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In Search of the Human Fractal
Published in Zlática Kraljevic, Borderless Leadership, 2018
In 1967 Benoit Mandelbrot published a paper entitled, How long is the coast of Britain? Statistical self-similarity and fractional dimension5. In his paper, Mandelbrot examined the “coastline paradox”: the fact that the length of the coastal line depends on the scale of measurement.
Geometric problem solving with strings and pins
Published in Spatial Cognition & Computation, 2019
Christian Freksa, Thomas Barkowsky, Zoe Falomir, Jasper van de Ven
In this kind of conceptualization, we also can evade a type of problem known as the coastline paradox (Mandelbrot, 1983). The coastline paradox demonstrates that the measured length of an unsmooth line depends on the granularity of the measuring device and can increase without limit if measuring resolution gets increasingly finer. It also demonstrates that the formalization of real-world entities may introduce structural incompatibilities in the conceptualization of spatial entities (here due to the discretization of curved lines). Like constructive geometry, the strings-and-pins-based conceptualization avoids discretization; the precision of argument is not limited by the granularity of a representation.
Origin, geomorphology and geoheritage potential of Australia’s longest coastal cliff lines
Published in Australian Journal of Earth Sciences, 2020
G. A. Wakelin-King, J. A. Webb
There is a larger, but non-quantifiable, confidence limit to horizontal measurement. According to the Richardson Effect or ‘coastline paradox’, the fractal nature of a coastline means that the measured length depends on the resolution of the measurement (Mandelbrot, 1967; Muller, 1986; inter alia). That being the case, exact length is not a meaningful concept unless the scale of measurement is defined. Comparative length is meaningful if measurement methods are consistent across the compared landscapes, as they are in this study.