Fractal Analysis

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Clifford Brown - Florida Atlantic University, USA
Larry Liebovitch - Florida Atlantic University, USA

Volume: 165

Series:
Quantitative Applications in the Social Sciences

Other Titles in:
Quantitative/Statistical Research

April 2010 | 112 pages | SAGE Publications, Inc

This primer uses straightforward language to give the reader step-by-step instructions for identifying and analyzing fractal patterns and the social process that create them. By making fractals accessible to the social science students, this book has a significant impact on the understanding of human behavior.

Key Features:

- Detailed examples help readers learn and understand the analytical methods presented.

- Matlab codes for programmes allow users to implement, on their own, some of the techniques described in the text. Visit http:/www.ccs.fau.edu/~liebovitch/larry.html for more details.

- Clear and logical explanations of fractals and their analysis enable the instructor to easily teach and the student to easily learn the material.

This is the only book designed to introduce fractal analysis to a general social science audience.

About the Authors

Series Editor's Introduction

Preface

Chapter 1. Introduction to Fractal Analysis

Mandelbrot

What Are Fractals?

Fractal Dimension: Quantifying Fractal Properties

The Formal Definition of Fractals

Discussion

Chapter 2. Fractal Analysis of Frequency Distributions

Power Laws

Summary

Chapter 3. Fractal Patterns Embedded in Two Dimensions

Estimating the Fractal Dimension of Empirical Data

Summary and Discussion

Chapter 4. Social Processes That Generate Fractals

How We Do Our "To Do" Lists: Preferential Priorities

How We Kill: Attendant Causes, Self-Organized Criticality, and Agent-Based Models

How We Network: Preferential Attachment

How We Decide Where to Live: Diffusion Limited Aggregation

How We Look for Food: Lévy Flights

How We Live Together: Balancing Cohesive and Disruptive Forces

Summary and Discussion

Chapter 5. Advanced Topics in Fractal Analysis

Multiscaling Fractal Patterns

Patterns Embedded in Three Dimensions

Self-Affine Fractals

Fractal Time Series

Multifractals

Lacunarity

Conclusion

Chapter 6. Final Considerations

Should I Try Fractal Analysis?

References

Author Index

Subject Index

Preview this book

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Clifford T. Brown

Dr. Clifford T. Brown was awarded a B.A. in archaeology cum laude from Yale University. He earned his Master’s and doctoral degrees from Tulane University. He has published a number of articles on fractal analysis in archaeology and anthropology. He teaches both undergraduate and graduate classes in the Department of Anthropology at Florida Atlantic University. Among the graduate classes is a required seminar entitled “Quantitative Reasoning in Anthropology’ that includes extensive statistical content for social scientists. More About Author

Larry S. Liebovitch

Dr. Larry S. Liebovitch was awarded a B.S. in physics summa cum laude from the City College of New York and his A.M. and Ph.D. in astronomy from Harvard University. He has published articles on fractal and nonlinear analysis in biophysical, medical, and psychological systems. He teaches both undergraduate and graduate classes in psychology, interdisciplinary science, and mathematics at Florida Atlantic University. Among his undergraduate courses are Applications of Fractals to Psychology for psychology students. More About Author

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