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 differentiated by their lacunarity -- 3.1.2. Codimension as a relative fractal dimension -- 3.2. Some corrections to the power laws: semifractals, parabolic fractals and log-periodic distributions -- 3.2.1. Semifractals and double or truncated Pareto distributions -- 3.2.2. The parabolic fractal model -- 3.2.3. Log-periodic distributions -- 3.3. A routine technique in medical imaging: fractal scanning -- 3.4. Multifractals used to describe all the irregularities of a set defined by measurement -- 3.4.1. Definition and characteristics of a multifractal -- 3.4.2. Two functions to interpret: generalized dimension spectrum and singularity spectrum.

3.4.3. An approach that is classical in geosciences but exceptional in social sciences -- 3.4.4. Three potential generalizations -- 3.5. Conclusion -- Chapter 4. Calculation and Interpretation of Fractal Dimensions -- 4.1. Test data representing three categories of fractals: black and white maps, grayscale Landsat images and pluviometric chronicle series -- 4.2. A first incontrovertible stage: determination of the fractal class of the geographical phenomenon studied -- 4.2.1. Successive tests using Fourier or wavelet decompositions -- 4.2.2. Decadal rainfall in Barcelona and Beirut are fractional Gaussian noise -- 4.3. Some algorithms for the calculation of the fractal dimensions of auto-similar objects -- 4.3.1. Box counting, information and area measurement dimensions for auto-similar objects -- 4.3.2. A geographically inconclusive application from perception -- 4.4. The fractal dimensions of objects and self-affine processes -- 4.4.1. A multitude of algorithms -- 4.4.2. High irregularity of decadal rainfall for Barcelona and Beirut -- 4.5. Conclusion -- Chapter 5. The Fractal Dimensions of Rank-size Distributions -- 5.1. Three test series: rainfall heights, urban hierarchies and attendance figures for major French museums -- 5.2. The equivalence of the Zipf, Pareto and Power laws -- 5.3. Three strategies for adjusting the rank-size distribution curve -- 5.3.1. A visual approach using graphs -- 5.3.2. Adjusting the only linear part of the curve -- 5.3.3. Choosing the best adjustment, and therefore the most pertinent law -- 5.3.4. Which rank-size distribution should be used for Italian towns, the main French agglomerations and all French communes? -- 5.4. Conclusion -- Chapter 6. Calculation and Interpretation of Multifractal Spectrums.

6.1. Three data sets for testing multifractality: a chronicle series, a rank-size distribution and satellite images -- 6.2. Distinguishing multifractal and monofractal phenomena -- 6.2.1. An initial imperfect visual test -- 6.2.2. A second statistical test: generalized correlation dimensions -- 6.3. Various algorithms for calculation of the singularity spectrum -- 6.3.1. Generalized box-counting and variogram methods -- 6.3.2. Methods derived from wavelet treatment -- 6.3.3. Interpretation of singularity spectrums -- 6.4. Possible generalizations of the multifractal approach -- 6.5. Conclusion -- Chapter 7. Geographical Explanation of Fractal Forms and Dynamics -- 7.1. Turbulence generates fractal perturbations and multifractal pluviometric fields -- 7.2. The fractality of natural hazards and catastrophic impacts -- 7.3. Other explanations from fields of physical geography -- 7.4. A new geography of populations -- 7.5. Harmonization of town growth distributions -- 7.6. Development and urban hierarchies -- 7.7. Understanding the formation of communication and social networks -- 7.8. Conclusion -- Chapter 8. Using Complexity Theory to Explain a Fractal World -- 8.1. A bottomless pit debate -- 8.2. General mechanisms for explaining power laws -- 8.3. Four theories on fractal universality -- 8.3.1. Critical self-organization theory -- 8.3.2. Béjan's constructal theory -- 8.3.3. Nottale's scale relativity theory -- 8.3.4. A general theory of morphogenesis -- 8.3.5. Chaos and fractal analysis theory -- 8.4. Conclusion -- Chapter 9. Land-use Planning and Managing a Fractal Environment -- 9.1. Fractals, extreme values and risk -- 9.1.1. Under-estimated hazards in preliminary risk assessments -- 9.1.2. Fractal networks, fighting epidemics and Internet breakdowns -- 9.2. Fractals, segmentation and identification of objects in image processing.

9.2.1. New image processing tools -- 9.2.2. Some little-used fractal approaches using a GIS -- 9.3. Fractals, optimization and land management -- 9.4. Fractal beauty and landscaping -- 9.5. Conclusion -- Conclusion -- C.1. Some tools and methods for quantifying and qualifying multiscale coarseness and irregularity -- C.2. A recap on geographical irregularities and disparities -- C.3. A paradigm that gives rise to new land-use management practices -- Appendices -- A.1. Preliminary thoughts on fractal analysis software -- A.2. Instructions for the following programs -- A.3. Software programs for the visual approach of a satellite or cartographicseries or image -- A.4. Software programs for calculating fractal dimensions for a chronicle orfrequency series -- A.5. Software programs for calculating the fractal dimensions of a satellite image or map -- A.6. Software programs for calculating multifractal spectrums of a series and an image -- Bibliography -- Index.