Fractured Fractals and Broken Dreams: Self-Similar Geometry Through Metric and Measure

Fractal patterns have emerged in many contexts, but what exactly is a pattern? How can one make precise the structures lying within objects and the relationships between them? This book proposes new notions of coherent geometric structure to provide a fresh approach to this familiar field. It develops a new concept of self-similarity called BPI or big pieces of itself, which makes the field much easier for people to enter. This new framework is quite broad, however, and has the potential to lead to significant discoveries. The text covers a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. Although fractal geometries arise in many different ways mathematically, comparing them has been difficult. This new approach combines accessibility with powerful tools for comparing fractal geometries, making it an ideal source for researchers in different areas to find both common ground and basic information.


Author: Guy David, Stephen Semmes
Publisher: Clarendon Press
Published: 02/19/1998
Pages: 224
Binding Type: Hardcover
Weight: 1.08lbs
Size: 9.21h x 6.14w x 0.56d
ISBN: 9780198501664

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