The theory of epigenesis is the undisputed paradigm of embryology, and it is still based on the classical concept proposed by Aristotle: the idea that embryonic development is a generation of structures which takes place according to a design--today we say a set of instructions--already present in the fertilized egg. This is a doctrine which can be referred to as 'pre-information', since it claims the preexistence of information exactly as the old theory of preformation claimed the preexistence of form. Here, however, it is shown that a more general version of epigenesis can be held, because of a new principle which states that it is mathematically possible to obtain not only a convergent generation of form, or structure, but also a convergent generation of information.