# Lissajous-like Kolam

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

x(t)=sin(t+)

ω

x

δ

x

y(t)=cost+

ω

y

δ

y

Here we construct Lissajous curves that resemble Sikku Kolams made from an dot array by taking =N, =M, =0, 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.

N×M

ω

x

ω

y

δ

y

δ

x

M

N,

x

x

x

z

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.

GCD(N,M)

GCD(N,M)≥2

C=2N×M-(N+M)

C

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."

x

y

z

z