Fractal Dimensions of Cell Wall in Growing Cotton Fibers

Abstract

In this research, fractal properties of a cell wall in growing cotton fibers were studied. It was found that dependences of specific pore volume (P) and apparent density (ρ) on the scale factor, F = H/h, can be expressed by power-law equations: P = Po F(Dv−E) and ρ = ρo F(E−Dρ), where h is minimum thickness of the microfibrilar network in the primary cell wall, H is total thickness of cell wall in growing cotton, Dv = 2.556 and Dρ = 2.988 are fractal dimensions. From the obtained results it follows that microfibrilar network of the primary cell wall in immature fibers is loose and disordered, and therefore it has an increased pore volume (Po = 0.037 cm3/g) and low density (ρo = 1.47 g/cm3). With enhance days post anthesis of growing cotton fibers, the wall thickness and density increase, while the pore volume decreases, until dense structure of completely mature fibers is formed with maximum density (1.54 g/cm3) and minimum pore volume (0.006 cm3/g). The fractal dimension for specific pore volume, Dv = 2.556, evidences the mixed surface-volume sorption mechanism of sorbate vapor in the pores. On the other hand, the fractal dimension for apparent density, Dρ = 2.988, is very close to Euclidean volume dimension, E = 3, for the three-dimensional space.

Fractal Parameters as Independent Biomarkers in the Early Diagnosis of Pediatric Onset Inflammatory Bowel Disease

“…Here, a total of 18 grid cell sizes were used to obtain data points for fitting the regression curves to describe the scale-count power law dependence. Specifically, grid cells sized ε ∈ {5, 6,7,8,9,10,12,14,16,18,20,23,27,30,35,40,46, 52} px were used in both the box counting method and the cumulative mass method. Figure 1 shows an example binary image of a nucleus and also illustrates the typical nucleus size and the look of the chromatin texture, covered by grid cells of different sizes, ε.…”

“…Fractal Fract. 2023, 7, 619 2 of 16 The dependences of the structural or functioning-related parameters of interest on the scale can be expressed by the power-law equations [1,7,8]. The fractal dimension (FD), which corresponds to the first-order mass moment of probability of finding a certain fractal measure amount at a certain scale [9,10], can be easily determined from the power-law dependence.…”