
Brownian motion sample path: fake or genuine?
Posted:
Apr 3, 2013 3:17 AM


I used snow (white noise) from an analog cathode ray tube TV, recorded with a webcam, as the source of entropy for supposedly random bits.
I had 1.8 gigabytes of digital video, which I whittled down to about 2.5 megabytes of "random bits".
16384 Bernoulli(1205, 1/2) r.v.s were generated, with k in {0, ... 1205} associated to the #0 s minus #1s : 2k1205 in the range {1205, 1203, ... 1, 1, 3, 5, ... 1203, 1205}. This number, 2k1205, stood in for a Gaussian r.v. of mean zero. The result was a random walk with steps of +1 and 1, sampled every 1205 steps; 16384 samples were taken, without counting x(0) = 0 [starting point].
16384*1205 = 19,742,720 (bits) or 2,467,840 bytes.
The graphic drawn with MatLab is here:
http://img203.imageshack.us/img203/9220/brown1.png
Maybe it's a fake, not random. I don't know ...
David Bernier
 $apr1$LJgyupye$GZQc9jyvrdP50vW77sYvz1

