Random and Pseudorandom Sequences

  • Ronald T. Kneusel


Randomness is a fuzzy and difficult concept. In this chapter we side-step the philosophical issues and instead focus on random and pseudorandom sequences. We discuss what we mean by a random sequence and give examples of processes that generate randomness. We then conduct an experiment that shows humans are bad at randomness. Pseudorandom sequences are introduced next, along with an experiment showing that the quality of a pseudorandom sequence matters. We conclude with a quick look at hardware random number generation as supported by modern CPUs.


  1. 1.
    Augustine of Hippo, Confessiones lib xi, cap xiv, sec 17, circa 400 AD.Google Scholar
  2. 2.
    Volchan, Sergio B. “What is a random sequence?.” The American mathematical monthly 109.1 (2002): 46–63.Google Scholar
  3. 3.
    Diaconis, Persi, Susan Holmes, and Richard Montgomery. “Dynamical bias in the coin toss.” SIAM review 49.2 (2007): 211–235.Google Scholar
  4. 4.
    Forsythe, G. E., H. H. Germand, and A. S. Householder. “Monte carlo method.” NBS Applied Mathematics Series 12 (1951).Google Scholar
  5. 5.
    Cheng, Ta-Pei, and Brian H. Benedict. A college course on relativity and cosmology. Oxford University Press, 2015.Google Scholar
  6. 6.
  7. 7.
    Mlodinow, Leonard. The drunkard’s walk: How randomness rules our lives. Vintage, 2009.Google Scholar
  8. 8.
  9. 9.
  10. 10.
  11. 11.
    John von Neumann, “Various techniques used in connection with random digits,” in A.S. Householder, G.E. Forsythe, and H.H. Germond, eds., Monte Carlo Method, National Bureau of Standards Applied Mathematics Series, vol. 12 (Washington, D.C.: U.S. Government Printing Office, 1951): pp. 36–38.Google Scholar
  12. 12.
    Bernard Widynski, “Middle Square Weyl Sequence RNG”,,
  13. 13.
    Barnsley, Michael F., and Stephen Demko. “Iterated function systems and the global construction of fractals.” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. Vol. 399. No. 1817. The Royal Society, 1985.Google Scholar
  14. 14.
    Barnsley, Michael F. Fractals everywhere. Academic press, 2014.Google Scholar
  15. 15.
    Park, Stephen K., and Keith W. Miller. “Random number generators: good ones are hard to find.” Communications of the ACM 31.10 (1988): 1192–1201.MathSciNetCrossRefGoogle Scholar
  16. 16.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ronald T. Kneusel
    • 1
  1. 1.ThorntonUSA

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