  Technology of data collection and information transmission is based on
various mathematical models of encoding. The words "Geometry of information"
refer to such models, whereas the words "Moufang patterns" refer to various
sophisticated symmetries appearing naturally in such models. In this paper we
show that the symmetries of spaces of probability distributions, endowed with
their canonical Riemannian metric of information geometry, have the structure
of a commutative Moufang loop. We also show that the F-manifold structure on
the space of probability distribution can be described in terms of differential
3-webs and Malcev algebras. We then present a new construction of
(noncommutative) Moufang loops associated to almost-symplectic structures over
finite fields, and use then to construct a new class of code loops with
associated quantum error-correcting codes and networks of perfect tensors.
