Can someone explain to me in simple terms, how Sobol sequences work? The wikipedia article is fairly technical.
They look pretty interesting. So I shall describe (whatever little I know) in short the results to someone who is not aware of what Sobol sequences do- One can use Sobol sequences to fill up a space with "random" points. The nice thing about it is that the points distribute themselves fairly evenly and therefore sample the space uniformly (to a good extent) without having a pattern per se. Here is the distribution of points in 2D, as number of points increase.
As shown in the last figure, putting together all the points also follows the same property - uniform distribution of points.
There has been a related question The mathematics behind Sobol sequences, but that is asking for sources to study about Sobol sequences from, not an explanation.
Sobol sequences belong to the class of Quasi Random Generators (by opposition of Pseudo Random Generators).
Quasi Random Generators by construction minimize the discrepancy between the sub square (ie sub interval). Discrepancy is the (maximum) between 2 points inside sub-interval.
Quasi Random Generators are deterministic generators of points.
Sobol uses initial polynome to generate unform across one dimension. In d dimension, there are d Sobol generators (determined by d polynomes of initilization).
However, Sobol has flaws. The graph you shown is valid only a lower dimensions.