We study the behavior of random systems algorithmically.

This notebook gives a DEMONSTRATION of the useful functions which yield true random numbers produced live from an experiment in quantum mechanics. They are contained in the randquantum Python module under the quantum directory.

Reliable and unbiased random numbers are needed for a range of applications from numerical modeling to cryptographic communications. While there are algorithms that can generate pseudo random numbers, they can never be perfectly random nor indeterministic. ANU researchers are generating true random numbers from a physical quantum source by splitting a beam of light into two beams and then measuring the power in each beam. Because light is quantised, the light intensity in each beam fluctuates about the mean. Those fluctuations, due ultimately to the quantum vacuum, can be converted into a source of random numbers.

The rate at which the live bits are streamed is limited by the bandwidth of your internet connection. Every number is randomly generated in real time and cannot be predicted beforehand. Most pseudo-random numbers have a finite period after which the sequence repeats. The output herein will not have such periodicity.

We develop a faster stochastic hybrid method which integrates authentic and pseudo generators to induce independence and eliminate predictable periodicity. This has PASSED Marsaglia Diehard, NIST STS, and RGB Dieharder tests.

For each digit, plot/plot_digitangle.py pushes the turtle (an arrow) directionally at a specific angle for a fixed distance. That push creates a plot where the colors are determined by the input digits. Thus the script visualizes any sequence of digits.

If circular angles are mapped on a random sequence of digits we will see a drunkard walk across the screen. Furthermore, if the sequence comes from a "normal" number, we can expect recurrent behavior, i.e. the drunk turtle will return to where it started its journey, though it may take a long time to do so theoretically.

Here is a plot of the first 10,000 digits of pi using pi-digits.txt:

Revision date : 2017-10-02