# Fractal Analysis and Time Series Application in ZY-4 SEM Micro Fractographies Evaluation

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Part

#### 2.1. Fractal Dimension

#### 2.2. Lacunarity

#### 2.3. Time Series

_{t}, called the time average, is determined by

_{x}signifies a time mean of $\left\{F\left({f}^{i}\left(x\right)\right)\right\}$ and m

_{y}signifies the time mean of $\left\{F\left({f}^{i}\left(y\right)\right)\right\}$.

#### 2.4. Phase Space Reconstruction

#### 2.5. SEM Image Evaluation

## 3. Results and Discussion

^{2}(R-Squared or coefficient of determination) was equal to 0.9994, representing that the very good data fit the regression model used.

^{2}(R-Squared or coefficient of determination) was equal to 0.9842, representing that the very good data fit the regression model used.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Attractor reconstruction from Figure 1.

**Figure 5.**Attractor reconstruction from Figure 4.

**Figure 7.**The slope of the autocorrelation dimension versus the embedding dimension for the modified area.

**Figure 14.**Attractor reconstruction from Figure 13.

**Figure 16.**The slope of the autocorrelation dimension versus the embedding dimension for the normal area.

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**MDPI and ACS Style**

Paun, M.-A.; Paun, V.-A.; Paun, V.-P.
Fractal Analysis and Time Series Application in ZY-4 SEM Micro Fractographies Evaluation. *Fractal Fract.* **2022**, *6*, 458.
https://doi.org/10.3390/fractalfract6080458

**AMA Style**

Paun M-A, Paun V-A, Paun V-P.
Fractal Analysis and Time Series Application in ZY-4 SEM Micro Fractographies Evaluation. *Fractal and Fractional*. 2022; 6(8):458.
https://doi.org/10.3390/fractalfract6080458

**Chicago/Turabian Style**

Paun, Maria-Alexandra, Vladimir-Alexandru Paun, and Viorel-Puiu Paun.
2022. "Fractal Analysis and Time Series Application in ZY-4 SEM Micro Fractographies Evaluation" *Fractal and Fractional* 6, no. 8: 458.
https://doi.org/10.3390/fractalfract6080458