Fractal Dimension

“Fractal Dimension” is a computer programme for calculating the fractal dimension of time series.

The calculation algorithm is based on the macros of the Visual Basic programming language.

Input the data of the studied time series into Column B (“InputData” page). 

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

Fractal dimension calculation:

– By pressing the buttons “Fractal Dimension” and “Fractal Dimension (averaged)”, the k, L, k_aver and L_aver values are calculated.

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

Calculation results are presented on the charts (“InputData” page) and on the “Fractal Dimension” and “Fractal Dimension(averaged)” pages.

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 (InputData page) for analysis

In this program, the value of  (the number of differences between the neighbouring measurements) is not considered, but is determined from the equation

where  – is the number of measurements,  – the measurement step (interval between measurements).

For the averaged case

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.