> You could pick lots of different functions, including simple linear motion (z = c * t)

that was also my first intuition when making this, but turned out making the z function linear won't make it a sphere.

to make a sphere, you have to configure it in a way so that it forms a circle with the other axes. In this vis, its the sin(0.02 * πt) and cos(0.02 * πt) part that do this.

someone makes an interactive version here: https://www.desmos.com/3d/t66etxi1y8 (thanks!) so you can try changing the z function for yourself.