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Fractal Examples 1
The Triadic Cantor Dust 1
The Sierpinski Gasket 7
A Space of Strings 11
Turtle Graphics 14
Sets Defined Recursively 18
Number Systems 31
Remarks 35
Metric Topology 41
Metric Space 41
Metric Structures 48
Separable and Compact Spaces 57
Uniform Convergence 65
The Hausdorff Metric 71
Metrics for Strings 75
Remarks 81
Topological Dimension 85
Zero-Dimensional Spaces 85
Covering Dimension 91
Two-Dimensional Euclidean Space 99
Inductive Dimension 104
Remarks 113
Self-Similarity 117
Ratio Lists 117
String Models 122
Graph Self-Similarity 125
Remarks 133
Measure Theory 137
Lebesgue Measure 137
Method I 146
Two-Dimensional Lebesgue Measure 152
Metric Outer Measure 155
Measuresfor Strings 159
Remarks 162
Fractal Dimension 165
Hausdorff Measure 165
Packing Measure 169
Examples 177
Self-Similarity 185
The Open Set Condition 190
Graph Self-Similarity 199
Graph Open Set Condition 205
Other Fractal Dimensions 210
Remarks 216
Additional Topics 225
Deconstruction 225
Self-Affine Sets 229
Self-Conformal 234
A Multifractal 238
A Superfractal 242
Remarks 247
Appendix 251
Terms 251
Notation 254
Examples 255
Reading 255
References 257
Index 261
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Add Measure, Topology, and Fractal Geometry, For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so , Measure, Topology, and Fractal Geometry to the inventory that you are selling on WonderClubX
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Add Measure, Topology, and Fractal Geometry, For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so , Measure, Topology, and Fractal Geometry to your collection on WonderClub |