A white shirt in the shade
On a sunny day a white shirt stepping into the shade of a tree can reflect less light than a grey stone in the sun. Yet we see the shirt as white and the stone as grey. Our eye does not work like a light meter; it estimates how much of the incoming light comes from the surface and how much from the illumination.
In this experiment you try to separate a square from its context in six scenes and set its grey. In every scene the dotted square has a twin: the two are exactly the same grey, but one is in the shadow and the other in the light, or one is on a dark background and the other on a light one. At the end we remove the context and show the twins side by side.
The shadow illusion
Edward Adelson's checker-shadow illusion, published in 1995, is one of the best-known images in vision science. A cylinder casts a shadow on a checkerboard; a light square in the shadow and a dark square in the light reflect the same light, yet one looks light and the other dark. The shadow scene in this experiment follows the same idea but was drawn from scratch: an orange block casts a soft-edged shadow onto a floor of light and dark tiles.
We computed the scene physically: the shadow reduces the light to 45 per cent, and the light tiles reflect exactly that much more light than the dark ones. So the light tile in the shadow and the dark tile in the light are drawn with the same pixel value. If you set the tile in the shadow as light, your visual system did the right thing: it took the shadow into account and saw the tile itself.
Simultaneous contrast
A grey square in the middle of a dark background looks lighter than the same square in the middle of a light background. This simultaneous contrast illusion has long been known. Heinemann measured it systematically in 1955: he varied the luminance of the surround and of the test field step by step and recorded how bright the test field looked.
In this experiment the background changes smoothly from dark on the left to light on the right; the two squares are exactly the same grey. In one round you match the square at the dark end, in the other the square at the light end. According to the anchoring theory proposed by Gilchrist and colleagues in 1999, the brain takes the lightest surface in a framework to be white and scales the other surfaces relative to it; the square with a dark surround is the 'lightest' in its own small framework, so it looks lighter.
White's illusion
In 1979 Michael White published a strange illusion in the journal Perception. When parts of horizontal black and white stripes are replaced with the same grey, the grey patches on black stripes look lighter than those on white stripes. What's strange is this: most of the edges of a grey patch on a black stripe border white. Simple contrast should make it look darker; the result is the opposite.
At first sight the direction of the effect looks as if the grey patch takes on the colour of the stripe it sits on. But in 1991 Kingdom and Moulden showed that their measurements did not support this 'assimilation' explanation, and that the effect could be explained by two contrast mechanisms, one local and one acting over a wider area. In 1999 Blakeslee and McCourt explained White's effect and simultaneous contrast in a single framework with a model built from orientation-sensitive filters.
Early filters, or interpretation?
How much of these illusions comes from early filters in the eye and primary visual cortex, and how much from a higher-level interpretation of the scene, is still debated. In 1993 Adelson showed in Science that small changes to the stimuli, which hardly changed the contrast at all, greatly changed the strength of an illusion: how the shapes were grouped determined the grey we saw.
In 2011 Fred Kingdom summed up the past quarter century of this field as 'new ideas, captivating demonstrations and unrelenting controversy'. Among the most promising approaches he listed multi-scale filter models and the idea that the visual system splits the image into layers of reflectance, illumination and transparency. This experiment won't settle that debate, but it puts side by side how much the same people diverge in three illusions.
Your score and your screen
Each round's score is calculated from the L* difference between the grey you set and the square's true grey: 10 / (1 + (|difference| / 8)^1.6). A 4-unit difference earns about 7.5 points and 8 units earns 5 points; the six rounds add up to at most 60 points. L* is a lightness scale from 0 (black) to 100 (white) on which equal numerical differences look roughly equal to the eye.
Screens are not calibrated. We recommend turning brightness up and switching off night mode and blue-light filters. Whatever screen you use, the twin squares have the same pixel value; the strength of the illusion depends not on the quality of the screen but on the structure of the scene.