Fig. 6: A folded cross-section considered as a one-dimensional random walk.
From: A model for the fragmentation kinetics of crumpled thin sheets
a A sample segmented sheet with dashed line indicating a vertical cross section. b The distribution of segment lengths from all such cross-sections of the sheet in a (filled points), with Eq. (15) plotted as a solid curve. No additional fit is performed; the value of the shape parameter a which appears in Eq. (15) is uniquely determined from Eq. (8) and the best fit τ to the facet area distributions. c A schematic of the analog between the folding of a one-dimensional strip in an axially confined sheet and a one-dimensional random walk whose time axis is extended vertically for clarity. The filled curve represents the distribution of the walker’s final displacement, with darker shaded regions denoting the fraction of walks which lie outside a given confinement. d Simplified illustration of one-dimensional folding which facilitates a geometric estimate of the critical confinement w, further detailed in Supplementary Note 4.
