Fractured Fractals and Broken Dreams
Self-Similar Geometry Through Metric and Measure
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Fractal geometrics can arise in many different ways mathematically. This book proposes notions of coherent geometric structure, asking what exactly is a fractal "pattern"? A wide range of problems are dealt with, and examples given, which connect to other diverse areas of mathmatics.
This book proposes new notions of coherent geometric structure. Fractal patterns have emerged in many contexts, but what exactly is a `pattern' and what is not? How can one make precise the structures lying within objects and the relationships between them? The foundations laid herein provide a fresh approach to a familiar field. From this emerges a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics.
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