# Monte Carlo Simulation - Random Number Motivation

For Monte Carlo simulations, or any other numerical methods that rely heavily on the quality of the pseudo-random numbers generated (i.e even/desired distribution on a certain domain) for that matter, why aren't evenly-spaced and perfectly/accurately distributed numbers (not pseudo-random) used as opposed to pseudo-random numbers?

The reason I ask this is because I would imagine the main purpose of sampling tons of pseudo-random data as opposed to non-random data would be to speed up the time taken by the program that is sampling that data, much like how throwing a bunch of paintballs at a canvas/wall would, more easily and quickly, cover up that canvas/wall than carefully painting it with a paintbrush would. However, many pseudo-random number generator algorithms that I have seen look more complicated and time-consuming than just using non-pseudo-random, perfectly distributed data.

Clearly I have a misunderstanding of this topic. Could anybody help clear this issue up?

• en.wikipedia.org/wiki/Quasi-Monte_Carlo_method
– k20
Commented Jun 27, 2014 at 20:11
• By "evenly-spaced and perfectly/accurately distributed numbers ", a certain period has been assumed implicitly. Commented Jun 27, 2014 at 20:54
• Yes, a period of 1. For example, in the ever-so-famous example of approximating pi with a Monte Carlo simulation, why is it more practical to use a large set of pseudo-random points, rather than making a grid of evenly distributed points (like a matrix of a bunch of these perfectly distributed points in the first quadrant) and using that? Here's what I mean. Commented Jun 27, 2014 at 21:34
• The example of a circle is misleading, since the dimension (2) is fixed and very small. The number of uniform points you need for a good covering grows exponentially with the dimension, while this is not the case for random points. Monte Carlo only becomes competitive if the dimension is large (say, 100 and above). Commented Jun 27, 2014 at 21:47
• To elaborate: Take the same number of points as in your sketch, and repeat the experiment for a sphere. Now do the same with a four-dimensional hypersphere. Watch the result for uniform sampling get worse much faster than for random sampling. Commented Jun 27, 2014 at 22:08