang Formation of...
As urbanization progresses in China, the importance of preserving traditional settlements, particularly those located in mountainous areas, is increasingly recognized. To reveal the spatial morphology of mountain settlements influenced by topography,...
In order to cope with climate change and achieve the goal of carbon neutrality, the use of carbonization technology to enhance the performance of cement-based materials and achieve the purpose of carbon sequestration has become a very promising resea...
The Fractal Dimension (FD) of an image defines the roughness using a real number which is highly associated with the human perception of surface roughness. It has been applied successfully for many computer vision applications such as texture analysi...
It is widely acknowledged that the quality of greenway landscape resources enhances the visual appeal of people. While most studies have evaluated visual perception and preference, few have considered the relationship between the distribution of gree...
The present work reports the results of a systematic study on the evolution of the morphological properties of porous carbons derived from coffee waste using a one-pot potassium-hydroxide-assisted process at temperatures in the range of 400–900...
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, th...
(1) Background: An approach for skin cancer recognition and classification by implementation of a novel combination of features and two classifiers, as an auxiliary diagnostic method, is proposed. (2) Methods: The predictions are made by k-nearest ne...
Allometric scaling originates in biology, where it refers to scaling relations between the size of a body part and the size of the whole body when an organism grows. In cities, various allometric relations have also been discovered, such as those bet...
In this paper, we present a second partial solution for the problem of cardinality calculation of the set of fractals for its subcategory of the random virtual ones. Consistent with the deterministic case, we show that for the given quantities of the...
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper i...
Fractal dimension, as a common nonlinear dynamics metric, is extensively applied in biomedicine, fault diagnosis, underwater acoustics, etc. However, traditional fractal dimension can only analyze the complexity of the time series given a single chan...
Frank Lloyd Wright, one of the world’s most famous architects, produced several masterworks in his career, possibly the most celebrated of which is the Kaufmann House, better known as Fallingwater. One of the common arguments historians make ab...
The theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in the explicit volume formula for the tubular neighborhoods of a p-adic fract...
We propose both a probabilistic fractal model and fractal dimension estimator for multi-spectral images. The model is based on the widely known fractional Brownian motion fractal model, which is extended to the case of images with multiple spectral b...
This article is aimed at reviewing and studying the effects of the 2d-3d crossover on the effective fractal and spatial dimensions, as well as on the critical exponents of the physical properties of bulk and bounded systems at criticality. Here we co...
This research aimed to estimate the length of the Citarum watershed boundary because the data are still unknown. We used the concept of fractal’s power law and its relation to the length of an object, which is still not described in other resea...
Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptot...
How many fractals exist in nature or the virtual world? In this paper, we partially answer the second question using Mandelbrot’s fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure. We prove the ex...
Due to the fractal nature of retinal blood vessels, the retinal fractal dimension is a natural parameter for researchers to explore and has garnered interest as a potential diagnostic tool. This review aims to summarize the current scientific evidenc...
In this article, we consider an iterated functions system on the non-Euclidean real projective plane which has a linear structure. Then, we study the fractal dimension of the associated curve as a subset of the projective space and like a set of the...
In order to perform quantitative analysis and predict the wear of the forming channel, this study makes biomass pellets as experimental samples. The surface morphology was scanned by a scanning electron microscope (SEM), and the surface morphology da...
This paper analyzes the extreme limit of iterated function systems (IFSs) when the number of contractions drops to one and the resulting attractors reduce to a single point. While classical fractals have a strictly positive fractal dimension, the deg...
In a famous architectural discussion, Colin Rowe links the geometric properties of two sixteenth century villas by Andrea Palladio and two twentieth century villas by the architect Le Corbusier. Rowe observed that different structural systems produce...
The macroscopic physical properties of rocks are profoundly determined by their microstructure, and the research of accurately characterizing rock pore structure has been extensively carried out in the fields of petroleum engineering and geoscience....
Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D) and power spectrum decay rate (β). Although a relationship between these measures has been derived mathematically, empirical validation across meas...
The complexity and heterogeneity of pore structures in carbonate reservoirs pose significant challenges for accurately characterizing the influence of different pore micro-parameters on reservoir physical properties. Drawing upon the principles of fr...
We introduce a mathematical framework to characterize the hierarchical complexity of AI-generated fractals within the finite resolution constraints of digital images. Our method analyzes images produced by text-to-image models at multiple intensity t...
Let f and g be two continuous functions. In the present paper, we put forward a method to calculate the lower and upper Box dimensions of the graph of f+g by classifying all the subsequences tending to zero into different sets. Using this method, we...
This review article delves into the growing recognition of fractal structures in mesoscale phenomena. The article highlights the significance of realistic fractal-like aggregate models and efficient modeling codes for comparing data from diverse expe...
In this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact...
Tree precise classification and identification of forest species is a core issue of forestry resource monitoring and ecological effect assessment. In this paper, an independent tree species classification method based on fractal features of terrestri...
In tunnel construction, predicting the roughness of discontinuity is significant for preventing the collapse of the excavation face. However, currently, we are unable to use a parameter with invariant properties to quantify and predict the roughness...
A new fusion sensing (FS) method was proposed by using the improved fractal box dimension (IFBD) and a developed maximum wavelet coefficient (DMWC) for fault sensing of an online power cable. There are four strategies that were used. Firstly, the tra...
This article introduces a kind of composite material made of kapok fibre and polycaprolactone by the hot-pressing method. The effects of volume density, mass fraction of kapok fibre, and thickness on the sound-absorption performance of composites wer...
Sampling programs for suspended sediment were carried out in the Usumacinta River and its tributary Grijalva River in Mexico during the years 2016 and 2017. Suspended sediment samples collected during these sampling programs were analyzed in the labo...
The microfractured tight reservoirs in Yongjin Oilfield have low permeability and a complex pore structure. The development of microfractures in reservoirs is crucial for their impact on productivity. To understand the impact of pore structure and mi...
Recently, there is increasing interest in identifying benign and malignant nodules by using ultrasound diagnostic technology, which should be helpful to release patients with benign thyroid nodules from suffering unnecessary needle biopsy. In this wo...
Fractal dimension, a measure of self-similarity in a structure, is a powerful physical parameter for the characterization of structural property of many partially filled disordered materials. Biological tissues are fractal in nature and reports show...
of 41