Simple algorithm to generate a Mondrian “Random Grid”

Hello,

I was wondering if there is a simple way or algorithm that can generate 2-d grids resembling Mondrian paintings like the boogie woogie grid ( http://nuit-blanche.blogspot.com/2010/12/cs-boogie-woogie-grid.html ) or similar grid (http://www.google.com/images?q=mondrian)

Igor.

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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:

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wow, what an answer! –  Gil Kalai Jan 2 '11 at 19:04