Lissajous
The initial image below (before you grab it and rotate it) corresponds to a parametrized curve in R2 given by
x(t) = sin(m t),
y(t) = cos(n t),
0 ≤ t < 2π,
for positive integers m and n.
But actually (as you see when you turn it about) it is a curve in R3. It is given by
x(t) = sin(m t),
y(t) = cos(n t),
z(t) = cos(m t),
0 ≤ t < 2π,
and is initially viewed from a distant point on the z-axis. The curve is essentially a sine curve wrapped around a cylinder.