Monte Carlo π Estimation

Stanislaw Ulam & John von Neumann, 1949

Pioneered by Ulam and von Neumann in 1949 during nuclear weapons research, Monte Carlo methods use random sampling to obtain numerical results. This visualization drops random points into a unit square with an inscribed quarter-circle. The ratio of points inside the circle to total points, multiplied by 4, converges toward π. Teal dots fall inside; gray dots fall outside.