The mode atlas.

Every pattern a cylindrical cell can hold, drawn the way the live dish draws them - crests red, troughs blue, the still lines left on the page. Read across for spokes, down for rings; each square is one of the container's own natural shapes, computed from the same catalogue the overview and sandbox run.

The mode atlas. Each tile is one natural mode of a water cell 50 mm in radius and 10 mm deep, its surface free to slide at the wall, frozen at the instant of deepest relief: red where the surface lifts, blue where it dips, the page tone along the lines that never move. Across the columns, m counts spokes - nodal diameters; down the rows, n counts rings - nodal circles. The shapes are exactly the ones the dish draws on the overview and sandbox; click any cell there to set the pattern in motion.