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Fractal Analysis [Minkštas viršelis]

  • Formatas: Paperback / softback, 112 pages, aukštis x plotis: 215x139 mm, weight: 140 g
  • Serija: Quantitative Applications in the Social Sciences
  • Išleidimo metai: 15-Jun-2010
  • Leidėjas: SAGE Publications Inc
  • ISBN-10: 1412971659
  • ISBN-13: 9781412971652
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 112 pages, aukštis x plotis: 215x139 mm, weight: 140 g
  • Serija: Quantitative Applications in the Social Sciences
  • Išleidimo metai: 15-Jun-2010
  • Leidėjas: SAGE Publications Inc
  • ISBN-10: 1412971659
  • ISBN-13: 9781412971652
Kitos knygos pagal šią temą:
Fractal patterns were first identified and are mostly widely known in the natural world, but they also appeared in the social sciences as early as the late 19th century. Brown (anthropology) and Leibovitch (psychology, interdisciplinary science, and mathematics; both Florida Atlantic U.) offer a primer on applying fractal mathematics and statistics to social phenomena. They assume no mathematical background at all, and start with basic ideas like sets and distributions. They also want to persuade social scientists and students that fractal analysis is relevant to their field. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

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.

About the Authors vii
Series Editor's Introduction viii
Preface ix
Introduction to Fractals
1(25)
Mandelbrot
1(1)
What Are Fractals?
2(13)
Sets
2(1)
Self-Similarity
3(2)
Scale Invariance
5(1)
Power Law Relations
5(10)
Fractal Dimension: Quantifying Fractal Properties
15(5)
The Formal Definition of Fractals
20(3)
Topological Dimension
21(1)
Hausdorff Besicovitch Dimension
21(2)
Discussion
23(3)
Fractal Analysis of Frequency Distributions
26(14)
Power Laws
26(13)
Three Methods: Histogram PDF, Multiscale PDF, and Cumulative Distribution
27(5)
Examples With Lots of Data
32(4)
Examples With a Small Amount of Data
36(3)
Summary
39(1)
Fractal Patterns Embedded in Two Dimensions
40(16)
Estimating the Fractal Dimension of Empirical Data
45(9)
The Divider Method: How Long Is the Coast of Britain?
46(2)
The Box-Counting Method
48(5)
Applying the Method in Practice
53(1)
Summary and Discussion
54(2)
Social Processes That Generate Fractals
56(8)
How We Do Our "To Do" Lists: Preferential Priorities
56(1)
How We Kill: Attendant Causes, Self-Organized Critically, and Agent-Based Models
57(2)
How We Network: Preferential Attachment
59(1)
How We Decide Where to Live: Diffusion Limited Aggregation
60(1)
How We Look for Food: Levy Flights
61(1)
How We Live Together: Balancing Cohesive and Disruptive Forces
62(1)
Summary and Discussion
62(2)
Advanced Topics in Fractal Analysis
64(11)
Multiscaling Fractal Patterns
65(2)
Patterns Embedded in Three Dimensions
67(1)
Self-Affine Fractals
67(1)
Fractal Time Series
68(4)
Multifractals
72(1)
Lacunarity
73(1)
Conclusion
74(1)
Final Considerations
75(4)
Should I Try Fractal Analysis?
75(4)
Caveats
76(3)
References 79(6)
Author Index 85(3)
Subject Index 88
Dr. Clifford T. Brown was awarded a B.A. in archaeology cum laude from Yale University. He earned his Masters 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.