Problem:

When tired and it was dark, I noticed that if I focused on a dim light source and moved my eyes fairly rapidly sideways, the resulting images that lingered for a short while were not smoothly blurred together, but were discrete.
I assume this is not due to the brain's inability to process the data fast enough or the retinas not repairing fast enough when light breaks part of them down, so I am lead to the conclusion that eyes (if not generally, sometimes) move in very small sudden jolts rather than smoothly.

Question: Is this correct? What is the reason for this (is it due to the eye muscles being unable to sustain motion for a long time, or something to do with the mechanics of the eye)?

Was this result anomalous? Please describe.