Fractals and Chaos Simplified for the Life Sciences

2017-07-07 02:10:07

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

Page xi



		CONTENTS



		Part I Fractals



		Introduction



		1.1.1 The Difference between Non-Fractal and Fractal Objects



		4



		1.1.2 The Sizes of the Features of Non-Fractal and Fractal Objects



		6



		1.1.3 The Properties of Fractals



		8



		Self-Similarity



		1.2.1 Two Types of Self-Similarity



		12



		1.2.2 Examples of Self-Similarity in Space



		14



		1.2.3 Examples of Self-Similarity in Time



		16



		1.2.4 he Currents through Ion Channels Are Self-Similar in Time



		18



		1.2.5 The Open and Closed Times of Ion Channels Are Statistically Self-Similar



		20



		1.2.6 More Examples of Self-Similarity



		22



		1.2.7 Biological Implications of Self-Similarity



		24



		Scaling



		1.3.1 Self-Similarity Implies a Scaling Relationship



		28



		1.3.2 Scaling Relationships



		30



		1.3.3 Example of a Power Law Scaling of a Spatial Object: The Length of the Coastline of Britain



		32



		1.3.4 Examples of Power Law Scalings of Spatial Objects: The Surfaces of Cell Membranes



		34



		1.3.5 Example of a Power Law Scaling of a Process in Time: Ion Channel Kinetics



		36



		1.3.6 The Physical Significance of the Scaling Relationship of Ion Channel Kinetics



		38



		1.3.7 More Examples of Scaling Relationships



		40



		1.3.8 Biological Implications of Scaling Relationships



		42

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

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