Fractured Fractals and Broken Dreams Self-similar Geometry Through Metric and Measure

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 ofmathematics.