Using box-counting and spatial regression, this paper analyzes the morphological characteristics of coastal settlement patterns and their spatial determinants, with a case of the Wen-Tai region on the Chinese eastern coast. Coastal settlement pattern...
The objective of this study is to evaluate the trabecular structure in hypodivergent individuals using fractal analysis, with a particular focus on specific mandibular regions. This study aims to assess the impact of hypodivergent growth patterns on...
We present a mathematical framework for analyzing fractal patterns in AI-generated images using persistent homology. Given a text-to-image mapping
Understanding the spatial patterns of urban land use at both the macro and the micro levels is a central issue in global change studies. Due to the nonlinear features associated with land use spatial patterns, it is currently necessary to provide som...
As a typical pattern recognition method, communication signal modulation involves many complicated factors. Fractal theory can be used for signal modulation feature extraction and recognition because of its good ability to express complex information...
The quantification of the irregular morphology and distribution pattern of mineral grains is an essential but challenging task in ore-related mineralogical research, allowing for tracing the footprints of pattern-forming geological processes that are...
In order to obtain the automatic simulation generation of traditional handmade batik patterns in a computer, this paper proposes the automatic generation method of batik flower patterns based on fractal geometry. Firstly, we analyze the fractal chara...
The Yangtze River Basin serves as a vital ecological barrier in China, with its water conservation function playing a critical role in maintaining regional ecological balance and water resource security. This study takes the Minjiang River Basin (MRB...
In this paper, we present mathematical geometric models and recursive algorithms to generate and design complex patterns using fractal structures. By applying analytical, iterative methods, iterative function systems (IFS), and L-systems to create ge...
Sulfate attack tests were performed on concrete samples with three water-to-cement ratios, and micro-crack growth patterns on concrete surfaces were recorded. The expansive stress and crack nucleation caused by delayed ettringite formation (DEF) were...
Fractal analysis is a mathematical approach employed to study and describe complex patterns and structures across various disciplines, including mathematics, physics, computer science, biology and finance. Introduced by mathematician Benoit Mandelbro...
River networks are spatially complex systems difficult to describe by using simple morphological indices. To this concern, fractal theory arises as an interesting tool for quantifying such complexity. In this case of study, we have estimated for the...
The nymphalid groundplan is an archetypical color pattern of nymphalid butterflies involving three major symmetry systems and a discal symmetry system, which share the basic morphogenesis unit. Here, the morphological and spatial relationships among...
The intersection of fractals, non-Euclidean geometry, spatial autocorrelation, and urban structure offers valuable theoretical and practical application insights, which echoes the overarching goal of this paper. Its research question asks about conne...
This paper reports fractal patterns identified in the complex musical composition DIAPHONIES by Michael Paouris via power-law fractal analysis with sliding-windows of size 1024. From 7,647,232 analysed musical segments of DIAPHONIES, 3,222,832 (42.4%...
Fractal-like nanoparticle two-dimensional patterns forming in diffusion-limited aggregation show variant spatial patterns. However, they have invariant statistical properties in their network topologies, even though their formation is completely in s...
Understanding the urban land-cover spatial patterns is of particular significance for sustainable development planning. Due to the nonlinear characteristics related to the spatial pattern for land cover, it is essential to provide a new analysis meth...
Multiferroic systems are of great interest for technological applications. To improve the fabrication of thin films, stereometric and fractal analysis of surface morphology have been extensively performed to understand the influence of physical param...
The most hydrodynamic swimming position occurs with the head submerged, highlighting the benefit of reduced breathing frequency for efficiency. This study aimed to characterize and compare kinematics between two breaststroke breathing patterns—...
The past several years have witnessed much progress in landscape ecology and fractal analysis. In landscape ecology, the gradient model of landscape patterns (i.e., landscape gradient) has emerged as a new operating paradigm, where most landscape met...
Dendrite, a typical geological pattern, is developed along the bedding plane in limestone and dolomite strata in Jinzigou area, Zhoukoudian, Beijing, China, with a self-similar dendritic morphology. In order to reveal the dynamic mechanism of its for...
Conventional cancer drugs are small molecules that target specific pathways. We introduced PCMS, a 26 kDa supramolecule combining sensors (S), molecular motors (M), and switching molecules (C), integrated within a fourth-generation PAMAM structure (P...
This study models customer patterns using fractal analysis and examines how touchpoints and customer journey mapping shape value to enhance sustainable organizational and customer performance. The analysis is made at cell-level using mathematical mod...
Fractal symmetry is symmetry across scale. If one looks at a branch of a tree its branching pattern is reminiscent of the tree as a whole. Plants exhibit a number of different symmetries, including bilateral, rotational, translational, and fractal; d...
Soil erosion of sloping farmland in the Miyun reservoir area in Beijing has become a serious issue and has threatened the ecological environment and safety of the reservoir area. We used the Taishizhuang Village Non-point Source Pollution Prevention...
Due to their practicality and convenient parametrization, fractals derived from iterated function systems (IFSs) constitute powerful tools widely used to model natural and synthetic shapes. An IFS can generate sets other than fractals, extending its...
This paper investigates the usefulness of multi-fractal analysis and local binary patterns (LBP) as texture descriptors for classifying mammogram images into different breast density categories. Multi-fractal analysis is also used in the pre-processi...
This paper explores the working hypothesis that fractal patterns that closely match those found in nature are more likely to convey a strong sense of genius loci to humans by comparison with ‘Euclidean’ patterns that do not occur in natur...
Brain electrical activity recorded as electroencephalogram data provides relevant information that can contribute to a better understanding of pathologies and human behaviour. This study explores extant electroencephalogram (EEG) signals in search of...
In this paper, informational (Shannon) measures of symmetry are introduced and analyzed for patterns built of 1D and 2D shapes. The informational measure of symmetry
Based on the fractal geometry, a quantitative index describing the development degree of the internal corrosion expansion of reinforced concrete was proposed. This approach could describe the similarity and complexity of the development of corrosion-...
The paper presents an original approach to the localization and analysis of the cracking patterns of cement composites. The lime cement matrix modified with microsilica was evaluated under a two-phase thermal load. For quantitative detection and anal...
The objective of the work was to develop a non-invasive methodology for image acquisition, processing and nonlinear trajectory analysis of the collective fish response to a stochastic event. Object detection and motion estimation were performed by a...
This study aims to address the research gap in the digital analysis of traditional patterns by proposing an image-processing-driven parametric modeling method that combines graphic primitive function modeling with topological reconstruction. The imag...
In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the real...
Spatial heterogeneity of vegetation is an important landscape characteristic, but is difficult to assess due to scale-dependence. Here we examine how spatial patterns in the forest canopy affect those of understory plants, using the shrub Canada buff...
The acquisition of dynamic coastline change at fine spatial and temporal resolution is essential for enhancing sustainable coastal economic development and coastal environmental conservation. Port construction, land reclamation, urban development, an...
This study presents a comprehensive assessment of the hydrodynamic performance of a novel pipe network with tessellated geometry and allometric scales. Numerical simulations were used to evaluate flow behaviour and pressure drop. The comparison geome...
Biomimetic patterning emerges as a promising antibiotic-free approach to protect medical devices from bacterial adhesion and biofilm formation. The main advantage of this approach lies in its simplicity and scalability for industrial applications. In...
The spatiotemporal patterns of urban expansion have attracted worldwide attention and have been generalized into several prevalent hypotheses, such as the diffusion–coalescence hypothesis and the three-growth-type hypothesis. Although many stud...
The design of a 4 × 4 MIMO antenna for UWB communication systems is presented in this study. The single antenna element is comprised of a fractal circular ring structure backed by a modified partial ground plane having dimensions of 30 ×...
Urban form can be reflected by many city elements, such as streets. A street network serves as the backbone of a city and reflects a city’s physical structure. A street network’s topological measures and statistical distributions have bee...
The principles of fractal geometry have revolutionized the characterization of complex geometric objects since Benoit Mandelbrot’s groundbreaking work. Richardson’s method for determining the fractal dimension of boundaries laid the groun...
Land resources in cities are limited, and the cost of green space construction is high. Compared with increasing the amount of green space, maximizing the cooling effect of limited green space has important theoretical and practical significance. Gre...
Unconventional shale reservoirs and typical fine-grained rocks exhibit complicated, oriented features at various scales. Due to the complex geometry, combination and arrangement of grains, as well as the substantial heterogeneity of shale, it is chal...
This study reports a fractal analysis of one-year radon in groundwater disturbances from five stations in China amidst the catastrophic Wenchuan (
This study examines the effects of land use and slope aspect on soil erodibility (K-factor) and the fractal dimension (D) of soil particle size distribution (PSD) in calcareous soils at the watershed scale in western Iran. The study analyzed 113 soil...
Background/Objectives: The blood vessel network can be used as a potential marker of general health. In the oral cavity, it is possible to diagnose systemic diseases as the manifestations of many metabolic, cardiovascular, hematological, and autoimmu...
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 roughness of rock fractures has complex features that affect how fluids move through them. This research looks at how gas and water flows change in rough fractures when they are moved using a model based on fractal geometry. Rough surfaces are cr...
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