A Random Page by Dieter Beule

Here you find
PseudoRandomNumberGenerators , Test your PRNG , What are a good random numbers, Good random numbers, Other Stuff and The End

this page is dedicated to pi=3.14159........

What are a Good Random Numbers ?

I think a good random numbers should
  1. have no correlations i.e. the should be random !
  2. obey a certain distribution e.g. uniform in [0,1).
  3. be reproducible, in case you or someone else wants to check what you are doing !
  4. be cheap in production cost and time !
Lets first try ...

Pseudo Random Number Generators (PRNGs)

As they are called pseudo they won't be good random numbers but they will do for many applications. CESP has a great HTML lecture on how pseudo random number generation is done. And here is another book on Computer Generated Random Numbers by David W. Deley.

You should also check out the

THE WWW VIRTUAL LIBRARY:
RANDOM NUMBERS and MONTE CARLO METHODS
maintained by University of Salzburg's Mathematics Department.

PRNG Code

If you want something portable rand55 produces random numbers with all kinds of (Gauss, ... ) distributions. It is based on the recursion xi = xi-55 + xi-24 (i.e. lagged Fibunacci) and written by Thomas Fricke in C first read doc then get the code
Watch this space for more generators !

Test your PRNGs

Im just preparing a small test program that is based on the calculation of topological entropies. It is related to the poker and serial test. The idea is described in this paper that is unfortunately is only avialiable in german (sic!).

Another test program (DOS) called ENT by John Walker calculates ENTROPY, CHI-SQUARE TEST, ARITHMETIC MEAN, MONTE CARLO VALUE FOR PI, SERIAL CORRELATION COEFFICIENT.

Good Random Numbers ?

I recommend 3.141592653589793238462643... also know as Pi. It seems that there are no correlations in the digits of Pi. The same applies to other number like E or Sqrt(2).

Did this convince you ? ... and you want to try now ? ... get yourself 65536 decimal digits (32kB gzipped) to play with ... if you want to do something more serious you find 1M,2M,4M,32M digits on Ralph Horstmanns homepage.

These digit where calculated with the highly recommended HFLOAT package for long number computations by Jörg Arndt. He will also tell you how pi is computed and (most) of its cryptic properties and it is also the best FFT site on the net !

Here you can get 200 mio decimal digits (in .jp and pretty slow) or even the current world record of 6,400,000,000 decimal digits if you register.

Here you can get genuine random numbers, generated by radioactive decay but only at a rate of about 30 bytes per second.

There is a company offering a PC device that claims to produce virtually perfect true RNs at a rate of 10,000 bits per second.

Other Stuff ?

If I not playing around with random numbers ... I try to finish my Ph.D. thesis at the Lehrstuhl für Statistische Physik und Nichtlineare Dynamik, HU-Berlin, in a project called: Adiabatic Processes in Dense Plasma. I am dealing with Kinetics of Electron Transitions in Dense Plasma and Thermodynamic Properties of Dense Plasma if this sounds interesting to you then have a look at

my recent publications

I you think of blood if you hear about plasma you should not consider to check out Plasma on Internet or the Plasma Physics Newsgroup. But you should rather read this or learn that 99% of our universe consits of plasma ! Execptions are rare places ... like the earth.

I order to earn my living I work as a system administrator at the Innovationkolleg Theoretische Biologie

Other things I am really keen on ... are Density Functional Theory and Wavelets (check out Amara's Wavelet Page ) but I am still collecting material and links for this section

Finally some URLs that I use or recommend to use:

The End !

you might want to:
mail me: beule@physik.hu-berlin.de
trust me: my PGP public key
see me: no gifs here ! ... try to find me ... at place mentioned below !
call me: at work +49/(0)30-2093 9108, fax: 7638
or at home: +49/(0)30 - 691 37 63 (Q)
snail-mail me: at work: Invalidenstr. 42, 10115 Berlin, Germany
or at home: Urbanstr. 107, 10967 Berlin
find me: at work or at home (maps)
Thanks to everyone developing and improving free software !