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Lets return to the Hermann Grid now:
One explanation for the black dots is a theory called lateral inhibition. The idea comes from the way many of the retinal ganglion cells are "wired" to the light receptive cells that feed them stimulus.
Each retinal ganglion collects stimulous from a small area of light receptors. You might think that the ganglion cell would simply take the average of the stimulous from its receptive field, and pass that information along. This is probably the case for many ganglion cells, however, some of these cells perform a more complex operation on the stimulus they receive.
These cells are the lateral inhibition cells. They treat stimulous coming from the center of their receptive field as "positive", and stimulous coming from the edges of their field as "negative." This treatment of receptive information is useful for detecting edges where high contrast meets low contrast. In the diagram above, we see that although the white light in the middle of the squares induces a "positive" stimulous, the surrounding white light could produce a greater "negative" stimulous. Thus, the area in the middle could be perceived as being dark.