Sampling Method
Uniform Random
classic Monte Carlo · O(1/√n)
Halton Sequence
quasi-random base 2/3 · faster
Stratified Grid
one point per k×k cell
Latin Hypercube
uniform marginal coverage
Correlated (biased)
x = y — shows why independence matters
Speed
×1
×100
×5000
Show
○ Circle
↗ Convergence
↺ Reset
⏸ Pause
Cyan = inside circle.
Red = outside circle.
π/4 = fraction inside.
Halton
covers space
more evenly than random.
Correlated
samples
are biased: π̂ → 2√2 ≠ π.
method =
Uniform
n =
0
inside =
0
π̂ =
—
|error| =
—
1/√n =
—