Lissajous-like Kolam

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A Sikku Kolam is a design made of curved loops drawn around an array of dots. These designs bear a resemblance to Lissajous curves, which can be described by the parametric equations




Here we construct Lissajous curves that resemble Sikku Kolams made from an dot array by taking , , , and to be a function of , and the phase control. The phase changes the phase of to start drawing a loop. The phase draws the curves in three dimensions; it is enabled when "alternate crossings" is checked.

The number of possible loops is , but only two are shown if (the second is green). The number of crossings is . When the frequency in the third dimension equals the number of crossings , the crossings alternate.

The Lissajous curve has an phase and a phase, and a phase is introduced in a loop for the third dimension. When "alternate crossings" is checked, the phase of modulation is adjusted to make alternate crossings. The length of the curve is controlled with "tracing."


Contributed by: Shojiro Nagata (January 2015)
InterVision Institute
Open content licensed under CC BY-NC-SA




[1] S. Nagata, "How Many Loops Kolam Loop Pattern Consists Of," Forma, 30(1) special issue, 2015 pp. 9–18.

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