Which of these assortments of dots is more random?

The image on the left may appear more random, because there is no discernible pattern, while the image on the right has clusters of dots that may suggest shapes. In fact, these clusters result naturally from randomness, and the tendency to perceive them as non-random is known as the clustering illusion. The image on the right is truly random. The x and y coordinates of the dots in the right image are random numbers from 0 to 300 provided by random.org, which uses atmospheric noise to produce true random numbers. The image on the left was created to appear random by avoiding clusters.

Humans are pattern-seeking creatures, which is an evolutionary advantage. If you see a tiger’s face hidden in a pattern of jungle leaves, you may be able to escape, and the fact that you also see faces in clouds or shapes in constellations of stars is not a disadvantage. However, this tendency to see patterns within randomness can lead to cognitive errors. When a gambler sees red come up on a roulette wheel four times in a row, she may falsely believe that the wheel is on a red streak, and red is more likely to come up again. Conversely, she may believe that since red has come up four times in a row, black is now due to come up. This is the gambler’s fallacy. In fact, the odds are the same regardless of previous spins of the wheel.

The fact is, there is a high probability of many improbable things happening. As I was collecting the numbers for the x and y coordinates for the image on the right above, the same number came up twice in a row. For a moment, this seemed like a strange coincidence and made me question whether the numbers were truly random. However, in collecting 100 random numbers from 0 to 300, there is about a 1/3 chance of seeing the same number twice in a row: not improbable at all.