I have been researching the role that randomness plays in some forms of art, I already posted about Tom Phillips and his alteration of a victorian book to create A Humument. When thinking more broadly about this I ended up at collage - which links to the Hockney work you base this thread on.
Collage is a distinctively twentieth century art form that explores the boundary between random juxtaposition and conscious arrangement. For example, the Dadaist artist Hans (Jean) Arp (1887-1966) is supposed to have made `chance collages' by tearing paper into pieces, dropping them onto a larger sheet of paper and then gluing the pieces where they happened to fall.
However, when you look at actual examples of Arp's work, for example According to the Laws of Chance (1933), they show spatial arrangements of torn paper that are not typical of a truly random pattern, thus indicating that he did not fully relinquish his artistic control to the laws of chance.
This is shown in the Figure below (for a larger version see http://www.datadeluge.com/2010/12/hans-jean-arps-non-random-chance.html).
(a) A binarised version of According to the Laws of Chance by Hans (Jean) Arp made in 1933. This is a collage of painted pieces of paper that have been dropped at random onto a board and glued down. An image of this piece is shown on the Tate website.
(b) A small yellow dot has been placed at the rough centre of gravity of each of the 24 pieces of paper.
(c) Here just the 24 dots are shown in a box the same size as the original piece of art.
(d) A Poisson point process of 24 events within a bounding box the same size and shape as the original piece of art.
The Poisson point process is a standard way of analytically generating a pattern of a given number of events that show complete spatial randomness (CSR). The Poisson process has some very interesting properties, here it suffices to be used qualitatively as an example of a pattern that has been randomly generated. Note that in a Poisson process the points in the pattern can end up arbitrarily close to one another.
The Arp composition is very unlikely to have been generated by the Laws of Chance; the arrangement of the paper centres of gravity are too spread out (or regular) for a completely random pattern.
Have a great 2011
-- Matt R (email)