References
[1]. S. Chen, “Assessing Awareness, Interest, and Knowledge of Fractal Geometry among SecondaryMathematics Teachers in the United States and China,” Dissertations, 129, 2015. https://aquila.usm.edu/dissertations/129
[2]. Z. Khanbabaei, A. Karam, G. Rostamizad, “Studying Relationships between the Fractal Dimension of the Drainage Basins and Some of their Geomorphological CharacteristicsInternational,”J. Geosci., Vol.4, pp.636-642, 2013.
[3]. B. Jiang, “Scaling as a Design Principle for Cartography,”Annals of GIS, Vol.23, Issue.1, pp.67-79, 2017.
[4]. D.P. Feldman, “Chaos and Dynamical Systems,”Princeton University Press, Princeton, 2019.
[5]. M.F. Goodchild, “Reimagining the History of GIS,”Annals of GIS,Vol.24, Issue.1, pp.1–8, 2018.
[6]. Y. Chen, “Multi-scaling Allometric Analysis for Urban and Regional Development. Physica A, Vol.465, pp.673–689, 2017.
[7]. C.C. Hepcan, “Quantifying Landscape Pattern and Connectivity in a Mediterranean Coastal Settlement: The Case of the Urla District, Turkey,” Environ. Monit. Assess., Vol.185, pp.143–155, 2012.
[8]. C. Konijnendijk, “The 3-30-300 Rule for Urban Forestry and Greener Cities,”Biophilic Cities Journal,2021. Available online:https://static1.squarespace.com/static/5bbd32d6e66669016a6af7e2/t/6101ce2b17dc51553827d644/1627508274716/330300+Rule+Preprint_7-29-21.pdf
[9]. K. J. Kabo-bah, T. Guoan , X. Yang, J. Na L. Xiong,“Erosion Potential Mapping using Analytical Hierarchy Process (AHP) and Fractal Dimension,”Heliyon,7, e07125, 2021
[10]. G. Boeing,“Measuring the Complexity of Urban form and Design,”Urban Des. Int.,Vol.23, pp.281–292, 2018.
[11]. B.N.J. Persson,“On the Fractal Dimension of Rough Surfaces,”Tribology Letters,Vol.54, pp.99–106, 2014.
[12]. Jiang B. and Brandt A, “A Fractal Perspective on Scale in Geography,”ISPRS Int. J. Geo-Inf., Vol.5, Issue.6, p.95,2016. doi:10.3390/ijgi5060095e
[13]. S.G. Plexida, A.I. Sfougaris,I.P. Ispikoudis, V.P. Papanastasis,“Selecting Landscape Metrics as Indicators of Spatial Heterogeneity - a Comparison among Greek Landscapes,”Int. J. Appl. Earth Obs. Geoinf.,26, pp.26–35, 2014.
[14]. Y. Feng, Y. Liu,“Fractal Dimension as an Indicator for Quantifying the Effects of Changing Spatial Scales on Landscape Metrics,”Ecol. Indicat.,53, pp.18–27, 2015.
[15]. G. Chen, Q.Cheng, R. Zuo, “Fractal Analysis of Geochemical Landscapes using Scaling Noise Model,”J. Geochem. Explor.,161, pp.62–71, 2016.
[16]. W. He, Y. Huang, X. Dong, X. Yan, D. Li,“Study on Landscape Pattern Based on Landsat-8 in the Center of Chengdu City,” China. J. Environ. Protect.,Vol.7, Issue.7, p.1050, 2016.
[17]. J.-C. Kim, K.Jung, “Fractal Tree Analysis of Drainage Patterns,”Water Resour. Manag.,Vol.29, Issue.4, pp.1217-1230, 2016.
[18]. B.E. Vieux, “Watersheds and Drainage Networks. In: Distributed Hydrologic Modeling Using GIS,” Springer, pp.115–131, 2016.
[19]. H. Yang, B.A. Baudet, T. Yao,. , “Characterization of the Surface Roughness of Sand Particles using an Advanced Fractal Approach,”Proc. R. Soc. A, Vol.472, Issue.2194, p.20160524, 2016.
[20]. J.F. García-Hidalgo, J. Gil, M. Arias, P. Gumiel, B. Carenas,“Multifractal Characteristics of Bed Thickness in the Late Turonian–Early Coniacian Sequence (Iberian Ranges, Spain) ,”Rev. Soc. Geol. Espana,Vol.29, Issue.1, 2016.
[21]. S. Laurita, F. Agosta, F. Cavalcante, A. Rustichelli, M. Giorgioni, “Shearing of Synsedimentary Carbonate Breccia along Strike-slip Faults, Altamura Fm., Southern Italy,”Ital. J. Geosci.,Vol.135, Issue.1, pp.41-54, 2016.
[22]. Y. Liu, Y. Liu, L. Sun, J. Liu,“Multiscale Fractal Characterization of Hierarchical Heterogeneity in Sandstone Reservoirs,”Fractals,Vol.24Issue.3, 1650032, 2016.
[23]. A.A.Y. Sun, “WheelerLab: An interactive program for sequence stratigraphic analysis of seismic sections, outcrops and well sections and the generation of chronostratigraphic sections and dynamic chronostratigraphic sections,” SoftwareX, Vol.6, pp.19-24, 2017.
[24]. F. Peng,J. Li, M. Long,“Identification of Natural Images and Computer-generated Graphics Based on Statistical and Textural Features,”J. Forensic Sci.,Vol.60Issue. 2,pp.435–443, 2015.
[25]. J.F. Hughes, A. Van Dam, M. Mc Guire, D.F. Sklar, J.D. Foley, S.K. Feiner, K. Akeley,“Computer Graphics: Principles and Practice”, AddisonWesley Professional,2013.(UNIT I, II, III, IV). Bharathidasan Engineering College,2015.
[26]. H. Kim,M.J. Dorantes, D.G. Schulze, B. Benes, “Computer Graphics Procedural Modeling of Soil Structure. In: Digital Soil Morphometrics,” Springer, pp.133-144, 2016.
[27]. J.P. Reis, E.A. Silva, P. Pinho,“A Review of Spatial Metrics for Urban Growth And Shrinkage,”In: The Routledge Handbook Of Planning Research Methods, 279, 2014.
[28]. M. Jevric, M. Romanovich, “Fractal Dimensions of Urban Border as a Criterion for Space Management,”Procedia Eng., Vol.165, pp.1478–1482, 2016.
[29]. Y. Chen, “Defining Urban and Rural Regions by Multifractal Spectrums of Urbanization,”Fractals,Vol.24, 1650004, 2016.
[30]. H. Wang, S. Luo, T. Luo, “Fractal Characteristics of Urban Surface Transit and Road Networks: Case Study of Strasbourg, France,”Adv. Mech. Eng., Vol.9, 1687814017692289, 2017. [CrossRef]
[31]. M. Purevtseren, B. Tsegmid, M. Indra, M. Sugar, “The Fractal Geometry of Urban Landuse: The case of Ulaanbaatar city, Mongolia,”Land, Vol.7, 67, 2018.
[32]. K. Falconer, “Fractal Geometry: Mathematical Foundations and Applications,” 3rd ed.; Wiley: Chichester, UK, p.400, 2014.
[33]. Y. Chen, J. Wang, J. Feng, “Understanding the Fractal Dimensions of Urban Forms through Spatial Entropy,”Entropy,Vol.19, 600, 2017.
[34]. M. Purevtseren, M. Indra, G. Dashlegtseg, C. Badamdorj, D. Battumur, U. Dorjbaatar, “Urban Expansion Survey by Fractal Dimension (Case of Khovd Town, Mongolia),”Advances in Engineering Research,Vol.206, pp.126-132, 2021.
[35]. R. Lemoy, G. Caruso, “Evidence for the Homothetic Scaling of Urban Forms,”Environ. Plan. B Urban Anal. City Sci., Vol.47, pp.870–888, 2018.
[36]. F. Sémécurbe, C. Tannier, S.G. Roux, “Applying two Fractal Methods to Characterise the Local and Global Deviations from Scale Invariance of Built Patterns throughout Mainland France,”J. Geogr. Syst.,Vol.21, pp.271–293, 2019.
[37]. Q. Ma, J. Wu, C. He, G. Hu, “Spatial Scaling of Urban Impervious Surfaces Across Evolving Landscapes: From Cities to Urban Regions Landscape,”Urban Plan., Vol.175, pp.50–61, 2018.
[38]. M.G. Sreelekha, K. Krishnamurthy, M.V.L.R. Anjaneyulu,“Fractal Assessment of Road Transport System,”Eur. Transp., 5, 65, 2017.
[39]. D. Umemoto, N. Ito, “Power-law Distribution Found in City-scale Traffic Flow Simulation,”J. Phys. Conf. Ser.,Vol.2122, 012006, 2021.
[40]. F. Martínez, “Cities’ Power Laws: The Stochastic Scaling Factor,”Environ. Plan. B Plan. Des., Vol.43, pp.257–275, 2015.
[41]. Y. Chen, Y. Wang, X. Li, X. , “Fractal Dimensions Derived from Spatial Allometric Scaling of Urban Form,”Chaos Soliton Fract., Vol.126, pp.122–134, 2019.
[42]. Q. Nie, J. Xu, Z. Liu, Z. , “Fractal and Multifractal Characteristic of Spatial Pattern of Urban Impervious Surfaces,”Earth Sci. Inform., Vol.8, pp.381–392, 2015.
[43]. M. Purevtseren, B. Tsegmid, M. Indra, M. Sugar, “The Fractal Geometry of Urban Landuse: The Case of Ulaanbaatar City, Mongolia,”Land,Vol.7, Issue.67, 2018.
[44]. Y. Mo, J. Liu, S. Lv , “GIS-based Analysis of Fractal Features of the Urban Road Network,” IEEE,2015.
[45]. M. Karpinski, S. Kuznichenko, N. Kazakova, O. Fraze-Frazenko, D. Jancarczyk, “Geospatial Assessment of the Territorial Road Network by Fractal Method, Future Internet,Vol.12, pp.201-2013, 2020.
[46]. M.A. Shahsavari, P. Afzal, A. Hekmatnejad,, “Identification of Geochemical Anomalies Using Fractal and LOLIMOT Neuro-Fuzzy modeling in Mial Area, Central Iran. Journal of Mining & Environment, Vol.11, Issue.1, pp.99-117, 2020.
[47]. C. Ni, S. Zhang, Z. Chen, Y. Yan, Y. Li, “Mapping the Spatial Distribution and Characteristics of Lineaments Using Fractal and Multifractal Models: A Case Study from Northeastern Yunnan Province, China. Scientific Reports, Vol.7, 10511, 2017. DOI:10.1038/s41598-017-11027-0
[48]. K.J. Kabo-baha, T. Guoana, X. Yanga, J. Naa, L. Xionga, “ Erosion potential mapping using analytical hierarchy process (AHP) and fractal dimension,”Heliyon,Vol.7,e0712, 2021.
[49]. M.Y. Mahmoodi, A. Nourbakhsh, T. Kusky, “GIS-based Assessment of Surface Deformation Patterns using Fractal Analysis of Topography: Kharmankuh anticline, Zagros Mountains,”Iran. Journal of Himalayan Earth Sciences,Vol.49, Issue.2, pp.118-128, 2016.
[50]. M.D. Nurujjaman, A. Hossain, P. Ahmed, “A Review of Fractals Properties: Mathematical Approach,”Science Journal of Applied Mathematics and Statistics,Vol.5, Issue.3, pp.98-105, 2017. doi: 10.11648/j.sjams.20170503.11
[51]. B. Jiang, A. Brandt, “A Fractal Perspective on Scale in Geography,”ISPRS International Journal of Geo-Information, Vol.5, Issue.6, p.95, 2016. doi:10.3390/ijgi5060095e
[52]. B. Jiang, “Geospatial Analysis Requires a Different Way of Thinking: The Problem of Spatial Heterogeneity,”GeoJournal, Vol.80, pp.1–13, 2015.
[53]. J. Bendix, “Scale, Direction, and Patterns in RiparianVegetation-Environment Relationships,”Annals of the Associationof American Geographers, Vol.84, pp.652–665, 1994.
[54]. N.S.N. Lam, “Fractals and Scale in Environmental Assessment and Monitoring,”In Scale and Geographic Inquiry; Sheppard, E., McMaster, R.B., Eds.; Blackwell Publishing: Oxford, UK, pp.23–40, 2004.
[55]. M.F. Goodchild, “Reimagining the history of GIS,” Annals of GIS, 2018. Available from https://doi.org/10.1080/19475683.2018.1424737.
[56]. L. Yilmaz, “Meandering Fractals in Water Resources Management,”Applied and Computational Mathematics.Vol.9 Issue.2,pp.26-29, 2020. doi: 10.11648/j.acm.20200902.12
[57]. B. Zohuri, “Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists,” Springer International Publishing Switzerland, 2015.
[58]. G. Rodríguez-Iturbe, A.Rinaldo, “Fractal River Basin, Change and Self Organization,” Cambridge University Press, Cambridge, 547, 2001.
[59]. F. Terzi, H.S. Kaya, “Analyzing Urban Sprawl Patterns through Fractal Geometry: The Case of Istanbul Metropolitan Area,” Paper 144; Centre for Advanced Spatial Analysis: London, UK, 2008.
[60]. P.M. Torrens, M. Alberti, “Measuring Sprawl,” Paper 27; Centre for Advanced Spatial Analysis: London, UK, 2000.
[61]. M. Purevtseren, M. Indra, B. Otgongerel, “Urban Compactness Measurement of the Ulaanbaatar City,”Geogr., Vol.14, pp.51–59, 2015.
[62]. C. Reynoso C., “The Impact of Chaos and Complexity Theories on Spatial Analysis - Problems and Perspectives,”In the 2005 24th Research Symposium: Reading Historical Spatial Information from around the World: Studies of Culture and Civilization Based on GIS Data, Kyoto Japan, 7-11 February, Vol.63 Issue.2, pp.1037-1068, 2005.
[63]. K. Janowicz, R.Zhu, J. Verstegen, G. McKenzie, B. Martins, L. Cai, “Six GIScience Ideas That Must Die_AGILE,”GIScience Series,Vol.3, Issue.7, 2022, pp.1. Available from https://doi.org/10.5194/agile-giss-3-7-2022
[64]. S. Rezaei, M. Lotfi, P. Afzal, M. R. Jafari, and M. Shamseddin Meigoony, “Delineation of CU Prospects Utilizing Multifractal Modeling and Stepwise Factor Analysis in Noubaran 1:100,000 sheet, Center of Iran,” Arab. J. Geosci.,Vol.8, Issue.9, pp.7343–7357, 2015.
[65]. G. Chen and Q. Cheng, “Fractal Density Modelingof Crustal Heterogeneity from the KTB Deep Hole,” J.Geophys. Res. Solid Earth,Vol.122, Issue.3, pp.1919–1933, 2017.
[66]. P. Gao, A.A. Cushman, G. Liu, et al., “Fractal: a Tool for Characterizingthe Fractality of Landscape Gradients from a newPerspective,”ISPRS Int J Geo Inf, Vol.8, Issue.466, 2019.
[67]. N.C. Coops,T. Hermosilla, M.A. Wulder,et al., “A ThirtyYear, Fine-scale, Characterization of Area Burned in CanadianForests Shows Evidence of Regionally IncreasingTrends in the last Decade,” PLoS ONE,Vol.13, e0197218, 2018.
[68]. F. Sémécurbe, C. Tannier, S.G. Roux, “Applying two Fractal Methods to Characterise the Local and Global Deviations from ScaleInvariance of Built Patterns Throughout Mainland France,”J. Geogr. Syst., Vol.21, pp.271–293, 2019.
[69]. Y. Chen, Y. Wang, X. Li, “Fractal Dimensions Derived from Spatial Allometric Scaling of Urban Form,”Chaos Soliton Fractal.,Vol.126, 122–134, 2019.
[70]. R. Murcio, A.P. Masucci, E. Arcaute, M. Batty, “Multifractal to Monofractal Evolution of the London Street Network,”Phys. Rev. E,Vol.92, 062130, 2015.
[71]. J. Zhao, Y. Chen, S. Li, , “Bi-fractal Structure and Evolution of the Beijing–Tianjin–Hebei Region Urban Land-use Patterns,”Prog.Geogr., 38, 77, 2019.