Take a look from afar at the picture and tell me: how many black circles would fit in the free space between the bottom circle and one of the upper circles of four or five? Most likely you will answer that the four mug will fit freely, but for the fifth, perhaps the space will already missing. When you say that the gap is placed exactly three mug, no more - you won't believe. Take the same piece of paper or a compass and make sure that you are wrong.
The empty space between the bottom circle and each of the top seems like more than distance between outer edges of the upper circles. In reality, the distances are equal.
This strange illusion, due to which black areas appear to our eyes to be less than the white of the same magnitude, is called “irradiation”. It depends on the imperfection of our eye as an optical device does not fully meet the strict requirements of the optics. Its refractive medium did not give up on the retina of those sharp edges, which are obtained on the frosted glass well trained photographic apparatus due to the so-called spherical aberration in each light path is enveloped in a bright border that increases its size on the mesh layer of the eye. In the end, the light areas always seem to be more than equal to them black.
In his “Doctrine of flowers” the great poet Goethe, who was a keen observer of nature (though not always sufficiently careful theoretical physicist), writes about this phenomenon:
“Dark object seems less bright the same value. If we consider simultaneously the white circle on a black background and the black circle of the same diameter on a white background, the last we seem to 1/5 less than the first. If the black circle to make the more they seem equal. Young Crescent moon seems to belong to a circle of larger diameter than the rest of the dark part of the moon, which is sometimes the case with this distinguishable (“ashen light” of the moon. - J. P. ). In a dark dress people seem to be thinner than in the light. Light sources, seen from the edge, make it apparent neckline. The line that appears candle flame, is represented by a cut in this place. Rising and setting sun makes like the notch in the horizon”.
These observations are all true, but the assertion that white circle seems more black always equal to the same proportion. The increase depends on the distance from which mugs are considered. Now it becomes clear why this is so.
Move the figure with black circles away from the eyes, the illusion will become even stronger, even more striking. The reason is that the width of the extension rim is always the same; if so close it increased the width of the bright area is only 10%, far in the distance when the image itself will be reduced, the same additive will already be 10%, but, say, 30% or even 50% of its width. The specified feature of our eyes usually explain the strange property that the following diagram. Looking at it closely, you see a lot of white circles on a black field. But move the book away and look at the picture from a distance of 2-3 steps, and if you have very good eyesight, from a distance steps 6-8; figure significantly change your appearance: you will see in it instead of the white circles hexagons, like a bee cells.
At some distance mugs seem to be hexagons.
I am not quite satisfied with the explanation of this illusion irradiation, since I noticed that the black circles on a white background also seem from afar hexagonal (see Fig. below), although the irradiation here does not increase, and reduces mugs. I must say that in General existing explanations of visual illusions is not conclusive; the majority of illusions and does not even explain.
Black circles seem to be off by hexagons.