Pseudo Random Numbers

In Buffon's experiment the randomness needed to perform the experiment was obtained in a physical way. For computer experiments we need some algorithmic way to produce sequences of numbers that are independent and have the same distribution (eg. uniform, normal). We call such numbers pseudo random numbers.
Techniques to produce uniform pseudo random numbers include the middle-square-method (historical), congruential methods, and random bit techniques. Random points in a box are obtained by sampling in the interval of each coordinate.

For producing non uniform pseudo random numbers different techniques utilizing uniform pseudo random numbers are used.

Sometimes (eg. in integration) very uniformly distributed points are useful. They are like equidistant points but differ from these in that any number of them [1,i] i=1,2,3,... are very uniformly distributed. Examples of these are van der Corput sequences, Hammersley sequences, and Halton sequences, the two last for sampling in boxes.