If you statistically analyse a set of figures / values / voltage waveform, etc you can give it a measure of its randomness. The Autocorellation Function takes the set of values and, basically, sees how well the function correlates (what it has in common/how closely it resembles) with time shifted versions of itself. Any set of values correlate perfectly with itself when non-time shifted - obviously, because each value is identical to what it is being compared with.

If you take an endless sine wave (very non-random), it will correlate perfectly with a version of itself that has been shifted by one cycle, two cycles ad infinitum - so the autocorellation function will have an infinite series of peaks every time the original sine wave sits on top of the shifted version of itself. **Stay with me, here. **

The autocorellation function just shows you the way this corellation changes as you shift the waveform against itself.

Take a slightly more complicated waveform (still extremely/ infinitely long). As you compare it with shifted versions of itself, then there may be certain regular aspects of the pattern which correlate for sertain values of time shift. Its autocorellation function will consist of a main peak and a whole family of other smaller peaks.

A totally random waveform will ONLY have a peak when it actually coincides with itself. A 'slightly' random waveform will show a high peak of corellation and some smaller peaks of corellation with its shifted self. A very structured, repeated pattern will show autocorellation peaks all over the place.

So you can tell how random a set of data is by seeing how close its autocorellation function is to just one peak.

The SETI project has to subject its received data to this sort of scrutiny before ringing bells and saying they have found a genuine Extra Terrestrial source of signals.

Randomness is counter-intuitive. If you **try** to make up a long string of random numbers using the digits 0 to 9, it is very likely that they will fail this test because you would 'never' bring yourself to insert a row of 222222 in the set. However, this is just as likely as a row of 1426437.