However, it seems I have lost all mathematical ability since leaving school. I cannot for the time of my life come up with the algorithm! There is only half-ideas and flashes, but nothing like "start like so, then for every iteration check this and that, calculate the increment by whatever and increment"; I can design and implement complex applications, but I cannot

*see*this one algorithm.

When plotting the counter value it should look similar to this image (taken from a wikipedia article about Sigmoid functions

^{w}), more precisely like the upper right quadrant: it increases steeply at first and then flattens ever more.

**So here goes the challenge**:

Can anyone tell or show me the algorithm (easy, I think)

**and**can anybody explain this algorithm to me, maybe step by step.