## 3 Results  
Firstly, Figure 1 shows the original AFM images a-d of different areas of nanofiber mats, used for this study. Image a was taken in the middle of the upper surface of a nanofiber mat, image b near the outer border of the upper surface, c in the middle of the lower surface (during electrospinningning attached to the polypropylene substrate) and d near the outer border of the lower surface. Comparing these images subjectively, image d looks clearly different from the others, while a and b seem to be similar. Image c is subjectively located between the others, showing more clear fibers than d, but less and thicker ones than a and b. It must be mentioned that the scale visible in Figure 1 have to be deleted before Hurst exponent calculation; thus, they are not given in the following images after post-processing. It should be mentioned that this study did not aim at optimizing the nanofiber morphology, but oppositely searched for positions where the nanofibers looked subjectively different, to enable investigating interrelations with the gray-scale-resolved Hurst exponent distributions. Next, Figure 2 depicts the results of the aforementioned post-treatment operations, using sample \(a\) as an example. Comparing these images with the original one (Figure 1a), the first step, i.e., the polynomial background subtraction, apparently changes the brightness distribution strongly and can thus, be expected to result in a modification of the gray-scale-resolved Hurst exponent distributions. The next two steps do not show similarly well visible modifications. Nevertheless, deleting horizontal errors can be expected to have a certain impact since such horizontal errors, occurring in single lines, will disrupt smooth brightness distributions and, thus, introduce breaks in actually closed lines or areas, which are removed by deleting these horizontal errors. Finally, the sharpening step can also be expected to have a certain impact, as it is noticeable by comparing Figure 2c,d. The color images, transformed into the typical 256-levels gray-scale, can now be split into 32 sub-images of 8 gray-channels each. Figure 3 shows an example for the image depicted in Figure 2a. For the investigated pictures, intermediate gray scale values can be found along the edges of the fibers, while low-number-channels define the pores between them and the large channel numbers represent the middle regions of the cylindrical fibers. Applying random walks on these gray-scale-resolved monochromatic images, relations between \(\ln\) (\(\langle\Delta r^{2}\rangle\) and \(\ln\)(n) can be plotted, as shown in Figure 4a. By repeating these calculations, Hurst exponent distributions are gained, as depicted in Figure 4b. All 32 Hurst exponent distributions, for the 32 gray-channel ranges per image, are then merged into false-colored images, as they are given in the next figures. Figure 1: Original atomic force microscopy (AFM) images (**a–d**), taken on different positions of an electrospun nanofiber mat, as explained in detail in the text. Figure 2: Post-treatment steps, performed on sample \(a\): (**a**) polynomial background subtraction; (**b**) aligning rows; (**c**) deleting horizontal errors; (**d**) sharpening once. It should be mentioned that the Hurst exponent distributions (e.g., Figure 4b), as explained before, quantify the connection of the black area given in one image and the fineness of the black features. Hurst exponent values around 0.5 are expected for a completely black area, while they lie between 0.4 and 0.5 for fine black lines and those found in the range of 0.1-0.35 are characteristic for local dots of different sizes [35]. It can thus be expected that images with single small dots and larger areas or lines, such as Figure 3a, will result in a relatively broad Hurst exponent distribution. Generally, splitting the AFM images in gray-scale-resolved partial images will lead to finer features and more fine lines, as they would be gained by directly translating the original color image into one monochromatic image.