This tutorial is about making a basic perfectly looping gif with Processing: a dot doing a circular loop. The trajectory of the black dot can be described with maths: the angle depends on time and the radius is fixed. Hence if the radius of the circle is r, the position at time t can be defined with: Note that if t goes from 0 to 1 (which will always be the case in those tutorials), the position at t=0 is the same as t=1.