Deterministic sampling from uniform distributions with Sierpiński space-filling curves

In this paper the problem of sampling from uniform probability distributions is approached by means space-filling curves, a topological concept that has found number important applications in recent years. Departing theoretical fact they are surjective but not necessarily injective, investigation focused upon structure obtained when their domains swept and discrete manner, corresponding values used to build histograms, approximations true PDFs. This work concentrates on real interval [0,1] Sierpiński curve was chosen because its favorable computational properties. order validate results, Kullback–Leibler other divergence measures comparing several levels granularity with already established methods. truth, generation random numbers deterministic simulation randomness using numerical operations. fashion, sequences resulting sort process truly random. Despite this, be coherent literature, expression “random number” will along text mean “pseudo-random number”.