There was a very similar experiment carried out by Meyer and Packard(1992), whereby they emulated a data generating process based on a well known chaotic generator known as a Mackey-Glass equation used to model blood flow.  They ran genetic algorithms over many samples of data and optimized some boolean condition statements to predict an outcome based on embedded variables of the data set.
Their conclusion was that the prediction scheme was very robust on both training/optimizing and OOS data.  Packard went on to co-found prediction company as discussed in the laymen's book, the predictors
(How a Band of Maverick Physicists Used Chaos Theory to Trade Their Way to a Fortune on Wall Street).

The above experiment is described succinctly in the book, an introduction to genetic algorithms, by M. mitchell.  Also, google books
currently has a free preview of this section for those interested
(p. 56, predicting dynamical systems).

The unfortunate problem with this approach is that the data generating process of the markets is not the same as the Mackay-Glass, logistic, or any other well known chaotic model.  It is more akin to an EEG process, which  fills up a phase state-space with very little predictive signature. There are quite useful tricks to be found if you play around long enough with the concepts, however.

P.S.  bluelou, hope everything is going well on your trading.
I just wish we could find more good thinkers to add to all the discussions.  I check quite frequently, and rarely see anyone outside of Yury post (although I do certainly appreciate hearing from him).

Sorry - I didn't mean use the data from the chaotic generator to create a trading strategy.  The trading strategy should only be created from realised empirical data - otherwise, using a model-based DGP may introduce (potentially dangerous) side-effects into the resulting trading model.  What I meant was to just use the model-generated data purely to test the final strategy for robustness.  In a way, it might even be possible to test the strategy against an ensemble of data from using a range of paremeters for the chaotic-DGP (thus perhaps testing performance in a regime-switch?).

Of course, I'm not at all versed in the mechanics of chaos theory; just thought I'd just throw some ideas around.