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