Generate function between 0 and 1 on both axis

Question

I am trying to create different function between 0 and 1 on both axis which can take the following shape. (more like logit curve)

I want to experiment the shape as well a little more.

I was referring to this thread here, however the limits are between -1 to 1.

any idea how can I achieve it?

Answer 1

Your shape looks a bit like $$f(x)=x+b\sin(2\pi x)$$ for some constant $b$. If you want more wiggles you can try $$f(x)=x+b_1\sin(\pi x)+b_2\sin(2\pi x)+\cdots+b_n\sin(n\pi x)$$ and play around with the constants.