Hmm.

I do quite a bit of parametric modelling and I see how something like this could be made. Find the angles of the sun at specific times, project planes at a fixed distance and angle matching around your cylinder, sketch the time number you want on each plane with a fixed pitch and then project-cut back through the cylinder. Would be a pain in the ass though. And a pretty tough 3d print without soluble supports, given all those tiny tiny interior walls and cavities.