  By means of Monte Carlo simulations of extensive air showers (EAS), we have
performed a comprehensive study of the shower to shower fluctuations affecting
the longitudinal and lateral development of EAS. We split the fluctuations into
physical fluctuations and those induced by the thinning procedure customarily
applied to simulate showers at EeV energies and above. We study the influence
of thinning on the calculation of the shower to shower fluctuations in the
simulations. For thinning levels larger than 10^(-5) - 10^(-6), the
determination of the shower to shower fluctuations is hampered by the
artificial fluctuations induced by the thinning procedure. However, we show
that shower to shower fluctuations can still be approximately estimated, and we
provide expressions to calculate them. The influence of fluctuations of the
depth of first interaction on the determination of shower to shower
fluctuations is also addressed.
