Different people see different intensities of colors on this spinning disk. Why people see color here is not fully understood, but the illusion involves color vision cells in your eyes called cones.
There are three types of cones. One is most sensitive to red light, one to green light, and one to blue light. Each type of cone has a different latency time (the time in which it takes to respond to a color), and a different persistence-of-response time (the time it keeps responding after the stimulus has been removed). Blue-sensitive cones, for example, are the slowest to respond (have the longest latency time), but they keep responding the longest (have the longest persistence time).
When you gaze at one place on the spinning disk, you are looking at alternating flashes of black and white. When a white flash goes by, all three types of cones respond. But your eyes and brain see the color white only when all three types of cones are responding equally. The fact that some types of cones respond more quickly than others—and that some types of cones keep responding longer than others—leads to an imbalance that partly explains why you see colors.
The colors vary across the disk because at different radial positions on the disk the black arcs have different lengths. As a result, the duration of the flash on the retina is also different.
A complete explanation of the colors produced by a Benham’s disk is more complicated than the simple one outlined here (for example, the short black arcs on all Benham’s disks must also be thin, or no colors will appear), but this is the basis of much of what you see.
Benham’s disk was invented by Charles Benham, a nineteenth-century toymaker who noticed colors in a black-and-white pattern he had mounted on a top. Even now, tops with Benham’s disks can occasionally be found in toy stores.