The nestedness is about the topology of the surfaces, it means that most of the surfaces are concentric around a single point. The alternative is that there are

The nestedness is about the topology of the surfaces, it means that most of the surfaces are concentric around a single point. The alternative is that there are lots of little islands, so if you plot the 2d cross section there will be rings that are next to each other, instead of one being inside the other. In the extreme case you can get "stochastic" patterns, where there are infinitely many islands in a fractal pattern. See the e.g. figures here: http://iopscience.iop.org/article/10.1088/1367-2630/15/1/013061 http://iopscience.iop.org/article/10.1088/1367-2630/15/1/013... https://en.wikipedia.org/wiki/File:Stellarator_magnetic_field.png https://en.wikipedia.org/wiki/File:Stellarator_magnetic_fiel... In the hill metaphor, saying that the surfaces are nested corresponds to there being a single of peak of the hill.