**7. Testing methods for estimating fractal dimension**

To test the methods for evaluating the fractal dimension, two methods triangulation and DBC were considered. Testing was carried out with the help of fractal objects for which the dimension is known. **Table 2** presents the results of testing the above assessment methods using fractals with a known dimension value.

In **Table 2**, the following designations are made:

<sup>Δ</sup>*TM*% <sup>¼</sup> *<sup>D</sup>*^ *TM*�*<sup>D</sup> <sup>D</sup>* � 100% is the absolute error in estimating the dimension between the measured and the true value of the fractal dimension by the triangulation method.

<sup>Δ</sup>*DBC*% <sup>¼</sup> *<sup>D</sup>*^ *DBC*�*<sup>D</sup> <sup>D</sup>* � 100% is the absolute error in estimating the dimension between the measured and the true value of the fractal dimension by the DBC method.

<sup>Δ</sup>*AV*% <sup>¼</sup> *<sup>D</sup>*�*<sup>D</sup> <sup>D</sup>* � 100% is the absolute error of the average estimate of the fractal dimension obtained by two methods.


#### **Table 2.**

*Results of testing methods for measuring the fractal dimension.*

### *Fractal Analysis - Selected Examples*

The numerical data of the absolute errors of measurement of the dimension with the help of triangulation and DBC methods show that they give comparable results. The error of calculations for both methods does not exceed 5%. For practical use, it is advisable to use both methods, and the dimension values to find by averaging the results of both methods. In this case, the total error of calculations does not exceed 3%.
