Algorithm for normal random numbers

We propose a simple algorithm for generating normally distributed pseudorandom numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and that a Maxwell-like distribution that may be used as a source of normally distributed random deviates follows in the $\overrightarrow{N}\infty$ limit. The algorithm passes various performance tests, including Monte Carlo simulation of a finite two-dimensional Ising model using Wolff’s algorithm. It only requires four simple lines of computer code, and is approximately ten times faster than the Box-Muller algorithm.