{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:54:23Z","timestamp":1762869263147,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T00:00:00Z","timestamp":1706140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42101442","42171420","2022YFB3904202"],"award-info":[{"award-number":["42101442","42171420","2022YFB3904202"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["42101442","42171420","2022YFB3904202"],"award-info":[{"award-number":["42101442","42171420","2022YFB3904202"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Schematization is a process of generating schematic network maps (e.g., metro network maps), where the graphic complexity of networks is usually reduced. In the past two decades, various automated schematization methods have been developed. A quantitative and accurate description of the complexity variation in the schematization is critical to evaluate the usability of schematization methods. It is noticed that fractal dimension (F) has been widely used to analyze the complexity of geographic objects, and this indicator may be appropriate for this purpose. In some existing studies, although F has been employed to describe the complexity variation, the theoretical and experimental basis for adopting this approach is inadequate. In this study, experiments based on 26 Chinese cities\u2019 metro networks showed that the F of all these metro networks have decreased in schematization, and a significant positive correlation exists between the F of original networks and the reduction of F after schematization. The above results were verified to have similar trends with the subjective opinions of participants in a psychological questionnaire. Therefore, it can be concluded that F can quantitatively measure the complexity change of networks in schematization. These discoveries provide the basis for using F to evaluate the usability of schematization methods.<\/jats:p>","DOI":"10.3390\/ijgi13020038","type":"journal-article","created":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T08:44:07Z","timestamp":1706172247000},"page":"38","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Assessing the Suitability of Fractal Dimension for Measuring Graphic Complexity Change in Schematic Metro Networks"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8907-2603","authenticated-orcid":false,"given":"Tian","family":"Lan","sequence":"first","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8645-756X","authenticated-orcid":false,"given":"Zhiwei","family":"Wu","sequence":"additional","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}]},{"given":"Chenzhen","family":"Sun","sequence":"additional","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}]},{"given":"Donglin","family":"Cheng","sequence":"additional","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}]},{"given":"Xing","family":"Shi","sequence":"additional","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}]},{"given":"Guangjun","family":"Zeng","sequence":"additional","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}]},{"given":"Hong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geographic Sciences, East China Normal University, Shanghai 200241, China"},{"name":"Institute for Global Innovation and Development, East China Normal University, Shanghai 200062, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0278-035X","authenticated-orcid":false,"given":"Qian","family":"Peng","sequence":"additional","affiliation":[{"name":"Faculty of Resources and Environmental Science, Hubei University, Wuhan 430062, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lan, T., Li, Z.L., Wang, J.C., Gong, C.Y., and Ti, P. (2022). An ANNs-based method for automated labelling of schematic metro maps. ISPRS Int. J. Geo-Inf., 11.","DOI":"10.3390\/ijgi11010036"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/TVCG.2010.24","article-title":"Automatic metro map layout using multicriteria optimization","volume":"17","author":"Stott","year":"2011","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_3","unstructured":"N\u00f6llenburg, M. (2014, January 2\u20133). A survey on automated metro map layout methods. Proceedings of the 1st Schematic Mapping Workshop, Essex, UK."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.jvlc.2005.09.001","article-title":"Automatic visualisation of metro maps","volume":"17","author":"Hong","year":"2006","journal-title":"J. Vis. Lang. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ti, P., Wu, H., Li, Z.L., Li, M.Y., Dai, R.Y., and Xiong, T. (2023). Revealing schematic map designs with preservation of relativity in node position and segment length in existing official maps. ISPRS Int. J. Geo-Inf., 12.","DOI":"10.3390\/ijgi12080309"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zheng, M.-C., and Liu, Y.-W. (2021). Effect of compositions of MRT system route maps on cognitive mapping. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10080569"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1179\/000870403235002024","article-title":"The top ten maps of the twentieth century: A personal view","volume":"40","author":"Forrest","year":"2003","journal-title":"Cartogr. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1080\/17538947.2014.923942","article-title":"Rethinking the definition of the word \u2018map\u2019: An evaluation of Beck\u2019s representation of the London Underground through a qualitative expert survey","volume":"8","author":"Cartwright","year":"2015","journal-title":"Int. J. Digit. Earth"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1038\/nrc795","article-title":"A subway map of cancer pathways","volume":"2","author":"Hahn","year":"2002","journal-title":"Nat. Rev. Cancer"},{"key":"ref_10","unstructured":"Elroi, D.S. (1988, January 21\u201325). Designing a network line-map schematization software enhancement package. Proceedings of the 8th International ESRI User Conference, Redlands, CA, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1109\/TVCG.2010.81","article-title":"Drawing and labeling high-quality metro maps by mixed-integer programming","volume":"17","author":"Nollenburg","year":"2011","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1111\/j.1467-9671.2006.00242.x","article-title":"Automated production of schematic maps for mobile applications","volume":"10","author":"Taylor","year":"2006","journal-title":"Trans. GIS"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2305","DOI":"10.1080\/13658816.2019.1620237","article-title":"Integrating general principles into mixed-integer programming to optimize schematic network maps","volume":"33","author":"Lan","year":"2019","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ware, M., and Richards, N. (2013, January 20\u201323). An Ant Colony System algorithm for automatically schematizing transport network data sets. Proceedings of the 2013 IEEE Congress on Evolutionary Computation, Cancun, Mexico.","DOI":"10.1109\/CEC.2013.6557790"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Galvao, M., Ramos, F., Lamar, M., and Taco, P. (2017). Dynamic Visualization of Transit Information Using Genetic Algorithms for Path Schematization, Springer.","DOI":"10.1007\/978-3-319-61297-3_8"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1080\/13658811003766936","article-title":"A stroke-based method for automated generation of schematic network maps","volume":"24","author":"Li","year":"2010","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1080\/13658816.2013.855313","article-title":"Generation of schematic network maps with automated detection and enlargement of congested areas","volume":"28","author":"Ti","year":"2014","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1722","DOI":"10.1111\/tgis.12671","article-title":"Automated labeling of schematic maps by optimization with knowledge acquired from existing maps","volume":"24","author":"Lan","year":"2020","journal-title":"Trans. GIS"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.ijhcs.2012.09.004","article-title":"Objective versus subjective measures of Paris Metro map usability: Investigating traditional octolinear versus all-curves schematics","volume":"71","author":"Roberts","year":"2013","journal-title":"Int. J. Hum.-Comput. Stud."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.ijhcs.2016.06.003","article-title":"Preference versus performance: Investigating the dissociation between objective measures and subjective ratings of usability for schematic metro maps and intuitive theories of design","volume":"98","author":"Roberts","year":"2017","journal-title":"Int. J. Hum.-Comput. Stud."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Lloyd, P.B., Rodgers, P., and Roberts, M.J. (2018, January 18\u201322). Metro map colour-coding: Effect on usability in route tracing. Proceedings of the Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Proceedings 10, Edinburgh, UK.","DOI":"10.1007\/978-3-319-91376-6_38"},{"key":"ref_22","unstructured":"Burch, M., Raschke, M., Blascheck, T., Kurzhals, K., and Weiskopf, D. (2014, January 2\u20133). How do people read metro maps? An eye tracking study. Proceedings of the 1st Workshop on Schematic Mapping, Essex, UK."},{"key":"ref_23","unstructured":"Burch, M., Kurzhals, K., and Weiskopf, D. (2014, January 23). Visual task solution strategies in public transport maps. Proceedings of the 2nd International Workshop on Eye Tracking for Spatial Research, Vienna, Austria."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"421","DOI":"10.5194\/isprs-archives-XLI-B2-421-2016","article-title":"Impact of schematic designs on the cognition of underground tube maps","volume":"41","author":"Liu","year":"2016","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1080\/13875868.2016.1226839","article-title":"User performance and reading strategies for metro maps: An eye tracking study","volume":"17","author":"Netzel","year":"2017","journal-title":"Spat. Cogn. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/BF01035241","article-title":"Fractals and the accuracy of geographical measures","volume":"12","author":"Goodchild","year":"1980","journal-title":"J. Int. Assoc. Math. Geol."},{"key":"ref_27","first-page":"172","article-title":"The fractal features of the transport network of Henan Province","volume":"11","author":"Jing","year":"1998","journal-title":"J. Xinyang Norm. Univ. (Nat. Sci. Ed.)"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1179\/000870406X169883","article-title":"Measuring map complexity","volume":"43","author":"Fairbairn","year":"2006","journal-title":"Cartogr. J."},{"key":"ref_29","first-page":"29","article-title":"City shape and the fractality of street patterns","volume":"31","author":"Mohajeri","year":"2012","journal-title":"Quaest. Geogr."},{"key":"ref_30","first-page":"943","article-title":"Urban allometric scaling beneath structural fractality of road networks","volume":"109","author":"Lan","year":"2019","journal-title":"Ann. Am. Assoc. Geogr."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1080\/00330124.2021.1871765","article-title":"Exploring the structural fractality of urban road networks by different representations","volume":"73","author":"Zhang","year":"2021","journal-title":"Prof. Geogr."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1126\/science.156.3775.636","article-title":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","volume":"156","author":"Mandelbrot","year":"1967","journal-title":"Science"},{"key":"ref_33","unstructured":"Mandelbrot, B.B. (1982). The Fractal Geometry of Nature, WH Freeman."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1080\/00045608.2013.834239","article-title":"Ht-index for quantifying the fractal or scaling structure of geographic features","volume":"104","author":"Jiang","year":"2014","journal-title":"Ann. Assoc. Am. Geogr."},{"key":"ref_35","first-page":"1315","article-title":"Unified metrics for characterizing the fractal nature of geographic features","volume":"107","author":"Gao","year":"2017","journal-title":"Ann. Am. Assoc. Geogr."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1068\/a181143","article-title":"The fractal simulation of urban structure","volume":"18","author":"Batty","year":"1986","journal-title":"Environ. Plan. A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3825","DOI":"10.1073\/pnas.72.10.3825","article-title":"Stochastic models for the Earth\u2019s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands","volume":"72","author":"Mandelbrot","year":"1975","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0043-1648(86)90257-7","article-title":"Fractal approach to two-dimensional and three-dimensional surface roughness","volume":"109","author":"Gagnepain","year":"1986","journal-title":"Wear"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1068\/a271147","article-title":"A fractal analysis of the public transportation system of Paris","volume":"27","author":"Benguigui","year":"1995","journal-title":"Environ. Plan. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1068\/b3163","article-title":"Fractal dimension of a transportation network and its relationship with urban growth: A study of the Dallas-Fort Worth area","volume":"31","author":"Lu","year":"2004","journal-title":"Environ. Plan. B Plan. Des."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Lan, T., Peng, Q., Wang, H.Y., Gong, X.Y., Li, J., and Shi, Z.C. (2021). Exploring allometric scaling relations between fractal dimensions of metro networks and economic, environmental and social indicators: A case study of 26 cities in China. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10070429"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Prah, K., and Shortridge, A.M. (2023). Vertical vs. Horizontal fractal dimensions of roads in relation to relief characteristics. ISPRS Int. J. Geo-Inf., 12.","DOI":"10.3390\/ijgi12120487"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1167\/7.2.17","article-title":"Measuring visual clutter","volume":"7","author":"Rosenholtz","year":"2007","journal-title":"J. Vis."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/13\/2\/38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:49:18Z","timestamp":1760104158000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/13\/2\/38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,25]]},"references-count":43,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["ijgi13020038"],"URL":"https:\/\/doi.org\/10.3390\/ijgi13020038","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2024,1,25]]}}}