>In the last 15 years or so, researchers have created a number of tools to probe the geometry of these hidden structures. For example, you might build a model of the surface by first zooming in at many different points. At each point, you would place a drop of virtual ink on the surface and watch how it spread out.

It sounds to me like this 'ink drop' is a metaphor to explain some state-of-the-art dimensionality reduction technique. Does anyone know the common name of this technique?