FRACTAL SUCCOLARITY

Fractal succolarity is a parameter recently incorporated into the surface analysis of AFM images [1]. We used an approach like the one of Melo and Conci [2], as described by equation below:

where S_f is the fractal succolarity; P_0 is the number of occupied boxes per line (here the box-counting algorithm was adapted using boxes of length 1 pixel on the binary image); P_r is the pressure centroid abscissa referring to each box that can be occupied in the image; n is the total number of boxes per line.

References

[1] M.D.F. Albuquerque, R.A. Sim˜ao, R.S. Matos, E.P. Pinto, M.A. Pires, H.D. Fonseca Filho, M.B.M. Monte, Nanoscale stereometric and fractal evaluation of clathrate formation at quartz surface by atomic force microscopy, Miner. Eng. 170 (2021), 106988, https://doi.org/10.1016/j.mineng.2021.106988.

[2] R.H.C. Melo, A. Conci, How Succolarity could be used as another fractal measure in image analysis, Telecommun. Syst. 52 (2011) 1643–1655, https://doi.org/ 10.1007/s11235-011-9657-3.

Observation:

This R code is serves as a practical complement to our paper, "Comparing the nanoscale topography and interface properties of chitosan films containing free and nano-encapsulated copaiba essential oil: an atomic force microscopy (AFM) and fractal geometry study" (https://doi.org/10.1016/j.mtcomm.2023.105765).