We explore the visualization of violent wave dynamics and erosion by waves and jets in laser-cut reliefs, laser engravings, and three-dimensional printing. For this purpose we built table-top experiments to cast breaking waves, and also explored the creation of extreme or rogue waves in larger wave channels. Surprisingly, there are nano-scale analogues of these wave patterns in surface engineering with ion beams instead of water waves. Insights in applied mathematics and fluid dynamics, materials, fabrication and aesthetics informed our explorations. The resulting patterns give us not only new ways to communicate to specialist and general audiences about mathematics and fluid dynamics on different scales, they also provide new, abstract imagery which can be used in architectural and design applications.