257.

[Cover] [Abbreviated Contents] [Contents] [Index]

Page xii

		Dimension

		1.4.1 Dimension: A Quantitative Measure of Self-Similarity and Scaling

		46

		1.4.2 The Simplest Fractal Dimension: The Self-Similarity Dimension

		48

		1.4.3 More General Fractal Dimensions: The Capacity Dimension

		50

		1.4.4 More General Fractal Dimensions: The Hausdorff-Besicovitch Dimension

		52

		1.4.5 Example of Determining the Fractal Dimension: Using the Self-Similarity Dimension

		4

		1.4.6 Example of Determining the Fractal Dimension: Using the Capacity Dimension and Box Counting

		56

		1.4.7 Example of Determining the Fractal Dimension: Using the Scaling Relationship

		58

		1.4.8 The Topological Dimension

		60

		1.4.9 The Embedding Dimension

		62

		1.4.10 Definition of a Fractal

		64

		1.4.11 Example of the Fractal Dimension: Blood Vessels in the Lungs

		66

		1.4.12 More Examples of the Fractal Dimension

		68

		1.4.13 Biological Implications of the Fractal Dimension

		70

		Statistical Properties

		1.5.1 The Statistical Properties of Fractals

		74

		1.5.2 Self-Similarity Implies That the Moments Do Not Exist

		76

		1.5.3 Example Where the Average Does Not Exist: The St. Petersburg Game

		78

		1.5.4 Example Where the Average Does Not Exist: Diffusion Limited Aggregation (DLA)

		80

		1.5.5 Example Where the Variance Does Not Exist: The Roughness of Rocks

		82

		1.5.6 Example Where the Variance Does Not Exist: Electrical Activity in Nerve Cells

		84

		1.5.7 Statistical Analysis of the Electrical Activity in Nerve Cells

		86

		1.5.8 Example Where the Variance Does Not Exist: Blood Flow in the Heart

		88

		1.5.9 Example Where the Variance Does Not Exist: Volumes of Breaths

		90

		1.5.10 Example Where the Variance Does Not Exist: Evolution

		92

		1.5.11 The Distribution of Mutations Is the Same as in the St. Petersburg Game

		94

		1.5.12 Statistical Properties and the Power Spectra

		96

		1.5.13 How to Measure the Properties of Fractal Data

		98

		1.5.14 More Examples of the Statistical Properties of Fractals

		100

		1.5.15 Biological Implications of the Statistical Properties of Fractals

		102

		1.5.16 Biological Implications of the Statistical Properties of Fractals (continued)

		104

 

[Cover] [Abbreviated Contents] [Contents] [Index]