Fractal geography / André Dauphiné.

Includes bibliographical references (pages 221]-238) and index.

Print version record.

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 era1.4. 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 lacunarity3.1.2. Codimension as a relative fractal dimension; 3.2. Some corrections to the power laws: semifractals, parabolicfractals 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 setdefined by measurement; 3.4.1. Definition and characteristics of a multifractal.

3.4.2. Two functions to interpret: generalized dimension spectrumand singularity spectrum3.4.3. 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 classof the geographical phenomenon studied.

4.2.1. Successive tests using Fourier or wavelet decompositions4.2.2. Decadal rainfall in Barcelona and Beirut are fractionalGaussian noise; 4.3. Some algorithms for the calculation of the fractal dimensionsof auto-similar objects; 4.3.1. Box counting, information and area measurementdimensions 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.

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 writ.