The article discusses a novel way of looking at Mondrian's nonfigurative paintings. Different periods of Mondrian's life correspond to distinct types of nonfigurative compositions, but can the distinction be formalized? How many bits or numbers are needed to characterize a typical composition? Can the rules of a composition type be expressed in the language of the computer? If distinct composition types require different computer programs, can these be based on a common frame-work, a mechanism, perhaps? The findings presented here are only tentative, but it is interesting to note that some characteristics can be modeled reasonably well, whereas others still resist formalization in the presented framework. The author's approach borrows principles from genetic programming. Employing a built-in random number generator, it can be used to explore a large space of "compositions."