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