Lissajous-like Kolam

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."


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