The Hermann Grid Illusion involves the perception of gray dots at the intersections of white lines outside of the fovea. The traditional Baumgartner Model explains this based on the activity of on-center ganglion cells, but as János Geier points out this explanation is insufficient. He has shown that the illusion can be eliminated by simply adding curvature to the white lines, which would have no impact on the on-center ganglion mechanism. In the demo below, you can try this for yourself and watch as the gray dots disappear with increasing curvature. The same trick also eliminates the scintillation seen in the variation of the illusion with gray lines and white dots at each intersection.

Mouse Y: Amount of twist
Hold mouse button: Show dotted intersection version

In their paper Straightness as the main factor of the Hermann grid illusion, Geier et al suggest that this effect is due to the central role of straight edges in this illusion. The demo below is inspired by another of their stimuli (fig 5c in the paper), where they interrupted the white lines with circles rather than curving them to remove their straightness. This also eliminates the gray dots.

Mouse X: circle size
Mouse Y: circle luminance

In his graduate thesis, David Bodkin also reports that the strength of the Hermann grid illusion is angle-dependent; becoming weaker as the lines approach 45 degrees. To play with this idea, we also produced a simple demo for viewing a rotating Hermann grid.