Box-counting program to estimate fractal dimension of real line subset (e.g. Cantor set)

Question

I'm working with several data frames of 500000 real numbers which, mathematically speaking, if $df$ is one of the data frames I'm working with, then $df\subseteq C\subset [0,1]$, where $C$ denotes the middle third Cantor set.

A program is needed to compute the fractal dimension of every data frame using numerical methods; such as box-counting programs. Our objective is to characterize the data frames in two groups by their fractal dimension: the first group (control condition) with a fractal dimension (significantly) less than $\frac{\log(2)}{\log(3)}$ and the second group (experimental condition) with a fractal dimension very close to $\frac{\log(2)}{\log(3)}$, where $\frac{\log(2)}{\log(3)}$ is the fractal dimension of Cantor set.

I have found two MatLab programs to estimate the box-counting dimension for one-dimensional data: https://www.mathworks.com/matlabcentral/fileexchange/13063-boxcount which with random methods computes the dimension, but most of the time fails, and section A.2 of https://fse.studenttheses.ub.rug.nl/12313/1/DimensionofFractals.pdf, page 26, but it doesn't display the fractal dimension computed

(Information for the data frame)

Data used is generated using that sequence space of $0$'s and $2$'s, $\{0,2\}^\mathbb{N}$, is homeomorphic to the middle third Cantor set. So, taking $n$ elements of $\{0,2\}^\mathbb{N}$ where only the first $100$ entries are randomly generated and the rest of the entries are $0$'s and then I compute the ternary representation (the homeomorphism) of each of the $n$ elements to obtain the $n$ elements in the Cantor set.

Answer 1

I took the code from section A.2 of https://fse.studenttheses.ub.rug.nl/12313/1/DimensionofFractals.pdf, page 26, as a reference to write a Python code to estimate the fractal dimension of real line subsets.

import numpy as np
import math
import pandas as pd
#file.txt is data frame of n x 1 dimensions. Data are all real numbers
F=pd.read_table("file.txt", header= None)
rows = 12 #Can be increased to improve accuracy
cols = 2
size = rows*cols
R = np.array(([0]*size),dtype=np.float64).reshape(rows,cols)
#Box size parameter (adjustable)
r=0.00489 #Parameter for our data
for l in range(rows):
    N=math.ceil(4.0/r)
    G=np.zeros((N),dtype=np.int16)
    N=len(F)
    C=0
    for i in range(N):
        m=max(math.ceil((F[0][i]+2)/r),1)
        if G[m]==0:
            G[m]=1
            C=C+1
    R[l][0]=r
    R[l][1]=C
    r=r/2.0

print('Fractal dimension is: ',np.log(R[rows][1])/-np.log(R[rows][0]))