Ripples at edges of blooming lilies and torn plastic sheets

Ripples arise at edges of petals of blooming Lilium casablanca flowers and at edges of torn plastic sheets. In both systems, ripples are a consequence of excess length along the edge of a sheet. Through the use of both time-lapse videos of blooming lilies and still images of torn plastic sheets, we find that ripples in both systems are well-described by the scaling relationship [Formula], where a is amplitude, w is wavelength, and L is arc length. By approximating that the arc length is proportional to the wavelength, we recover a phenomenological relationship previously reported for self-similar ripple patterns, namely [<]a[>] {propto} [<]w[>]. Our observations imply that a broad class of systems in which morphological changes are driven by excess length along an edge will produce ripples described by [Formula]. Significance StatementEarly in the blooming process of Lilium casablanca flowers, large ripples appear in the edges of their petals. As blooming progresses, smaller ripples arise on top of the original ones. All ripples are characterized by three variables, an amplitude, a wavelength, and an arc length. Here, we derive an equation that relates these variables. To test the equation, we collect movies of blooming lilies. We find that the equation quantitatively describes single ripples in the petals. The equation is general, so it applies to all systems in which ripples arise by the same mechanism. To illustrate this point, we show that the equation holds for single ripples that appear at the edges of torn plastic sheets.