The muggu

A muggu is laid out at dawn on the swept ground before a Telugu household: a lattice of rice-flour dots, then loops drawn around them in one moving hand. By evening it is walked away, and the next morning there is a new one. The version above obeys the same contract — it is generated when you arrive, and no two visits see the same drawing.

The grammar of a floor drawing

These patterns have a formal-language literature, which delights me beyond reason. In the 1970s, Gift Siromoney's group in Madras began writing array grammars for kolam patterns — rewriting systems that generate two-dimensional pictures the way ordinary grammars generate sentences. The dot-grid drawings turn out to be a natural home for picture languages, cycle languages, and even knot-theoretic questions: which patterns can be drawn in a single unbroken line, and why?

The generator here leans on one small piece of that structure. It chooses a random set of cells in the dot lattice, symmetric under the eight symmetries of the square, and XORs their boundaries together. Whatever comes out belongs to the cycle space of the grid — every dot is touched by an even number of strands, which is exactly the condition for the drawing to resolve into smooth closed loops. Each dot then renders its strands as quarter-circle arcs centred on the corners of its cell, and because adjacent dots share those corners, neighbouring arcs lie on the same circle and join without a seam. The loops close themselves; the program never has to check.

The story of building it is told in projects; a shorter note on why it sits at the bottom of every page is planted in writing.