A structure is the geometric scaffold a design is built on — the answer to “what holds this pattern together?” before any motif appears. The dominant scaffold across South Indian practice is the counted grid of dots, but lines can also weave around dots without touching them, radiate from a centre, run as pure bands, or dispense with scaffolding altogether. The articles in this chapter describe each structural mode; every design in the library carries exactly one.
Geometry runs deeper here than scaffolding. The threshold arts carry, in drawn form, ideas that formal mathematics names symmetry groups, lattices, Eulerian paths, algorithms, and tilings — developed inside the practice by hand and eye, and described (never defined) by the research that later found them. The essays in this chapter teach that mathematics through the designs themselves: the four symmetries, the grid as a coordinate system, the one-line problem, the rules that grow patterns, and the seventeen ways a pattern can repeat.