Dynamical systems in two music compositions

The utilization of dynamical systems and the resulting fractals in the area of music composition has produced a number of notable works. Musical uses of two dynamical systems, the "chaoticgingerbreadman" (see [3]), in which X n+1 = 1 - Y n+ |X n| Y n+1 = X n. and the Henon Map as defined in [6] by X (n-1) = 1 + Y n 1.4(X n) 2 Y (n+1) = 0.3(X n). are described. In particular, two musical compositions, A Noite, Porém, Rangeu E Quebrou and Help Me Remember, (both by Waschka) which employ these systems, are analyzed. Similarities and differences in the musical utilization of these systems are described.