  We describe an alternative method (to compression) that combines several
theoretical and experimental results to numerically approximate the algorithmic
(Kolmogorov-Chaitin) complexity of all $\sum_{n=1}^82^n$ bit strings up to 8
bits long, and for some between 9 and 16 bits long. This is done by an
exhaustive execution of all deterministic 2-symbol Turing machines with up to 4
states for which the halting times are known thanks to the Busy Beaver problem,
that is 11019960576 machines. An output frequency distribution is then
computed, from which the algorithmic probability is calculated and the
algorithmic complexity evaluated by way of the (Levin-Zvonkin-Chaitin) coding
theorem.
