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 time-lapse videos of blooming lilies and published images of torn plastic sheets, we find that ripples in both systems are well described by the scaling relationship $a\propto \sqrt{w\left(L-w\right)}$, where $a$ is amplitude, $w$ is wavelength, and $L$ is arc length. A phenomenological relationship previously reported for self-similar ripple patterns, namely $⟨a⟩\propto ⟨w⟩$, can be recovered by assuming that buckling stress is constant. Excess length along petal edges can also influence their overall Gaussian curvature, such that petals invert from a cup shape to a saddle shape upon blooming. Previous simulations of these shape changes have assumed that petal thickness decreases at least quadratically. Here, we evaluate tomograms of several varieties of lily buds and find that this assumption is valid along the short axis of the buds, but not the long axis. A challenge of employing traditional tomography methods to measure petal thickness is that the sample is destroyed; a single bud cannot be followed through the entire blooming process. To address this challenge, we provide proof of principle that the nondestructive, label-free method of x-ray tomography produces high-contrast three-dimensional scans on time scales short enough to follow lily blooming.

盛开的卡萨布兰卡百合花的花瓣边缘和撕裂的塑料片的边缘会出现波纹。在这两种系统中，波纹都是由于纸张边缘长度过长造成的。通过使用盛开的百合花的延时视频和已发布的撕裂塑料片的图像，我们发现两个系统中的波纹都可以通过缩放关系很好地描述$A\propto \sqrt{w（L-w）}$， 在哪里$A$是振幅，$w$是波长，并且$L$是弧长。先前报道的自相似波纹模式的现象学关系，即$⟨A⟩\propto ⟨w⟩$，可以通过假设屈曲应力恒定来恢复。花瓣边缘的过长也会影响它们的整体高斯曲率，使得花瓣在开花时从杯形反转为马鞍形。先前对这些形状变化的模拟假设花瓣厚度至少呈二次方减小。在这里，我们评估了几种百合花蕾的断层图，发现这一假设在花蕾的短轴上有效，但在长轴上则不然。采用传统断层扫描方法测量花瓣厚度的一个挑战是样品会被破坏；无法跟踪单个花蕾的整个开花过程。为了应对这一挑战，我们提供了非破坏性原理证明，