How to calculate Information Dimension

Question

I am trying to implement this paper by Tian Bian and Yong Deng. In this paper, after applying probability they have gotten information entropy values
$l_a(r)=(1.3741,0.6930,0.6385,0) , (r=1,2,3,4)$
On these values they have implemented this information dimension (Page 5, figure 3)
$D_a = -\lim\limits_{r \to 0} \frac{l_a(r)}{lnr}$
for which they have gotten the final value of $D_a=-0.8927$
I am stuck on how Information Dimension is calculated and author gotten the final value of -0.8927 from $l_a(r)$ values. I am trying to implement it in python. I am stuck in the mathematical formulation of this statement and conversion of mentioned 4 values into -0.8927
Process of obtaining $Da$ value

Answer 1

The value -0.8927 is the slope from a linear regression (X,Y) where Y = [1.3741, 0.6930, 0.6385, 0] and X = [np.log(1), np.log(2), np.log(3), np.log(4)].

This method is used to compute fractal dimensions see here

Eventually, one calculates the regression line between the independent variable log (ηi) and the dependent variable log (N(ηi)), where i=1, …, S. D is given by the absolute value of the lineslope.