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What is Fractal

Handbook of Research on Financial and Banking Crisis Prediction through Early Warning Systems
A natural phenomenon or a mathematical set that exhibits a repeating pattern which can be replicated at every scale.
Published in Chapter:
Understanding Chaos as an Indicator of Economic Stability
Rohnn B. Sanderson (Brescia University, USA)
DOI: 10.4018/978-1-4666-9484-2.ch017
Abstract
With what appears to be the increasing sensitivity of economic/financial systems to various events, whether they be natural disaster, changing financial products or government policy, the need to understand how volatility has changed in modern economic systems and how to recognize when volatility will occur is a topic that is extremely important. This topic has been categorized under various topics such as: business cycles, chaos, dynamic systems, fractals, Brownian motion and super cycles just to name a few. The author believes that all of these areas need to be considered at once when analyzing dynamic phenomena which may have varying degrees of the aforementioned. This chapter will implement a Hicksian Accelerator to develop a framework for stylized facts of general dynamic macroeconomic behavior. The chapter will then implement the model and begin the process of estimating the degree of and sensitivity to volatility in a macro economy.
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An Edge Detection Approach for Fractal Image Processing
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Higher Dimensions of Clusters of Intermetallic Compounds
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Unlocking the Hidden Power of the Mobile
A fractal is an image that comprises two distinct attributes: infinite detail and self-similarity. Examples of such images include the Mandelbrot and Julia Sets, the Koch Curve and the Menger Sponge.
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Folds and Refolds: Space Generation, Shapes, and Complex Components
Geometric pattern repeated at progressively smaller scales, where each iteration is about a reproduction of the image to produce completely irregular shapes and surfaces that can not be represented by classical geometry. Fractals are generally self-similar (each section looks at all) and are not subordinated to a specific scale. They are used especially in the digital modeling of irregular patterns and structures in nature. Defined in 1975 by the mathematician Benoit Mandelbrot.
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Higher-Dimensional Space of Nanoworld
The set is self-similar, that is, uniformity at different scales.
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The Interpretation of Vernacular Architecture through Fractal Models: In the Case of Iran, Masouleh Village
The theory of perceiving non-linear shapes, which are especially inspired from nature. The term fractal comes from the Latin word ‘fractus’ meaning ‘broken’ or ‘irregular’ or ‘unsmooth’.
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Entropy, Chaos, and Language
Curves or shapes that has the property of self-similarity (chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size).
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Fractal Dimension of the EEG in Alzheimer's Disease
A self-similar structure whose geometrical and topographical features are recapitulated in miniature on finer and finer scales.
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A Comparison Between the Microstrip and the Co-Planar Wave-Guide Antennas in Ultra-Wide-Band Applications by Using Fractal Geometry
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