## 3 Results and Discussion
### AFM Analysis
#### 3.2.4 Fractal Analysis of Leaf Surface  
The analysis of fractal objects in nature has its importance for describing their unique spatial patterns and started with the excellent work of [PERSON] [77]. Such description can be made using several branches of fractal theory, e.g., power spectrum density (PSD), fractal dimension (FD), fractal lacunarity (FL), and fractal succolarity (FS), as we report in this approach. The power spectrum density of the leaf abaxial side images with different sizes is displayed in Figure 6. Figure 6a-c shows the Average PSD of the leaf abaxial surface of S50, S20, and S10 (S50), where we highlight the fractal region chosen to estimate the Hurst coefficient (H) as a useful quantitative parameter in the analysis of the dominant spatial frequencies displayed by the surface as a function of the scale. The PSD decomposes the surface into contributions of different spatial frequencies (wave vectors) using the Fourier transform of the height distribution function. According to [PERSON] et al. [33], PSD is invariant concerning the size of the image and the number of pixels of the same. However, the enlargement of the image in the region of the stomata of the leaf can provide details of its internal topography. Thus, to confirm whether one of the enlargements reveals internal characteristics of the stomata, the Hurst coefficient (H) values were computed and are shown in Table 4. S50 and S20 show higher H values than S10. The variance analysis shows a significant global difference between samples, but Tukey test reveals that only S10 differs from S50 and S20 (\(p<0.05\)). A lower H indicates a higher contribution from higher frequencies, creating a larger space-filling profile when compared to a higher H value. Therefore, the results suggest that the internal topographic profile of the stomata presents a greater contribution of higher frequencies, with greater space-filling, about the external part. However, the stomata's internal and external topographic difference from the S10 image is still barely noticeable visually, as the difference in H between S10 and the other images (S50 and S20) is very small. However, this difference suggests that even greater scale size may reveal singular characteristics of the internal region of the stomata. [PERSON] et al. [33] emphasize that two surfaces can have the same Sa value, the same phase, and be isotropic, but with a different H value, which establishes completely different roughness patterns. The fractal geometry has been used to study the spatial complexity of leaves on micro and nanometric scale, e.g., [19; 20]. The FD decreases S50 to S10, revealing a decrease of the spatial complexity (topographical irregularities) as a function of scale size. In this regard, the variance analysis shows a significant difference between the means (\(p<0.05\)), but Tukey test reveals that S10 and S20 are different from S50. Thus, it is possible to conclude that the surface microtexture changes according to the scale size, following a decrease in the roughness behavior. Furthermore, FL (Figure S3) confirms that scale size influences surface microtexture because the lowest \(\beta\) coefficients, estimated by linear fits on the lacunarity distribution, are obtained for S50 and S20 and the largest for S10 (Table 4). According to [PERSON] et al. [78], when \(\beta\) is lower, the surface has a microtexture more homogeneous, while the highest values are related to surface microtextures more heterogeneous. Thus,