Recognizing predictive patterns in chaotic maps

We investigate the existence of rules (in the form of binary patterns) that allow the short-term prediction of highly complex binary sequences. We also study the extent to which these rules retain their predictive power when the sequence is contaminated with noise. Complex binary sequences are derived by applying two binary transformations on realvalued sequences generated by the well known tent map. To identify short-term predictors we employ Genetic Algorithms. The dynamics of the tent map depend strongly on the value of the control parameter, r. The experimental results suggest that the same is true for the number of predictors. Despite the chaotic nature of the tent map and the complexity of the derived binary sequences, the results reported suggest that there exist settings in which an unexpectedly large number of predictive rules exists. Furthermore, rules that permit the risk free prediction of the value of the next bit are detected in a wide range of parameter settings. By incorporating noise in the data generating process, the rules that allow the risk free prediction of the next bit are eliminated. However, for small values of the variance of the Gaussian noise term there exist rules that retain much of their predictive power.