179.

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		1.3.3— Example of a Power Law Scaling of a Spatial Object: The Length of the Coastline of Britain

		Richardson measured the length of the coastline of Britain by laying small straight line segments of the same length, end to end, along the coastline. The length of these line segments set the spatial resolution of the measurement. The total length of the coastline was the combined length of all these line segments

		When he measured the coastline at finer resolution, the smaller line segments included the smaller bays and peninsulas that were not included in the measurement at coarser resolution. These additional smaller bays and peninsulas increased the total length of the coastline. He found that the length of the coastline was ever longer as he measured it at ever finer resolutions.

		He plotted the logarithm of the total length of the coastline, , versus the logarithm of the length of the line segments used to do the measurement, Log [r]. The data were a straight line. He found that was proportional to (-1/4) Log [r]. This means that the scaling relationship of the measurement of the length of the coastline has the power law form that is proportional to r-(1/4).

 

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