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