natural fractals

To explore the effect of different stress environments on fault-slip rockbursts. Bidirectional shear friction experiments with different lateral pressures were conducted on precracked syenogranites buried at 800 m. The macroscopic statistical parameters (cumulative number of AE events, magnitude and b value) and local characteristic parameters (amplitude and dominant frequency) of acoustic emission during the stick-slip process under different lateral pressures were investigated. In addition, based on fractal theory, the nonlinear characteristics of AE spectrum were analyzed...

The efficient patient-independent and interpretable framework for electroencephalogram (EEG) epileptic seizure detection (ESD) has informative challenges due to the complex pattern of EEG nature. Automated detection of ES is crucial, and Explainable Artificial Intelligence (XAI) is urgently needed to justify algorithmic predictions in clinical settings. Therefore, this study implements an XAI-based computer-aided ES detection system (XAI-CAESDs), comprising three major modules including of feature engineering module, a seizure detection module, and an explainable decision-making process module in a smart healthcare system...

In this paper, we investigate a fractal-fractional-order mathematical model with the influence of hospitalized patients and the impact of vaccination with fractal-fractional operators. The respective derivatives are considered in the Caputo, Caputo Fabrizio, and Atangana-Baleanu senses of fractional order <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> and fractal dimension <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math> ...

Comparisons of the beneficial effects of nature-based versus indoor physical activity have been extensively reported, but existing research addresses mainly aerobic activity (running, jogging), not other types. It is unclear if the psychological effects extend to functionality, i.e., if participants perform their activities better in nature. The present study investigated how engaging in similar exercise in nature-based and indoor settings differs in affective valence, perceived exertion, visual attention, movement adaptability, heart rate variability, and performance...

This paper presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. Using two interfering moiré potentials, we generate a supermoiré pattern that renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we use electronic transport measurements to identify the position of these gaps as a function of the carrier density...

Characterizations in terms of fractals are typically employed for systems with complex and multiscale descriptions. A prominent example of such systems is provided by the human brain, which can be idealized as a complex dynamical system made of many interacting subunits. The human brain can be modeled in terms of observable variables together with their spatio-temporal-functional relations. Computational intelligence is a research field bridging many nature-inspired computational methods, such as artificial neural networks, fuzzy systems, and evolutionary and swarm intelligence optimization techniques...

The concept of fractal was popularized by Mandelbrot as a tool to tame the geometrical structure of objects with infinite hierarchical depth. The key aspect of fractals is the use of simple parsimonious rules and initial conditions, which when applied recursively can generate unbounded complexity. Fractals are structures ubiquitous in nature, being present in coast lines, bacteria colonies, trees, and physiological time series. However, within the field of cognitive science, the core question is not which phenomena can generate fractal structures, but whether human or animal minds can represent recursive processes, and if so in which domains...

People are continually exposed to the rich complexity generated by the repetition of fractal patterns at different size scales. Fractals are prevalent in natural scenery and also in patterns generated by artists and mathematicians. In this chapter, we will investigate the powerful significance of fractals for the human senses. In particular, we propose that fractals with mid-range complexity play a unique role in our visual experiences because the visual system has adapted to these prevalent natural patterns...

In parallel to medical applications, exploring how neurons interact with the artificial interface of implants in the human body can be used to learn about their fundamental behavior. For both fundamental and applied research, it is important to determine the conditions that encourage neurons to maintain their natural behavior during these interactions. Whereas previous biocompatibility studies have focused on the material properties of the neuron-implant interface, here we discuss the concept of fractal resonance - the possibility that favorable connectivity properties might emerge by matching the fractal geometry of the implant surface to that of the neurons...

The fractal dimension of cognition refers to the idea that the cognitive processes of the human brain exhibit fractal properties. This means that certain patterns of cognitive activity, such as visual perception, memory, language, or problem-solving, can be described using the mathematical concept of fractal dimension.The idea that cognition is fractal has been proposed by some researchers as a way to understand the complex, self-similar nature of the human brain. However, it's a relatively new idea and is still under investigation, so it's not yet clear to what extent cognitive processes exhibit fractal properties or what implications this might have for our understanding of the brain and clinical practice...

The structural complexity of brain tumor tissue represents a major challenge for effective histopathological diagnosis. Tumor vasculature is known to be heterogeneous, and mixtures of patterns are usually present. Therefore, extracting key descriptive features for accurate quantification is not a straightforward task. Several steps are involved in the texture analysis process where tissue heterogeneity contributes to the variability of the results. One of the interesting aspects of the brain lies in its fractal nature...

Several natural phenomena can be described by studying their statistical scaling patterns, hence leading to simple geometrical interpretation. In this regard, fractal geometry is a powerful tool to describe the irregular or fragmented shape of natural features, using spatial or time-domain statistical scaling laws (power-law behavior) to characterize real-world physical systems. This chapter presents some works on the usefulness of fractal features, mainly the fractal dimension and the related Hurst exponent, in the characterization and identification of pathologies and radiological features in neuroimaging, mainly, magnetic resonance imaging...

Among the significant advances in the understanding of the organization of the neuronal networks that coordinate the body and brain, their complex nature is increasingly important, resulting from the interaction between the very large number of constituents strongly organized hierarchically and at the same time with "self-emerging." This awareness drives us to identify the measures that best quantify the "complexity" that accompanies the continuous evolutionary dynamics of the brain. In this chapter, after an introductory section (Sect...

This chapter begins by showing the difference between fractal geometry and fractal analysis. The text shows the difference between mathematical and natural fractals and how they are best defined by explaining the concept of fractal analysis. Furthermore, the text presents the most famous technique of fractal analysis: the box-counting method. Defining this method and showing the methodology that leads to the precise value of the fractal (i.e., the box) dimension is done by demonstrating the images of human dentate neurons...

We applied four fractal dimension estimation algorithms on the temporal electrical impedance signal of normal MDCK type II cell cultures monitored by ECIS technique and showed that the fractal dimension due to micromotion allows discriminating processes not sensed by the spectral impedance of the culture. In this work we subjected cell cultures to electric current damage and drug exposure to analyze the changes in the fractal structure of the temporal signal. Among the changes presented and detected are the differentiation between a healthy monolayer and one exposed to a drug, as well as the distinction between a seeding process and a wound-healing process performed by electric current...

This article presents a new design of a compact fractal antenna that operates across various wireless communication applications with wideband functionality. With a peak gain of 6.8 dB and a radiation efficiency ranging from 91% to 94%, the designed antenna operates in the frequency range of 3.2-7.5 GHz. The antenna consists of a rectangular radiator with integrated rectangular slots on one side of an FR4 substrate, while a partial ground plane is etched on the other side. The fabricated prototype was tested and measured...

In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class...

Microstructure reconstruction serves as a crucial foundation for establishing process-structure-property (PSP) relationship in material design. Confronting the limitations of variational autoencoder and generative adversarial network within generative models, this study adopted the denoising diffusion probabilistic model (DDPM) to learn the probability distribution of high-dimensional raw data and successfully reconstructed the microstructures of various composite materials, such as inclusion materials, spinodal decomposition materials, chessboard materials, fractal noise materials, and so on...

The macro petrographic compositions and its pore characteristics of coal reservoir play critical role in the accumulation and development of coalbed methane (CBM). In this paper, the pore characteristics of vitrain and durain were analyzed through the experiment and fractal theory. The results indicated that the micropores and microfractures develop in vitrain, and that transitional pores develop in durain. The pore volume and specific surface area (SSA) of vitrain are larger than those of durain, with the micropore SSA of vitrain being 35% higher than that of durain...

Electroencephalography (EEG) is a crucial non-invasive medical tool for diagnosing neurological disorder called encephalopathy. There is a requirement for powerful signal processing algorithms as EEG patterns in encephalopathies are not specific to a particular etiology. As visual examination and linear methods of EEG analysis are not sufficient to get the subtle information regarding various neuro pathologies, non-linear analysis methods can be employed for exploring the dynamic, complex and chaotic nature of EEG signals...