Fractal and multifractal characterization of the scaling geometry of an urban bus-transport network

• A FD around D  = 1.5 characterizes the fractal nature of the bus-transport network of Cordoba (Spain) for small spatial scales.

[1]  Brian Berkowitz,et al.  Fractal and multifractal measures of natural and synthetic , 1997 .

[2]  Pierre Frankhauser,et al.  The fractal approach. A new tool for the spatial analysis of urban agglomerations , 1998, Population.

[3]  M. Maiolo,et al.  On the fractal description of natural channel networks , 1996 .

[4]  Zu-Guo Yu,et al.  Determination of multifractal dimensions of complex networks by means of the sandbox algorithm. , 2014, Chaos.

[5]  Segun Goh,et al.  Emergence of Criticality in the Transportation Passenger Flow: Scaling and Renormalization in the Seoul Bus System , 2014, PloS one.

[6]  Roberto Gaudio,et al.  Multifractal analysis of river networks: Sandbox approach , 2004 .

[7]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[8]  C. Tricot Curves and Fractal Dimension , 1994 .

[9]  Roberto Gaudio,et al.  Multifractal behaviour of river networks , 2000 .

[10]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[11]  J. Hołyst,et al.  Statistical analysis of 22 public transport networks in Poland. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Francisco J. Jiménez-Hornero,et al.  Multifractal analysis of axial maps applied to the study of urban morphology , 2013, Comput. Environ. Urban Syst..

[13]  Kousuke Yakubo,et al.  Multifractality of complex networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Sankaran Mahadevan,et al.  Box-covering algorithm for fractal dimension of weighted networks , 2013, Scientific Reports.

[15]  Pan Di,et al.  Weighted complex network analysis of travel routes on the Singapore public transportation system , 2010 .

[16]  Zu-Guo Yu,et al.  Multifractal analysis of complex networks , 2011, 1108.5014.

[17]  S. Havlin,et al.  Self-similarity of complex networks , 2005, Nature.

[18]  Antoine Saucier,et al.  Textural analysis of disordered materials with multifractals , 1999 .

[19]  S. Havlin,et al.  How to calculate the fractal dimension of a complex network: the box covering algorithm , 2007, cond-mat/0701216.

[20]  Ignacio Rodriguez-Iturbe,et al.  On the multifractal characterization of river basins , 1992 .

[21]  T. Vicsek,et al.  Determination of fractal dimensions for geometrical multifractals , 1989 .

[22]  I. Rodríguez‐Iturbe,et al.  Self-organized fractal river networks. , 1993, Physical review letters.

[23]  E. Wang,et al.  Spontaneous fractal aggregation of gold nanoparticles and controlled generation of aggregate-based fractal networks at air/water interface. , 2005, The journal of physical chemistry. B.

[24]  Stéphane Roux,et al.  Spatial distribution of human population in France: exploring the modifiable areal unit problem using multifractal analysis , 2016 .

[25]  Azeddine Beghdadi,et al.  Entropic analysis of random morphologies , 1994 .

[26]  Xinping Xu,et al.  Scaling and correlations in three bus-transport networks of China , 2007, 0708.2606.

[27]  G. D. Jeong,et al.  Fractal characteristics of dense stream networks , 2001 .

[28]  L. Benguigui,et al.  The fractal dimension of some railway networks , 1992 .

[29]  Lucien Benguigui,et al.  The fractal structure of Seoul’s public transportation system , 2003 .

[30]  S. Gabriele,et al.  Lithologic control on the multifractal spectrum of river networks , 2006 .

[31]  Pierre Frankhauser,et al.  Fractal Dimensions of the Built-up Footprint: Buildings versus Roads. Fractal Evidence from Antwerp (Belgium) , 2013 .

[32]  J. M. Antón,et al.  under a Creative Commons License. Nonlinear Processes in Geophysics , 2022 .

[33]  Manfred Schroeder,et al.  Fractals, Chaos, Power Laws: Minutes From an Infinite Paradise , 1992 .

[34]  A. Marangoni,et al.  Microstructure and fractal analysis of fat crystal networks , 2006 .

[35]  Isabelle Thomas,et al.  Defining and characterizing urban boundaries: A fractal analysis of theoretical cities and Belgian cities , 2013, Comput. Environ. Urban Syst..

[36]  Rainer A. Leitgeb,et al.  Imaging of the parafoveal capillary network and its integrity analysis using fractal dimension , 2011 .

[37]  Lei Li,et al.  Multifractal and singularity analysis of weighted road networks , 2014 .

[38]  Jensen,et al.  Erratum: Fractal measures and their singularities: The characterization of strange sets , 1986, Physical review. A, General physics.

[39]  A. Rinaldo,et al.  Configuration entropy of fractal landscapes , 1998 .

[40]  T. Vicsek,et al.  Multifractal Geometry of Diffusion-Limited Aggregates , 1990 .

[41]  I. A. El-Sonbaty,et al.  Prediction of surface roughness profiles for milled surfaces using an artificial neural network and fractal geometry approach , 2008 .

[42]  Yanguang Chen,et al.  Spatiotemporal Evolution of Urban Form and Land-Use Structure in Hangzhou, China: Evidence from Fractals , 2010 .

[43]  Local entropy characterization of correlated random microstructures , 1996, cond-mat/9611015.

[44]  M. Batty The Size, Scale, and Shape of Cities , 2008, Science.

[45]  I. Rodríguez‐Iturbe,et al.  The fractal nature of river networks , 1988 .

[46]  Zu-Guo Yu,et al.  Multifractal analysis of weighted networks by a modified sandbox algorithm , 2015, Scientific reports.

[47]  Jing Z. Liu,et al.  A three-dimensional fractal analysis method for quantifying white matter structure in human brain , 2006, Journal of Neuroscience Methods.

[48]  Michael Batty,et al.  Multifractal to monofractal evolution of the London street network. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Nacim Betrouni,et al.  Fractal and multifractal analysis: A review , 2009, Medical Image Anal..

[50]  Michael Batty,et al.  Fractal Cities: A Geometry of Form and Function , 1996 .

[51]  L Benguigui,et al.  A Fractal Analysis of the Public Transportation System of Paris , 1995 .