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The Geometry of Fractal Percolation [PDF]
, 2014 A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost every realization of fractal percolation.
Rams, Michal, Simon, Károly
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Fractal geometry of music. [PDF]
Proceedings of the National Academy of Sciences, 1990 Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
K J, Hsü, A J, Hsü
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Advanced Functional Materials, EarlyView.Free‐standing plasmonic gold‐based fractal antennas are fabricated by 3D nanoprinting, employing focused electron beam induced deposition and an optimized purification method to remove carbon while conserving structural fidelity. Simulation and experiment show broadband plasmonic activity, including customizable polarizability, thereby paving the way ...
Verena Reisecker +6 more
wiley +1 more source
An Empirical Study Investigating the Relationship between Land Prices and Urban Geometry
ISPRS International Journal of Geo-Information, 2019 Land prices are among the most important parameters of urbanization and have been an important subject of urban geography studies for many years. The relationship between urban geography and land prices was examined in the first established models, which
Ismail Ercument Ayazli
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Applied Sciences, 2021 In this work, the complex geometry of beams obtained from topology optimization is characterized through the fractal dimension (FD). The fractal dimension is employed as an efficiency measure of the mass distribution in the beams, that is, the capacity ...
Pablo Pavón-Domínguez +3 more
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The 100th anniversary of fractal geometry: From Julia and Fatou through Hausdorff and Besicovitch to Mandelbrot [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамика, 2020 The purpose of this article is to present the biographies of the main creators of fractal geometry from the moment the first ideas arose, when the term «fractal» did not exist, to the present day.
Vdovina, Galina Mihajlovna +1 more
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Smart Catheters for Diagnosis, Monitoring, and Therapy
Advanced Healthcare Materials, EarlyView.This study presents a comprehensive review of smart catheters, an emerging class of medical devices that integrate embedded sensors, robotics, and communication systems, offering increased functionality and complexity to enable real‐time health monitoring, diagnostics, and treatment. Abstract This review explores smart catheters as an emerging class of
Azra Yaprak Tarman +12 more
wiley +1 more source
An approach to study of methods for urban analysis and urban fabric renewal in observation of a city as a multiple fractal structure [PDF]
Arhitektura i Urbanizam, 2007 Urban forms and processes can be observed as fractal structures since in their seemingly chaotic development and complexity it can be noticed an internal order and regularity, which could be quantified and described by the methods of fractal analysis ...
Bogdanov Ana +2 more
doaj
Fractals: An Eclectic Survey, Part II
Fractal and Fractional, 2022 Fractals are geometric shapes and patterns that can describe the roughness (or irregularity) present in almost every object in nature. Many fractals may repeat their geometry at smaller or larger scales.
Akhlaq Husain +3 more
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Advanced Materials, EarlyView.The water permeability of amorphous carbon dots (CDs) is demonstrated by investigating their plasticization. Novel polyamide‐based and amorphous nanoparticles are synthesized by controlling their inner packing density. Water plasticization is evidenced by the decrease of the CDs glass transition temperature with increasing the hydration degree.
Elisa Sturabotti +8 more
wiley +1 more source