pryrt Thank you very much indeed. Thanks to your leads; I've ended up finding the Logistic function, which with its tunable slope and rotational symmetry is exactly the function I was looking for, despite that I didn't know it existed :)

I'm still getting to grips with how the tunable parameter(s) affect the curve; and I need to deal with the fact that at steep slopes, the y values stay hard at the bottom and top of the range for too long -- I think I'll need to fiddle with x-range to ensure that I start and finish at the beginning and end of the curves rather than well before and after; but I think I can handle that.