# 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 Jun 27 '14 at 20:11
• By "evenly-spaced and perfectly/accurately distributed numbers ", a certain period has been assumed implicitly. – lorniper Jun 27 '14 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. – Arturo don Juan Jun 27 '14 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). – Christian Clason Jun 27 '14 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. – Christian Clason Jun 27 '14 at 22:08