Link to bioRxiv paper:

http://biorxiv.org/cgi/content/short/2020.08.05.235176v1?rss=1

Authors: Portet, T., Holmes, P. N., Keller, S. L.

Abstract:

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 a {propto} {surd}(w(L - w)), 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 a {propto} {surd}(w(L - w)).

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