Here is one algorithmification (if I may coin a word!) of Mondrian paintings, by
Tom Gedeon, "Neural Network for Modeling Esthetic Selection,"
*Neural Information Processing*,
Springer *Lecture Notes in Computer Science*, 2008, Volume 4985/2008, 666-674.
From the Abstract:

Our domain is the automatic generation of Mondrian-like images with an interactive interface for the user to select images.

Here is one of the figures from the paper:

(The Springer link needs an access subscription. Here is a Google books link.)
Gedeon cites an analysis of Mondrian paintings by the physicist Richard Taylor:
"Fractal Expressionism - Where Art Meets Science," *Art And Complexity*, Ed. J. Casti and A. Karlqvist, Elsevier Science, Amsterdam (2003).

Here is a second: "The Mondrian Process" by Daniel Roy and Yee Teh,
*Adv. in Neural Inform. Processing Syst*, 21, p.27, 2009. From the Abstract:

We describe a novel class of distributions, which we call Mondrian processes, which can be interpreted as probability distributions over $k$d-tree data structures.

Here is their first figure: