A sigmoid function is useful for lots of graphics applications, it’s yer classic ease-out, ease-in curve for animation, and its a film-look response curve for colour. Here’s one I’m using in a script I’m working on, it has variable power and for both x and y 0 <= x <= 1

The function is defined for y, given x and p:

y = g(1-x) / (g(x) + g(1-x))

where g(x) = (1/x)^{p}

p is any positive number > 0 (it flatlines at p=0)