Title of article :
Dynamics of coin tossing is predictable
Author/Authors :
Strza?ko، نويسنده , , J. and Grabski، نويسنده , , J. and Stefa?ski، نويسنده , , A. and Perlikowski، نويسنده , , P. and Kapitaniak، نويسنده , , T.، نويسنده ,
Abstract :
The dynamics of the tossed coin can be described by deterministic equations of motion, but on the other hand it is commonly taken for granted that the toss of a coin is random. A realistic mechanical model of coin tossing is constructed to examine whether the initial states leading to heads or tails are distributed uniformly in phase space. We give arguments supporting the statement that the outcome of the coin tossing is fully determined by the initial conditions, i.e. no dynamical uncertainties due to the exponential divergence of initial conditions or fractal basin boundaries occur. We point out that although heads and tails boundaries 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 results of tossing.
Keywords :
quaternions , Coin tossing , Coin modeling , predictability , basins of attraction
Journal title :
Astroparticle Physics