Dynamics and predictability

Abstract

We present the results of the experimental observations and the numerical simulations of the coin toss, die throw, and roulette run. We give arguments supporting the statement that the outcome of the mechanical randomizer is fully determined by the initial conditions, i.e., no dynamical uncertainties due to the exponential divergence of initial conditions or fractal fractal basin boundary basin boundaries basin boundary occur. We point out that although the boundaries between basins of attraction basin of attraction of different final configurations in the initial condition space are smooth, the distance of a typical initial condition from a basin boundary is so small that practically any uncertainty in initial conditions can lead to the uncertainty of the outcome. © 2009 Springer-Verlag Berlin Heidelberg.