Perimeter-area relation and measurement of Hausdorff dimensionality (Q2365798)

The aim of this paper is to point out the correct method of using the perimeter-area relation from the views of dimensional analysis. The relation between the initial length, level and yardstick is clarified from the measurement angles. The influence of level and initial length on Hausdorff dimensionality \(D_ m\) and ratio factor \(\alpha\) measured are discussed using the results from the computer simulation. The conditions necessarily to be met in measurement with the perimeter-area relation are indicated and the physical meaning of these conditions is discussed.