Sigma Motion



Warning: this may take a little practice to see, but I feel it’s worth it.


What to see & do


The grating above will flicker wildly. Now move your finger along it, with a speed such that you travel the distance in about 2 seconds, while following the finger with your gaze. When you hit the right speed, you should perceive a smooth rightwards motion of the stripes. Now move your finger back. If you follow it again with your eyes, you will see smooth leftwards motion of the stripes! After a little practice, you can voluntarily switch movement direction without your finger as a guiding target.




While you perceive the illusory motion, your eyes do a “smooth pursuit motion” with occasional backwards saccades, altogether known as oculokinetic nystagmus.


The stimulus is just a rapid phase reversal of a bar pattern (black becomes white, white becomes black, etc.). The occasional jerks are due to aliasing of the reversal frequency by the raster frequency of your display and would not occur if I could perfectly synchronize to your temporal screen refresh.


You can experiment with the reversal rate (rps): the faster the rate, the faster the seeming movement (within even divisors of your VDU's framerate). You can also change bar width (px): the finer the bars, the slower the movement.


This phenomenon was named “Sigma Motion” by O. J. Grüsser, but first reported by James Pomerantz. It demonstrates the interaction of image reversal and eye movements: efference copy at work.




Behrens F, Grüsser OJ (1979) Smooth pursuit eye movements and optokinetic nystagmus elicited by intermittently illuminated stationary patterns. Exp Brain Res 37:317–336

Adler B, Collewijn H, Curio G, Grüsser OJ, Pause M, Schreiter U, Weiss L (1981) Sigma-movement and sigma-nystagmus: a new tool to investigate the gaze-pursuit system and visual-movement perception in man and monkey. Ann NY Acad Sci 374:284–302

Pomerantz JR (1970) Eye movements affect the perception of apparent (beta) movement. Psychonomic Science 19:193–194



Created: 2012-05-07

Last update: 2013-10-04