Random Number Generation

Uniform Distribution of Numbers

This visualization generates and plots 500 integers in the range [0, 10).

Normal distribution of numbers

Box-Muller Transform for Generating Gaussian-Distributed Numbers

• Wikipedia - Box-Muller Transform

• Summary of steps

  1. Generate two uniformly distributed random numbers in range (0, 1): $U_1$, $U_2$
  2. Let $R^2 = -2 * lnU_1$
  3. Let $\theta = 2\pi U_2$
  4. Then $Z_1 = R * cos(\theta)$ and $Z_2 = R * sin(\theta)$ are two independent numbers with a standard normal distribution.
• Play with it below! 🕹
  • When the mouse is within the grey area (1x1 rectangle), mouse x is used as $U_1$ and mouse y is used as $U_2$.
  • Result $Z_1$ is drawn on top, and $Z_2$ is drawn on the right