In:
Cartographica: The International Journal for Geographic Information and Geovisualization, University of Toronto Press Inc. (UTPress), Vol. 53, No. 3 ( 2018-09), p. 203-210
Abstract:
It is commonly believed in the literature that smooth curves, such as circles, are not fractal, and only non-smooth curves, such as coastlines, are fractal. However, this article demonstrates that a smooth curve can be fractal, under a new, relaxed, third definition of fractal – a set or pattern is fractal if the scaling of far more small things than large ones recurs at least twice. The scaling can be rephrased as a hierarchy, consisting of numerous smallest, a very few largest, and some in between the smallest and the largest. The logarithmic spiral, as a smooth curve, is apparently fractal because it bears the self-similarity property, or the scaling of far more small squares than large ones recurs multiple times, or the scaling of far more small bends than large ones recurs multiple times. A half-circle or half-ellipse and the UK coastline (before or after smooth processing) are fractal if the scaling of far more small bends than large ones recurs at least twice.
Type of Medium:
Online Resource
ISSN:
0317-7173
,
1911-9925
DOI:
10.3138/cart.53.3.2017-0032
Language:
English
Publisher:
University of Toronto Press Inc. (UTPress)
Publication Date:
2018
SSG:
7,26
SSG:
14,1
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