Fractal Geography

Our daily universe is rough and infinitely diverse. The fractal approach clarifies and orders these disparities. It helps us to envisage new explanations of geographical phenomena, which are, however, considered as definitely understood. Written for use by geographers and researchers from similar disciplines, such as ecologists, economists, historians and sociologists, this book presents the algorithms best adapted to the phenomena encountered, and proposes case studies illustrating their applications in concrete situations. An appendix is also provided that develops programs written in Mathematica. Contents 1. A Fractal World. 2. Auto-similar and Self-affine Fractals. 3. From the Fractal Dimension to Multifractal Spectrums. 4. Calculation and Interpretation of Fractal Dimensions. 5. The Fractal Dimensions of Rank-size Distributions. 6. Calculation and Interpretation of Multifractal Spectrums. 7. Geographical Explanation of Fractal Forms and Dynamics. 8. Using Complexity Theory to Explain a Fractal World. 9. Land-use Planning and Managing a Fractal Environment.

Cover -- Title Page -- Copyright Page -- Table of Contents -- Introduction -- Chapter 1. A Fractal World -- 1.1. Fractals pervade into geography -- 1.1.1. From geosciences to physical geography -- 1.1.2. Urban geography: a big beneficiary -- 1.2. Forms of fractal processes -- 1.2.1. Some fractal forms that make use of the principle of allometry -- 1.2.2. Time series and processes are also fractal -- 1.2.3. Rank-size rules are generally fractal structures -- 1.3. First reflections on the link between power laws and fractals -- 1.3.1. Brief introduction into power laws -- 1.3.2. Some power laws recognized before the fractal era -- 1.4. Conclusion -- Chapter 2. Auto-similar and Self-affine Fractals -- 2.1. The rarity of auto-similar terrestrial forms -- 2.2. Yet more classes of self-affine fractal forms and processes -- 2.2.1. Brownian, fractional Brownian and multi-fractional Brownian motion -- 2.2.2. Lévy models -- 2.2.3. Four examples of generalizations for simulating realistic forms -- 2.3. Conclusion -- Chapter 3. From the Fractal Dimension to Multifractal Spectrums -- 3.1. Two extensions of the fractal dimension: lacunarity and codimension -- 3.1.1. Some territorial textures di…