A sea can look unpredictable without being complicated at every level. Sometimes the interesting part is how a few simple things refuse to agree.
One wave is a beginning.
Take a smooth wave and send it across a flat plane. Its amplitude tells us how far it rises. Its wavelength tells us the distance between crests. Its direction tells us where it travels. One wave gives us a rhythm, but it gives away the pattern almost at once.
The sea in the Living Atlas uses six such waves. They have different wavelengths, different directions, and different starting phases. At any point on the surface, their heights add together. What looks intricate is a conversation between simple parts.
Six components / Four parameters each / One sum
The slope is part of the story.
A surface is more than a collection of heights. It also has a direction at every point. The derivatives of the wave equation tell us how quickly height changes as we move across it. Together, those slopes give us a surface normal.
The same relationship appears twice in the scene: in the light reflected by the water, and in the attitude of the small ship. The ship samples the geometric field beneath it. Fine shading ripples add texture to the light, but they do not shake the hull. This is a visual model, with deliberate simplifications rather than a full fluid simulation.
Height + two derivatives / One surface normal
A change of view, not a change of sea.
As you scroll, the camera rises and the shaded surface becomes a drawing. The grid and contours are evaluated on the same moving geometry. There is no separate animation trying to keep up with the first one.
An edition fixes the six wave coefficients with a repeatable seed. The printed plate samples them at time zero. It is the same mathematical surface held still and projected onto paper. The title, the navigation, and this text remain ordinary readable HTML around it.
Edition 70806d5e / Authored study / Frozen at t = 0
The drawing does not explain away the sea. It gives you another way to see it.