The late mathematician Benoît Mandelbrot (1924–2010) published in Science, over a half century ago, the remarkable landmark paper, “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension.” This paper directly triggered the establishment of fractal geometry, which has found many interests and applications in a variety of disciplines over the past decades – not only in science but also in art and design – including cartography and geographic information science (GIScience). Mandelbrot relaxed the definition of fractal from traditionally the strict sense of the first definition, like the Koch curve, to then the statistical sense of the second definition, like coastlines, thus opened new horizons for seeing fractals in nature. The second definition was further relaxed recently, leading to some striking results and opening of new frontiers in research. For instance, the third definition of fractal – a set or pattern is fractal if the notion of far more smalls than larges recurs multiple times – enables us to see fractals more easily that pervasively exist, not only in nature but also in what we make and build. The new definition implies that all geographic features might be fractal if they are seen from the right perspective and scope. To mention a few examples, a country could be fractal where there are far more small cities than large ones in it; a city could be fractal where it consists of far more short streets than long ones; a street or a smooth curve could be fractal where it can be seen as a set of far more small bends than large ones.

The editorial team of Cartographica invites paper submissions of original research on applications of fractal geometry in cartography and GIScience. Suggested topics include, but are not limited to, the following:

  • Review of fractal geometry in cartography and GIScience,
  • Fractals for map generalization and data classification,
  • Fractals for visualization and perception of beauty,
  • Characterizations of map complexity using ht-index and fractal dimension,
  • Sensitivities of ht-index and fractal dimension,
  • Fractal patterns captured by eye-tracking experiments,
  • Fractals for map design and cartographic arts.

Keywords: scaling law, map generalization, data classification, eye-tracking experiments, pattern recognition, image analysis

Editors:

  • Bin Jiang, PhD and Professor in GeoInformatics, University of Gävle, Sweden
  • Carlo Cattani, PhD and Professor in Mathematics, University of Tuscia, Italy
  • Submission Instructions:

Submit original manuscripts through our online peer review management system ScholarOne Manuscripts by the specified deadline above. Prior to submitting your manuscript, you will have to register for an account if you do not already have one. When you submit the manuscript, please follow these instructions:

  1. Select the article type as "Special Issue."
  2. Paper submissions must be up to 6,000 words long and contain the title and abstract. Upload the file designation as the "Main Document."
  3. Include a title page with the author(s) name(s), affiliation(s), contact details (post, phone, fax, email), and a brief biography of author(s) (up to 100 words). Upload the title page as a separate document with the file designation as "Supplemental File NOT for Review" and order this document first. (If you include a cover letter to the editor, please also select the file designation as "Supplemental File NOT for Review" and order the cover letter first, the title page second, and the main document third.)
  4. Authors may wish to refer to Cartographica’s submission guidelines at http://bit.ly/Cartsub. 

References

  • Batty, M., and P. Longley. 1994. Fractal Cities: A Geometry and Form and Function. London: Academic Press.
  • Buttenfield, B. 1985. “Treatment of the Cartographic Line.” Cartographica 22(2): 1–26. https://doi.org/10.3138/FWV8-3802-2282-6U47.
  • Cattani, C., and A. Ciancio. 2016. “On the Fractal Distribution of Primes and Prime-Indexed Primes by the Binary Image Analysis.” Physica A: Statistical Mechanics and its Applications 460: 222–29. https://doi.org/10.1016/j.physa.2016.05.013.
  • Chen Y.G. 陈彦光. 2008. 分形城市系统: 标度·对称·空间复杂性 [Fractal Urban Systems: Scaling, Symmetry, and Spatial Complexity]. Beijing: Science Press.
  • Frankhauser, P. 1994. La fractalité des structures urbaines. Paris: Economica.
  • Goodchild, M.F., and D.M. Mark. 1987. “The Fractal Nature of Geographic Phenomena.” Annals of the Association of American Geographers 77(2): 265–78. https://doi.org/10.1111/j.1467-8306.1987.tb00158.x.
  • Jiang, B. 2015a. “The Fractal Nature of Maps and Mapping.” International Journal of Geographical Information Science 29(1): 159–74. https://doi.org/10.1080/13658816.2014.953165.
  • Jiang, B. 2015b. “Head/Tail Breaks for Visualization of City Structure and Dynamics.” Cities 43: 69–77. https://10.1016/j.cities.2014.11.013. Reprinted in Capineri, C., M. Haklay, H. Huang, V. Antoniou, J. Kettunen, F. Ostermann, and R. Purves R. (eds.) 2016. European Handbook of Crowdsourced Geographic Information, 169–83. London: Ubiquity Press. https://doi.org/10.5334/bax.m. The image is used courtesy of the Bin Jiang.
  • Jiang, B., and J. Yin. 2014. “Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features.” Annals of the Association of American Geographers 104(3): 530–40. https://doi.org/10.1080/00045608.2013.834239.
  • Karaca, Y., and C. Cattani. 2017. “Clustering Multiple Sclerosis Subgroups with Multifractal Methods and Self-Organizing Map Algorithm.” Fractals 25(4): 1740001. https://doi.org/10.1142/S0218348X17400011.
  • Lam, N.S.-N., and L. De Cola. 2002. Fractals in Geography. New Jersey: Blackburn Press.
  • Mandelbrot, B.B. 1967. “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension.” Science 156(3775): 636–38. https://doi.org/10.1126/science.156.3775.636.
  • Mandelbrot, B.B. 1982. The Fractal Geometry of Nature. New York: W.H. Freeman.
  • Muller, J.-C. 1986. “Fractal Dimension and Inconsistencies in Cartographic Line Representations.” The Cartographic Journal: The World of Mapping 23(2): 123–30. https://doi.org/10.1179/caj.1986.23.2.123.