Computing Environment Effects on Finite Difference Approximations of Continuous Nonlinear Systems

We show techniques for graphical visualization of the inherent computer dynamics due to the truncation-rounding algorithm used in floating point arithmetic. We use the fractal structure of the images in a heuristic argument explaining why the Shadowing Lemma cannot be applied to numerical integration of trajectories of hyperbolic systems in floating point arithmetic. We illustrate this concept with an example of a piecewise linear closed loop control system.