| | | | | | 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. | | | | | | | | | 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. | | | | | | | | | 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. | | | | |