Visualisation of the Box-Muller transform. The coloured points in the unit square (u1, u2), drawn as circles, are mapped to a 2D Gaussian (z0, z1), drawn as crosses. Points within 1 standard deviation are drawn with more saturation. The plots at the margins are the probability distribution functions of z0 and z1. Note that z0 and z1 are unbounded; they appear to be in [-2.5, 2.5] due to the choice of the illustrated points. In the SVG file, hover over or tap a point to highlight it.
Own work
Cmglee