The picture is low quality and mostly shadow. Our brains try to make up for that quality/shadow issue by coloring it in for us. That’s why you can do things like scroll the picture up or down so that you can just see the edges of the dress in question and often see the opposite color than you initially saw. It’s also the reason you see one color pattern when looking then go back to the image and see another color pattern. It is always just your brain filling in the color for you.
Ignore the trim, and the photo shows a dress that is a pale, washed out blue tint shown silhouetted against bright sunlight coming through the window. It’s possible that it’s a blue dress, washed out in the photo by the bright light, or it is a white dress, shadowed blueish against the surrounding bright yellowy light. Your brain choose one possibility or the other, and corrected accordingly.
What helped me wrap my head around “the dress phenomenon” was watching an animated movie. In a live action movie (or in stop-motion animation), they control the lighting with the use of lights (obviously), but in animation (traditional or computer generated), they create the illusion of different lighting through color choices. Find two photos of the same character in a daylight scene and in a nighttime scene. You’ll find they used darker, bluish-tinted shades of the character’s colors to indicate the character is in darkness or shadow. Unless you consciously think about it, you don’t notice that Woody’s kerchief is now burgundy instead of red, you just perceive it as red but in shadow. Your brain perceives it as the color it thinks it “should be” in normal lighting conditions. That’s what happens with the photo of the dress.
Your eyes and brain do a lot of automatic “color balancing” where they figure out the actual color of an object based on the color your eyes see and the lighting. This is how you can, for example, park your car during the day under broad daylight and still identify it when lit by a streetlamp at night. The actual wavelength of light coming from the car is totally different, but you instinctively compare that light to other light near the car and figure out what the color _would_ be under standard lighting.
For example in this picture http://brainden.com/images/color-cube.jpg the labeled squares are all the same color on your computer screen, but your brain interprets them differently because it knows that in the real world the tile in shadow would have to be much lighter than the tile in the light to have the same apparent color.
The dress, because of the quality and the framing of the picture, sits _right_ on a knife edge where our brains aren’t sure how to interpret it and different people see it differently. As I noted, we interpret color based on the surrounding lighting…but what if people’s brains jump to different conclusions about what the background lighting is? That’s what’s happening here. If your color-balancing function in your brain thinks that the dress is being lit by blue light, then it will send you “gold and white” for the color because gold and white lit by blue light look like what you see in the picture. On the other hand, if your brain thinks the dress is being lit by yellow light, it will send you “blue and black” because blue and black lit by yellow light _also_ look like what you see in the picture. So you get a different color depending on your interpretation, and the picture is such that people get different interpretations. This bit happens subconsciously, so people don’t realize why they disagree.
Here’s some comparison pictures sort of illustrating the idea
https://i.pinimg.com/originals/35/0d/8f/350d8fdc2f5b900d2da2740e9effd583.jpg
https://collegian.com/wp-content/uploads/2015/03/Screen-Shot-2015-03-04-at-6.31.05-PM.png
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