Articles tagged with Fractals
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Study of abstract structures, patterns, quantities, relationships, and logical reasoning through pure and applied mathematical disciplines. Encompasses algebra, calculus, geometry, topology, number theory, analysis, discrete mathematics, mathematical logic, set theory, probability, statistics, and computational mathematics. Investigates mathematical structures, theorems, proofs, algorithms, functions, equations, and the rigorous logical frameworks underlying quantitative reasoning. Provides the foundational language and tools for all scientific fields, enabling precise description of natural phenomena, modeling of complex systems, and the development of technologies across physics, engineering, computer science, economics, and all quantitative sciences.
Researchers found that children's paintings share similarities with Pollock's work, featuring smaller fine-scale patterns and simpler trajectories. Adults' paintings, on the other hand, had higher paint densities and more complex fractal patterns.
A research team at the University of Turku developed a novel biomimetic fabrication technique to replicate bioinspired microstructures found in plant leaf skeletons. The resulting surfaces offer superior flexibility, breathability, and transparency, making them ideal for next-generation flexible electronics.
Researchers at Princeton University have directly observed a long-predicted quantum fractal pattern, known as Hofstadter's butterfly, in a real material. The discovery was made possible by a breakthrough in materials engineering and uses scanning tunneling microscopy to study the electron energy levels.
Researchers developed a fabrication technique to overcome design challenges for scalable single-photon detectors, enabling ultra-fast detection of photons regardless of direction or polarization. The study provides a comprehensive guide to fabricating high-quality fractal SNSPDs with improved sensitivity and system detection efficiency.
Using fractal math, researchers found that artists' preservation of a tree's branch diameter scaling exponent enables viewers to easily recognize trees, even without other distinguishing features. This universal factor applies across styles and cultures, linking artistic beauty with mathematical complexity.
Researchers found branch patterns in art to mirror those in nature, with values of α ranging from 1.5 to 2.8, corresponding to natural trees. Abstract artworks can be visually identified as trees using realistic α values, while works deviating from scaling exhibit reduced recognition.
A team of scientists has reported the experimental observation of a nonlinear fractal higher-order topological insulator, which supports a rich variety of topological corner states. The fractal structure can exhibit hybrid corner states and co-existing outer corner states with different internal structures.
Researchers have identified a universal blueprint for mammalian brain shape, describing the cerebral cortex as following a fractal pattern across species. The study suggests that cortices across primate species resemble this universal scaling law and self-similarity, revealing a common set of mechanisms governing cortical folding.
Theoretical physicists at Utrecht University have discovered that fractals might hold the key to making electric currents flow without energy loss. By growing fractal structures on top of semiconductors, scientists have created materials with zero-dimensional corner modes and lossless one-dimensional edge states.
A study discovers that traditional Chinese ice-ray lattice designs can provide unique stiffness and strength under asymmetric loads, offering an alternative to conventional gridshells. The research also explores the potential of integrating complex geometry into facade design and micro-scale material design.
Researchers analyzed the physical principles of dendritic painting, a technique that uses ink droplets to create intricate fractals. The study found that the thickness of the paint layer and the concentration of diluting medium are key factors in controlling the outcome of dendritic painting.
A novel method to monitor range shifts of protected organisms and expanding noxious species has been developed. By marking the average position of the 'connectivity limit' over time, researchers offer a statistically reliable approach to tracking changes in species distributions.
Researchers at Purdue University have discovered that superconductive images are actually 3D and disorder-driven fractals. The team used fractal mathematics to characterize the shapes of electrons in a cuprate high-temperature superconductor, revealing patterns that challenge current understanding of quantum materials.
Researchers found that rock ants display a striking regular meandering pattern when exploring their surroundings, combining systematic movement with random walks. This behavior may make their search more efficient by reducing the frequency of crossing their own paths.
Researchers from the University of Calabria used 3D printing to turn chaotic structures into unique jewelry, exploring the beauty of complex systems. The project combines art and science, allowing students to develop their knowledge and creativity by building and designing their own Chua circuit-inspired jewelry.
Scientists at University of Cambridge uncover dynamical fractal in spin ice material, with fractals visible in both dynamic and static properties. The discovery was made possible by analyzing magnetic noise from the material's electron spins.
A new study proposes a mathematical tool to understand the fractal structure of quark-gluon plasma, which is formed in high-energy collisions. The fractal structure explains some phenomena seen in these collisions, including particle momentum distributions that follow Tsallis statistics.
Researchers describe a simple argument showing that basins in high-dimensional systems should look like high-dimensional octopi. The volume of these basins cannot be correctly approximated by a hypercube, which fails to encompass the vast majority of points in the basin.
Researchers used fractal analysis to study brain network patterns while listening to a story. The results show that complex thoughts are reflected in high-order dynamic correlations in neural activity patterns.
Urban scaling laws, observed in cities worldwide, can be explained by the spatial geometry of a city. Researchers mapped building heights and assigned dots to people living in buildings to determine fractal dimensions, revealing a constant sublinear scaling exponent that determines city growth rates.
Researchers at the University of Oregon have discovered a fractal network of connecting neurons in the brain, which balances energy costs to facilitate communication between neurons. The study's findings have implications for designing implants to treat macular degeneration and other retinal diseases.
A study by University of Oregon researchers found that children aged 3 prefer visual fractal patterns, similar to adults, indicating an early development of this preference. The study suggests that exposure to Euclidean geometry in childhood may shape this preference.
A Brazilian research team developed a model to describe the spatial and temporal evolution of epidemic diseases. The SIR model predicts that contagion occurs discontinuously but follows a fractal pattern, which can help plan more effective social isolation programs with less socio-economic impact.
Researchers are developing an AI tool to analyze brain MRIs and identify indexes of structural complexity, providing insights into the development and progression of hereditary ataxia. The fractal dimension analysis could potentially predict clinical development and inform new treatment approaches.
The team used terahertz-frequency light to probe the vibrational modes of lysozyme, discovering that its glassy and fractal nature explains the anomalously large vibrations. The study may lead to improvements in industrial glass manufacturing by understanding disordered materials.
Researchers developed a new way to measure habitat complexity, which is crucial for understanding biodiversity and conservation status. The method uses three metrics: rugosity, fractal dimension, and height range, and can accurately predict the distribution of biodiversity in complex ecosystems.
Researchers created a photonic Floquet topological insulator in a periodically driven fractal lattice, exhibiting topological edge states with real-space Chern number 1. The simulations show wavepackets can propagate along the outer and inner edges without penetration or backscattering.
Researchers at Los Alamos National Laboratory have developed 3D printed fractal cubes with closely spaced voids that dissipate shockwaves five times better than solid cubes. The innovative design could lead to new types of lightweight armor and structural materials effective against explosions and impacts.
Researchers from Universidad Carlos III de Madrid analyze the physical behavior of hydrogen flames, revealing they can propagate in extremely narrow gaps and form fractal patterns. This unexpected behavior has significant implications for designing safe hydrogen storage systems and reducing greenhouse gas emissions.
Scientists at Tokyo University of Science develop a new quantum algorithm to analyze complex networks, finding that fractal properties play a crucial role in determining optimal computational time. The researchers propose a new scaling hypothesis to gain more insight into different fractal geometries.
Elderly individuals with random changes in daily movement are at greater risk of frailty, disability, and death. Analyzing daily motor activity using fractal physiology may help predict wellness and health outcomes.
Researchers have applied a novel method to model bacterial colony growth, replicating fractal patterns observed in nature. The study used agent-based modeling to simulate the behavior of bacteria, varying parameters such as cell division speed and mechanical forces.
Researchers at Rutgers University have developed a technique to assemble proteins into fractal shapes that resemble flowers, trees, or snowflakes. This innovation could lead to new technologies such as bioremediation filters and synthetic matrices for studying human disease and tissue engineering.
Scientists from the Polish Academy of Sciences analyzed mountain ranges worldwide and found a universal similarity in their structure. The analysis showed that the distribution of ridges and valleys follows a power-law nature, with most nodes having low degree and few hubs having high degree.
Researchers have simulated surface roughness creation and fractal characteristic emergence on multiple scales. The study proposes that subsurface crack propagation drives the self-affine nature of rough surfaces, with implications for earthquake prediction and material durability.
Researchers at EPFL's LSMS digitally simulated how surface roughness changes over time, capturing the entire process from initial geometry to final fractal geometry. Their findings suggest that wear debris is present for surfaces to develop self-affine roughness and could lead to significant reductions in energy consumption and costs.
Moritz Lang and Mikhail Shkonikov from IST Austria have discovered a new property of the Abelian sandpile model, showing that it can exhibit dynamics similar to those of real-world sand dunes. The researchers used a specific method to add sand grains to the model, which induced self-similar fractal patterns reminiscent of the Mandelbro...
Researchers demonstrate fractal light creation using laser technology, confirming a long-held prediction. The discovery has potential applications in various fields, including imaging and medicine.
The study discovered fractal characteristics in gene expression, enabling the prediction of gene-to-gene interactions. This knowledge can help scientists engineer cells to perform specific tasks, such as drug delivery for cancer treatment.
A new movement monitoring system using Real Time Location System (RTLS) technology helps identify residents at risk of falling, enabling early interventions to prevent hospitalizations. By tracking wristbands with RTLS sensors, a study found that fractal dimension values can indicate long-term cognitive impairment due to dementia.
A fractal-shaped electrode design enhances charge delivery for smaller neural stimulation targets, potentially prolonging device lifespan and improving resolution. The new shape facilitates faster Faradaic charge transfer, resulting in more efficient energy use.
Researchers at North Carolina State University have discovered that applying low voltage to gallium indium can induce the formation of unique fractal patterns. The discovery has significant implications for controlling liquid metals, as it allows for reversible and effective manipulation of surface tension.
Researchers at the University of Oregon have made significant progress in developing fractal-based retinal implants that could potentially restore vision to people with macular degeneration. The implants use fractal geometry to stimulate retinal neurons, achieving a 90% increase in neuron stimulation while using less voltage.
Balinese rice farmers' planting patterns create fractal designs that yield optimal harvests without global planning. The pattern's emergence is driven by water availability and pest damage, making the system more resilient. Farmers adapt locally, taking individual decisions that optimize their own harvests, resulting in a stable system.
Colorado State University scientists have shed light on the relationship between cell membranes and cortical actin cytoskeletons. They used superresolution imaging to visualize proteins on the cell surface, revealing sophisticated patterns of movement that are directly caused by the fractal nature of the actin network.
Researchers have unlocked the mystery of why people see multiple images in Rorschach inkblots by analyzing fractal characteristics at the blots' edges. The team found that higher fractal dimension values produce more visual perceptions, with inkblots generating up to 300 differently perceived images.
Researchers analyzed brushstrokes of famous artists' paintings for fractal patterns, detecting changes linked to neurodegenerative disorders. The study suggests a potential new method for identifying Alzheimer's disease in its early stages.
Researchers analyzed over 113 literary works, finding fractal and multifractal patterns in sentence length and narrative structure. The study suggests that literary texts exhibit hierarchical organization and correlations among data at various complexity levels.
Researchers from Penn State have developed a model that uses fractal geometry to describe the layering in silvery fish skin, which can guide the design of devices such as broadband mirrors. The technique has potential applications in advanced optical coatings, laser protection, infrared imaging systems, and photovoltaics.
A scholar of religion proposes a new theory on religious diversity, suggesting that religions share more commonalities than differences. He argues that interreligious theology can help believers overcome prejudices and develop appreciation for other religions.
Scientists have discovered a fractal pattern at the atomic level in metallic glasses, contradicting previous assumptions about empty space. This finding enables the study of material properties and has implications for fields like mathematics, physics, and computer science.
A US patent has been granted to Oregon researchers for their fractal-based approach to electronic implants that match up with specific neurons. The technology, developed by University of Oregon physicist Richard Taylor, aims to overcome biological rejection issues and toxicity concerns in current implant designs.
Scientists studying human cervical epithelial cells found that distinct fractal patterns emerge only at the point of progression towards cancer. These findings could inspire targeting specific weak points in pathways leading to cancer development. Fractal patterns may hold importance in understanding cancer metastasis, where cancer cel...
Researchers calculate tortuosity in Sierpinski carpet models using finite volume method, revealing a linear relationship between generations and tortuosity. This study enhances understanding of transport properties in porous media, crucial for various fields like oil recovery and groundwater engineering.
A new analysis method called fractal Fourier analysis breaks down complicated signals into well-understood building blocks, similar to conventional Fourier analysis. This approach could help scientists better understand natural phenomena like nerve impulses and brain waves.
A synopsis of the carabid beetle tribe Lachnophorini reveals 24 new species, shedding light on their diversity and evolution. The study aims to provide taxonomic relationships for carabid beetles using morphological and molecular attributes.
Researchers found that extreme market crashes contradict multi-fractal scaling, a phenomenon where financial data patterns self-similarly scale. The study suggests understanding multi-fractal structure can aid early detection of impending extreme events.
A new model shows that molecules in glassy materials settle into a fractal hierarchy of states, unifying mathematics and theory. The findings explain several behaviors seen in glasses, including avalanching, which leads to crystallization.
Researchers found fractal nature in football dynamics, with ball and player positions exhibiting self-similarity. The study suggests the superiority of one team persists for only 30 seconds before changing hands.
The study suggests that tree-like structures in lungs minimize energy losses and optimize proximity to alveoli, allowing efficient oxygen delivery. This evolutionary process led to the development of mammalian respiration, distinct from fish-style breathing.