In his Rhetoric, Aristotle states
It is a part of probability that many improbable things will happen.
Thus, given a long enough
sequence of bits, there is a very high probability that any finite subsequence will eventually appear.
In this artwork, the last six columns of dots were fixed in advance, some
random and some chosen to produce the specific text pattern IMPROBABLE.
A random binary sequence was then constructed
and the subsequence of bits between finding the specific six-bit patterns (waiting times) in successive rows were noted.
Each line represents the bit
strings between finding the given patterns.
For the 128 lines, the total bits used to find all patterns was 8522, giving an average
waiting time of 66.6, with the waiting times ranging from 6 in line 90 to 355 in line 51.
Mathematical Art Exhibition, Tri-Section Meeting of the Indiana, Illinois, and Michigan Sections of the MAA, Valparaiso University, 23–24 March 2018.