Here we discuss an application of HPC (not high performance computing, instead high precision computing, which is a special case of HPC)  applied to dynamical systems such as  the logistic map in chaos theory. defined as X(k) = 4 X(k) (1 - X(k-1)).  For all these systems, the loss of precision propagates exponentially, to the point that after 50 iterations, all generated values are completely wro…