To me, plane-filling curves are a mathematical concept that is inextricably linked to art. So naturally I feel the need to accompany any research breakthrough with the creation of visual art. This work addresses the generalization of simple curves and folding curves: the curve-set. More information can be found in „Puzzling plane-filling curves“ by Arndt and Handl.
A simple curve's border forms the jigsaw pieces of a puzzle
falling into place on the plane. Only one pure form in four
directions. Four pieces in four directions can be assembled in two
ways and give two beautiful lattice tilings.
But don’t let the tasty colors fool you, it’s not that simple. Out of the dark, a curve-set emerges: One curve has become a set of four! Now it’s four captivating forms, each in one direction, that are assembled in two ways to form two tiles. Can you spot the four vibrant tiles that could make a lattice?