The Geometry behind the kolams

01 A grid of dots segmented into rhombuses of different sizes

02 Constructing random walk paths by repeatedly choosing an unvisited neighbouring dot

03 Assigning a shape based on the dot's position in the walk

C corner

M middle

S start / stop

04 Building the kolam by arrangiing corresponding shapes around dots

05 Separating the forward and backward paths

06 Drawing the final kolam in traversal order, by alternating between forward and backward paths for dots along the walk

07 Repeating the same rule across the larger grid

15.01.23

02.04.23

18.08.23

14.01.24

21.07.24

31.10.24

15.01.25

27.03.25

18.08.25

14.01.26

A line