Titlebook: Measure, Topology, and Fractal Geometry; Gerald A. Edgar Textbook 19901st edition Springer-Verlag New York 1990 DEX.Mathematica.addition.a

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Metric Topology,would be the first chapter of the book; but I included instead some more fractal-like material as Chapter 1. Chapter 2 is a more technical chapter. Have patience! It really is useful for the understanding of the rest of the book.

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Springer-Verlag New York 1990

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Fractal Examples,A few basic mathematical examples of fractals will be introduced in this chapter. Their analysis, and especially the question of what makes them “fractals” must be postponed until much later in the book.

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Self-Similarity,There are several variant notions of “dimension” that may be classified as fractal dimensions. The most widely used is known as the Hausdorff dimension. It will be considered in Chapter 6. We begin here with the ., a fractal dimension that is easier to define (but not as useful).

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Hausdorff Dimension,Next we come to the “Hausdorff dimension”. This is the dimension singled out by Mandelbrot when he defined “fractal”. It is perhaps a bit more difficult to define than some of the other kinds of dimension that have been (and will be) considered. But it is also the most useful of the fractal dimensions.

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https://doi.org/10.1007/978-1-4757-4134-6DEX; Mathematica; addition; algebraic topology; algorithms; computer; fractal; fractal geometry; geometry; me