Interactive Apps

Explore Monte Carlo methods through interactive visualizations

Each app opens on its own. You’ll find every one of them, with the explanation around it, in the chapter it belongs to – and the Share button on any app gives a link or an <iframe> snippet for embedding it elsewhere.

Estimating π

Scatter points in a square and count how many land inside the circle.

Buffon’s Needle

Drop needles on a ruled floor; the fraction that cross a line estimates π.

Random Walk in a Region

Sample uniformly from a non-convex region with random-walk Metropolis, and tune the step size.

Metropolis–Hastings

A Metropolis chain for the standard normal: trace, rejected proposals and histogram.

Gibbs Sampling

Gibbs sampling a bivariate normal: watch correlation slow the staircase down.

Random Walks on Graphs

Watch a distribution spread over a graph and compare mixing times, bottlenecks and spectral gaps.