Fractal Analysis

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Overview

A specialized presentation of fractal analysis oriented to the social sciences

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 programs 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.

Learn more about “The Little Green Book” - QASS Series! Click Here

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Product Details

Meet the Author

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.

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.

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Table of Contents

Ch. 1 Introduction to Fractals 1

Mandelbrot 1

What Are Fractals? 2

Fractal Dimension: Quantifying Fractal Properties 15

The Formal Definition of Fractals 20

Discussion 23

Ch. 2 Fractal Analysis of Frequency Distributions 26

Power Laws 26

Summary 39

Ch. 3 Fractal Patterns Embedded in Two Dimensions 40

Estimating the Fractal Dimension of Empirical Data 45

Summary and Discussion 54

Ch. 4 Social Processes That Generate Fractals 56

How We Do Our "To Do" Lists: Preferential Priorities 56

How We Kill: Attendant Causes, Self-Organized Criticality, and Agent-Based Models 57

How We Network: Preferential Attachment 59

How We Decide Where to Live: Diffusion Limited Aggregation 60

How We Look for Food: Levy Flights 61

How We Live Together: Balancing Cohesive and Disruptive Forces 62

Summary and Discussion 62

Ch. 5 Advanced Topics in Fractal Analysis 64

Multiscaling Fractal Patterns 65

Patterns Embedded in Three Dimensions 67

Self-Affine Fractals 67

Fractal Time Series 68

Multifractals 72

Lacunarity 73

Conclusion 74

Ch. 6 Final Considerations 75

Should I Try Fractal Analysis? 75

References 79

Author Index 85

Subject Index 88

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