Comparing Rule 30 Pseudorandoms to a Uniform Distribution

The Demonstration "Using Rule 30 to Generate Pseudorandom Real Numbers" demonstrates an algorithm that uses the rule 30 cellular automaton to generate numbers that can be regarded as nearly random selections from the unit interval. This Demonstration compares the distribution of the numbers generated by that algorithm for a range of initial seeds with a uniform distribution over the unit interval.
The blue histogram displays the distribution of the pseudorandom numbers generated using rule 30 with the number of initial seeds selected. The area of each blue rectangle is the fraction of rule 30-generated pseudorandoms that fall in the interval that forms its base. The thick red line is the height the rectangles would be if these numbers were distributed in a perfectly uniform way among the intervals over which the rectangles sit.
The closeness of the blue area to the rectangle under the red line illustrates that rule 30-generated pseudorandom numbers in the unit interval are fairly uniform over that interval, that is, as likely to come from one section of it as any other of equal size. This uniformity makes rule 30 a good engine for generating pseudorandom numbers.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+