michaelslab

The experiment described here is currently offline.

The goal of the RANDOM project is to provde a free random number table. The idea is not new (read more), but it is an obvious application of the muon detector experiment.

There are already several free random number sources in the internet avaiable:

The setup is shown in the picture below. The background radiation detector consists of a P MT which is attached to a plastic szintilator. The mbus system contains the power supply and the counters which are used to count the events detected by the szintelator. The mfram contains an i2c to LAN adapter which allows to read out the counters via simple commands which are issued from the machine called bing. Bing is a thin client with an SD disk running tiny core. On this maschine a small application is running which reads out the counters of the PMT every minute and stores the result in files. The server hal, which is connected to the internet picks up the files on a regular basis and publishes the data into the internet.

Since bing is a thin client with the much lower power consumption as hal it creates less noise and it is possible to run this box even during night times.

Figure 1 - The figure above shows the processing steps which are involved in creating random numbers. Basically the setup consits of two major components, the detector setup the and data processing/publishing part of the installment.

The data processing is rather simple, from each measurement value only the lowest will will taken into considderation. Every hour a cron job is started on hal to create the list of zeros and ones which is published here. At the same time a few evaluation diagrams will be generated.

The result of this project is a list of 0 and 1 random numbers which can be used to generate random numbers.

The term random means for a seqeunce of events that the next event can't be calculated from the previous events. This means for a data set of numbers, that the data set does not contains any periodic patterns which could be used to determine any kind of generation law which could be used to derive from the known numbers the next number in the sequence.

In order to allow the generation on n-bit numbers from the result data set all samples have to be statistically independant which means there is not hidden relationship between the events.

Structureless

One of the attributes of beeing random is beeing unpredictable which means structure less.One way to examine random numbers is to create a visuliztion from the data. Humans are really good in spoting patters. The picture below shows on the left side a bitmap created out of the dataset of 164000 bits. On the right side, you find map of the same random numbers but a with an structure added artificially.

Original Data Set Dataset with pattern
D                  : 0.116786%
Average value      : 0.499228
Variance           : 0.706561
D                  : 0.903483%
Average value      : 0.526759
Variance           : 0.725782
Figure 2 - This figure shows for each data set a pixel map, the correlation diagram and the analysis results. The dataset on the left is the orginal one and the data set in the right column has been derived from the left one but a periodic pattern has been imposed to the data set.

A method of identifying repeating structures in a map like the above one is to apply the correlation function (1.1) to the dat where the function \(f(t)\) denotes some observable which is suspected to contains some periodics.

$$ R(\tau)=\int f(t)f(t+\tau)dt $$ 1.1

If the function \(R(\tau)\) exhibits more then the maxima at \(\tau=0\), the function \(f(t)\) shows some kind of periodicy as demonstrated in figure 2.

The autocorrelation function is shown for both data sets below the pixel map. In the random case on the left side, the correlation function shows only one peak at \(\tau=0\) which means the complete picture is only identical to it self.

In contrast to the function on the left, the pattern shown on the right exhibits small peaks indicating that there is some kind of periodicy which would allow the predict values in the data set.