  The correlation function of the trajectory exactly at the Feigenbaum point of
the logistic map is investigated and checked by numerical experiments. Taking
advantage of recent closed analytical results on the symbol-to-symbol
correlation function of the generating partition, we are in position to justify
the deep algorithmic structure of the correlation function apart from numerical
constants. A generalization is given for arbitrary $m\cdot 2^{\infty}$
Feigenbaum attractors.
