Closed loops of square bar that only ever run along the edges of a cube grid. Three tones are all it takes to read them as solid.
Self-avoiding polygons on the cubic lattice · Sumners & Whittington, 1988
Each loop begins as a single square and grows by pushing one of its edges out sideways into a U, wherever there is room, so it stays closed and never touches itself. Loops like this on the cubic lattice are a model for long molecules such as DNA, and in 1988 De Witt Sumners and Stuart Whittington proved that as they grow longer, almost all of them are knotted.
Seen down the cube's diagonal in isometric, one bar can pass behind another that it never touches in space, which is where the drawing starts to look impossible. Free threads two loops through each other like links of a chain and sets a small one apart; three loops are set a third of a turn apart around the centre; symmetric makes those turned copies of one. In motion the loops are laid down along their length, then taken up again.
Behind the mathematics
Almost all lattice loops are knotted, 1988
American mathematician at Florida State University who brought knot theory to the study of DNA, and in 1988 with Stuart Whittington proved that almost all long closed loops on the cubic lattice are knotted.