(New: somewhat larger description here:
http://www.win-vector.com/blog/2009/06/what-is-genetic-art/ )

The art system uses a genetic algorithm to create art (or, at least, pretty pictures). The "genetic" algorithm used is quite simple (and arbitrary):

To breed two formulae a random subexpression of one is replaced by a random subexpression of the other (the random subexpressions are selected uniformly from all subexpressions of the parse-tree of the formula). Finally, mutation is applied which changes one of the operations in the formula.
Sometimes instead of applying the genetic algorithm a random formula is generated or a saved formula for the old International Genetic Art II site is retrieved.
Scott's art exhibit used functions over the reals, this one uses functions over the quaternions (4 dimensional vectors) and gets color R/G/B values directly from three entries of the vectors. Quaternions were chosen because:
• They form a vector space (over the reals) large enough to conveniently hold the three vales: R,G and B.
• They form an associative division algebra over the reals (thus formulas over the quaternions should have some of the same properties as the formulas used in the first exhibit).
• Many Quaternion operations have geometric interpretation (example: the functions orth1 and orth2 are orthogonal maps of euclidian 3-space).
• The quaternions are somewhat unique (e.g. any normed associative real division algebra is isomorphic to the reals, complex numbers or the quaternions).

Bibliography

Ebbinghaus et al. Numbers Springer-Verlag, Second Edition, 1988.

Shumeet Baluja, Dean Pomerleau and Todd Jochem.
Simulating User's Preferences: Towards Automated Artificial Evolution for Computer Generated Images. Technical Report CMU-CS-93-198. Carnegie Mellon University. Pittsburgh, PA. October 1993.

Karl Sims.
Artificial Evolution for Computer Graphics. Proceedings of SIGGRAPH 1991.