  The Koch snowflake is one of the first fractals that were mathematically
described. It is interesting because it has an infinite perimeter in the limit
but its limit area is finite. In this paper, a recently proposed computational
methodology allowing one to execute numerical computations with infinities and
infinitesimals is applied to study the Koch snowflake at infinity. Numerical
computations with actual infinite and infinitesimal numbers can be executed on
the Infinity Computer being a new supercomputer patented in USA and EU. It is
revealed in the paper that at infinity the snowflake is not unique, i.e.,
different snowflakes can be distinguished for different infinite numbers of
steps executed during the process of their generation. It is then shown that
for any given infinite number~$n$ of steps it becomes possible to calculate the
exact infinite number, $N_n$, of sides of the snowflake, the exact
infinitesimal length, $L_n$, of each side and the exact infinite perimeter,
$P_n$, of the Koch snowflake as the result of multiplication of the infinite
$N_n$ by the infinitesimal $L_n$. It is established that for different infinite
$n$ and $k$ the infinite perimeters $P_n$ and $P_k$ are also different and the
difference can be infinite. It is shown that the finite areas $A_n$ and $A_k$
of the snowflakes can be also calculated exactly (up to infinitesimals) for
different infinite $n$ and $k$ and the difference $A_n - A_k$ results to be
infinitesimal. Finally, snowflakes constructed starting from different initial
conditions are also studied and their quantitative characteristics at infinity
are computed.
