Kolam

Continuous loops woven around a lattice of dots — the South Indian threshold art, and this workspace’s namesake.

What it is

A dot lattice (square, diamond or triangular) with smooth curves weaving diagonally around the dots. In the sikku (“knot”) style the curves are closed loops that enclose every dot; the prestige form is a single unbroken line around the entire lattice. Pulli style connects the dots directly. The curve knob sweeps from angular to fully rounded weave.

How to use

As line art for colouring or tracing. Tracing pages follow the loop with a finger or pencil in one continuous motion — the single-loop kolams exist for exactly that. As colouring pages, the weave’s over-alternating regions take alternating colours naturally.

Purpose

The namesake crate. Kolam is also a satisfying algorithmic object: loops emerge from local crossing decisions on the dual edge graph, and merging along a spanning tree walks the design from many small loops down to one — the same spanning-tree trick masyu uses for its Hamiltonian cycle.

History

Kolam is a daily practice in Tamil Nadu: women draw the design in rice flour at the threshold before dawn, an act of welcome and impermanence — walked away by the day, redrawn the next. The sikku tradition encodes real mathematics (array grammars and knot theory both study it), and specific family patterns pass down generations. Related forms: rangoli (North India), muggu (Andhra Pradesh).

This implementation

• Spec knobs: lattice (square/diamond/triangular), style (sikku/pulli), loops (1 = single continuous line), curve, spacing, show_dots.
• Generation: every dot starts as its own diamond loop; a union-find merge along randomly-ordered adjacent pairs fuses loops until the target count remains; the weave is traced through gate pairings and rendered as smoothed beziers.
• Guarantees: every dot enclosed, loop count reported honestly (loops_found vs loops_requested), all arcs used — each checked, not assumed.