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We consider stable periodic helixes as a generalization of stable periodicorbits. We see that in the studied class of iterated functions Chaos alwaysarise suddenly. Therefore, we shall study the route from chaos to order ratherthan the route from order to chaos. We show that, paradoxically, genuine Chaosmay 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 donot imply the existence of periodic orbits. We shall show that, within astrictly deterministic context, unpredictability, aperiodic order, sensitivedependence and chaos are completely different concepts and we shall try to showwhat this difference is made of. We shall also propose an example of nonchaotic aperiodic order.

About Stable Periodic Helixes, L-iteration and Chaos Generated by Unbounded Functions