Grid Illusions, curved, Herman Grid

from Michael’s Visual Phenomena & Optical Illusions


What to observe

Above you see the widely known Hermann-grid illusion with a new twist. When the grid lines are straight, dark patches appear in the street crossings, except the ones which you are directly looking at. When the streets are curving, the dark patches vanish.

What to do

You can make modifications to the figure as obvious from the button labeling. “Auto run” can get annoying, so you can stop it. I personally am amazed that a very small amplitude of the modulating sinusoid already kills the patches.


This demonstration is based on the ECVP2004 contribution by János Geier et al. (abstract below).

If you are acquainted with the “classical” explanation of the Hermann grid (previous page), it will be obvious to you that this demonstration immediately invalidates that explanation – the inhibitory patches should exert the same influence whether the streets are curved or straight.

I never found the receptive field explanation sufficient, because the convolution with the receptive field occurs with every retinal image and must be removed by cortical deconvolution anyway. The special thing about the Herman grid is the failure of this deconvolution, IMHO.

An extensive critique of the “old” Hermann grid explanation can be perused at Peter Schiller’s lab.


Schiller P et al. (Mar 2004, guessing from the file dates)

Geier J, Sera L, Bernath (2004) Stopping the Hermann grid illusion by simple sine distortion. ECVP 2004, abstract: “Almost the only explanation of the Hermann grid illusion is the Baumgartner model: the effect is generated by the response of cells having concentric ON–OFF or OFF–ON receptive fields (ie a Mexican-hat weighting function). This model predicts that the illusion is independent from the relative directions of the right-angled intersections. Some authors (Wolfe, 1984 Perception 13:33–40; for a review see Ninio and Stevens, 2000 Perception 29:1209–1217) show that the magnitude –not the existence– of the illusion depends on certain geometrical properties.
We made some simple distortions to the Hermann grid that make the illusion disappear totally while the Hermann-grid character remains. The most effective of these was to replace the straight lines with sine curves leaving the intersections right-angled. The illusion is found to disappear at a surprisingly small sine amplitude (amplitude/period <1/10). We supported these results with psychophysical measurements (n=29). Simple geometrical consideration shows that the distortions produced here do not change the weighted sum of the receptive field. We conclude that the Baumgartner model is not an adequate explanation of the Hermann grid illusion, because its prediction is contrary to the observations. The same distortions applied to the scintillating grid made the scintillations disappear.”

Lingelbach B, Ehrenstein W (2004) Neues vom Hermann-Gitter. Optikum.

Geier J, Bernáth L, Hudák M, Séra L (2008) Straightness as the main factor of the Hermann grid illusion. Perception 37:651–665

Bach M (2009) Die Hermann-Gitter-Täuschung: Lehrbucherklärung widerlegt. Der Ophthalmologe 106:913–917