177.

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		1.3.2— Scaling Relationships

		The scaling relationship describes how the measured value of a property depends on the resolution r used to make the measurement. It can have two different forms.

		1— Power Law

		The simplest and most common form of the scaling relationship is that , where B and b are constants.

		On a plot of the logarithm of the measured property, , versus the logarithm of the resolution used to make the measurement, Log [r], this scaling relationship is a straight line.

		Such power law scaling relationships are characteristic of fractals.

		Power law relationships are found so often because so many things in nature are fractal.

		2— Full Form

		The full form of the scaling relationship is that where B, b, and a are constants and f(x) is a periodic function such that f(l+x)=f(x).

		On a plot of the logarithm of the measured property, , versus the logarithm of the resolution used to make the measurement, Log [r], this scaling relationship is a straight line with a periodic wiggle.

 

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