What is a physical measure of spatial inhomogeneity comparable to the mathematical approach?

A linear transformation f(S) of configurational entropy with length scale d ependent coefficients as a measure of spatial inhomogeneity is considered. When a final pattern is formed with periodically repeated initial arrangeme nt of point objects the value of the measure is conserved. This property al lows for computation of the measure at every length scale. Its remarkable s ensitivity to the deviation (per cell) from a possible maximally uniform ob ject distribution for the length scale considered is comparable to behaviou r of strictly mathematical measure h introduced by Garncarek et al. in [2]. Computer generated object distributions reveal a correlation between the t wo measures at a given length scale for all configurations as well as at al l length scales for a given configuration. Some examples of complementary b ehaviour of the two measures are indicated.