Course: Advanced sampling techniques

Simulation of Biomolecules – p. 4
Monte Carlo: The Idea
⇒
π
#darts hitting shaded area
#darts hitting inside square = 4 r2
r 2 = π 4
π = 4
#darts hitting shaded area
#darts hitting inside square
• If you actually do this experiment, you’ll soon realize that it takes a
very large number of throws to get a decent value of π, well over
1 000.
• To make things easy on ourselves, nowadays we can use
computers and generate random numbers.
• If we say our circle’s radius is 1.0, for each throw we can generate
two random numbers between 0 and 1 for the x and y coordinate,
which we can then use to calculate the distance from the origin.
• If this distance is less than or equal to 1.0, it is within the shaded
area and counts as a hit.