non uniform subdivision(points) on curve by nudibranch

I am trying to find a group of points on a curve, they subdivide the curve in a typical non uniform way(the discipline is like the image.)

To make it clear, what I want to achieve is to have a group of points on the curve, and the distribution of these points on the curve is just in the density of the drawing(like this image), the start and end points are the two ends of the curve.