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Full Description
The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems.
This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.
Contents
1. Some Remarks on Multivariate Fractal Approximation 2. Fractal Interpolation: From Global to Local, to Nonstationary and Quaternionic 3. A Study on Fractal Operator Corresponding to Non-stationary Fractal Interpolation Functions 4. Fractal Calculus 5. Perspective of Fractal Calculus on Types of Fractal Interpolation Functions 6. On the Borel Regularity of the Relative Centered Multifractal Measures 7. A Mixed Multifractal Analysis of Vector-valued Measures: Review and Extension to Densities and Regularities of Non-necessary Gibbs Cases 8. Multifractal Dimensions and Fractional Differentiation in Automated Edge Detection on Intuitionistic Fuzzy Enhanced Image
