1.5.13 How to Measure the Properties of Fractal Data
The statistical properties, such as the average or variance, of a fractal object or process depend on the resolution used to measure them. Thus it does little good to measure these statistical properties at only one resolution.
The meaningful measurement is to determine how these statistical properties depend on the resolution used to measure them.
Usually, the scaling relationship for a statistical property will have the power law form that is proportional to rb, where r is the resolution. The exponent b is related to the fractal dimension.
A number of different statistical properties have been used to analyze fractal data, including the: