Fractal Dimension Data

“Fractal Dimension Data” is a computer programme  for calculating the fractal dimension of time series. The program allows you to better understand the proposed algorithm for calculating the fractal dimension.

The calculation algorithm is carried out in MS Excel using built-in functions.

The maximum number of data is 5000 values, assuming equal steps between measurements ∆t which is taken as 1.

The value of the interval between measurements ∆t varies from 1 to 11.

Input the data of the studied time series into Column B. 

Check that the column does not contain data from previous calculations.

The calculation results are shown on the graphs.

If the data is fractal (locally), for large values of k and k_aver, the dependencies Log(L)-Log(k) and Log(L_aver)-Log(k_aver) fall on a straight line, the slope of which determines the values of Fractal Dimension D (column H ) and Fractal Dimension (averaged) D_averaged (column S), coefficients A (column I) and A_averaged (column T) (the range of straightening is selected in the corresponding cells).

You can use the RSQ (column J) and RSQaveraged (column U) values to select the straightening range.

If the data is not straightened on the fractal plane Log(L)-Log(k) (non-fractal or multi-fractal data), you can use the value of the coefficient of variation (volatility) l (column K) for analysis

References

1. Suleymanov A.A., Abbasov A.A., Ismaylov A.J. Application of fractal analysis of time series in oil and gas production. Petroleum Science and Technology, 2009, Volume 27, Issue 9, 915-922. DOI:10.1080/10916460802455608.

2. Suleymanov A.A., Abbasov A.A., Malikov H.Kh. Fractal analysis of time series in oil and gas production. Chaos, Solitons and Fractals, 2009, Volume 41, Issue 5, pp. 2474-2483. DOI:10.1016/j.chaos.2008.09.039.

3. Suleymanov A.A., Abbasov A.A. Diagnosis of well production operations on the basis of nonparametric criteria of production data variations. Petroleum Science and Technology, 2011, Volume 29, Issue 22, pp. 2377-2383. DOI:10.1080/10916461003716673.

4. Suleymanov A.A., Abbasov A.A. About some criterion on the state of oil and gas production process diagnostics. SOCAR Proceedings, Issue 2, 2010, 42-49. DOI: 10.5510/OGP20100200020.

5. Suleymanov A.A., Abbasov A.A. et al. Fractal Analysis of Chaotic Fluctuations in Oil Production. Advances in Intelligent Systems and Computing, Springer Nature Switzerland AG 2019, 484-490. https://doi.org/10.1007/978-3-030-04164-9.