Of course, we can do rather more with computer graphics than the mechanical Spirograph toy, so the relationship may not be too obvious to start with and becomes less so as we move on.
For example, we can inscribe a repeating motif as we trace the curves. In all the examples in this Gallery, the motif involves doubling the curve and placing a motif between the two curves. In some of the examples a representation of a sphere is introduced at less frequent intervals round the trace.
In later examples, we do not need to be confined to keeping the same scale throughout the drawing exercise (the size of the cycles can gradually decrease as the drawing builds up). We can also change colours gradually, rather than a sudden switching of pens. Later examples replace the single drawing point by a rotating line, and the center of motion can be allowed to move left and right, up and down according to another layer of cyclic motions.
In some cases, the algorithm creating the pictures is partly controlled by the user: motions of the computer mouse adjust parameters in the mathematical algorithm "on-the-fly" to produce non-reproducible results.
