Middlesquares

Middlesquares is a pseudorandom number generator algorithm, developed by John von Neumann in 1946. It is a simple and early method for generating sequences of numbers that appear random. The algorithm works by squaring a number, then extracting the middle digits of the result to form the next number in the sequence. For example, if the starting number is 1234, squaring it gives 1522756, and the middle digits (2275) form the next number in the sequence.

The middlesquares algorithm is easy to implement and understand, but it has several limitations. It can produce sequences with short periods, meaning that the numbers may repeat after a relatively small number of iterations. Additionally, the algorithm can produce sequences with non-uniform distributions, where certain numbers appear more frequently than others. Despite these limitations, middlesquares was an important early step in the development of pseudorandom number generation and has influenced the design of more sophisticated algorithms.