  Simple methods permit to generalize the concepts of iteration and of
recursive processes. We shall see briefly on several examples what these
methods generate. In additive sequences, we shall encounter not only the golden
or the silver ratio, but a dense set of ratio limits that corresponds to an
infinity of conceivable recursive additive rules. We shall show that some of
these limits have nice properties. Identities involving Fibonacci and Lucas
sequences will be viewed as special cases of more general identities. We shall
show that some properties of the Pascal Triangle belong also to other similar
objects. In Dynamical Systems and Chaos Theory we shall encounter weird orbits,
whose order is higher than the number of its distinct elements and, beyond the
chaos point, a rather unexpected belated convergence to 0, after a pseudo
chaotic behaviour during as many terms as one may wish. Time and again, we
shall find here the Feigenbaum constant. In Formal Grammars we shall see that
recursive rules applied to concatenation are sometimes equivalent to formal
grammars although generally more restrictive.
