[thoughtcritical]

"figure of eight" curves .... perhaps the simplest is the lemniscate of Gerono, which has the parametrization:

x = cos(t); y = sin(2t) / 2; and looks like this:

Lemniscate of Gerono animation https://i.sstatic.net/VKBgs.gif

However, the lemniscate of Bernoulli may be visually more pleasing; it has a parametrization very similar to the lemniscate of Gerono, except that both axes are scaled by a factor of 1/(sin(t)^2 + 1) = 2/(3 - cos(2t)):

scale = 2 / (3 - cos(2t)); x = scale cos(t); y = scale * sin(2*t) / 2; It looks like this:

Lemniscate of Bernoulli animation https://i.sstatic.net/nOPMx.gif

per: https://gamedev.stackexchange.com/questions/43691/how-can-i-...