Middle-square method

The middle-square method is an early way of generating pseudorandom numbers. To produce a sequence of n-digit numbers, one starts with an n-digit seed, squares it to get a number of up to 2n digits, pads with leading zeros if needed, and takes the middle n digits as the next number, then repeats. John von Neumann invented the method and described it at a conference in 1949. He joked that anyone using arithmetical methods to produce random digits is in a state of sin, but he found them hundreds of times faster than reading random numbers from punch cards, which mattered for his ENIAC work. In practice the method is badly flawed: its period is usually very short, the sequence can fall to zero or lock onto a repeating cycle, and with n digits the period cannot exceed 8 to the power n. Modifying it with a Weyl sequence improves period and randomness.