This insightful work explains Mandelbrot's fractal geometry and describes some of its most interesting applications. Fractal geometry exploits a characteristic property of the real world--self-similarity--to find simple rules for the assembly of complex natural objects. Beginning with the foundations of measurement in Euclidean geometry, the authors progress from analogues in the geometry of random fractals to applications spanning the natural sciences, including the developmental biology of neurons and pancreatic islets, fluctuations of bird populations, patterns in vegetative ecosystems, and even earthquake models. Written to enable students and researchers to master the methods of this timely subject, the book steers a middle course between the formality of many papers in mathematics and the informality of picture-orientated books on fractals. It is both a logically developed text and an essential fractals for users handbook. It is an essential resource for researchers and students in ecology, biology, applied mathematics, and plant and environmental sciences.
PART I: Introduction 1. Our View of Nature PART II: The Mathematics of Random Fractals 2. Fractals and Power Law Scaling 3. Dimension of Patterns 4. Dimension of Graphs of Functions 5. The Fourier Transform PART III: The Bridge to Applications 6. Modelling Spatial and Temporal Patterns 7. Alternative Models 8. Examples 9. Fractal Analysis of Time Series PART IV: Case Studies 10. Case Studies: Pattern and Process in Vegetative Ecosystems 11. Scaling Behavior of Density-dependent Populations under Random Noise PART V: The Toolbox 12. Programs
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