  We consider stable periodic helixes as a generalization of stable periodic
orbits. We see that in the studied class of iterated functions Chaos always
arise suddenly. Therefore, we shall study the route from chaos to order rather
than the route from order to chaos. We show that, paradoxically, genuine Chaos
may look as much like Order and during as many iteration steps as one may wish.
  Then, we shall propose a generalization of the idea of map iteration that do
not imply the existence of periodic orbits. We shall show that, within a
strictly deterministic context, unpredictability, aperiodic order, sensitive
dependence and chaos are completely different concepts and we shall try to show
what this difference is made of. We shall also propose an example of non
chaotic aperiodic order.
