The specific model-case of the quadratic-iterator is an illuminating way of understanding the chaotic-behaviour. It is agreed that for the special-cases of iteration of transformations there are common characteristics of chaos: Sensitive dependence on initial conditions, mixing and dense, periodic points. Therefore discussion starts with an important metaphor in chaos-theory, kneading of dough, by 2 different uniform-processes performed iteratively each of them in unit-iterval: [1] Stretch the dough, fold it over in the middle and stretch it again (as often as required), and [2] stretch the dough, cut it in the middle, paste the 2 halfs together and stretch it again (as often as required). This processes guarantee that a pocket of spice inserted into the dough will be mixed thoroughly throughout the mass. Both kneading-processes were found to be compatible in view of their chaotic-characteristics. In a further step of discussion, equivalence could be shown between the 2 uniform kneading-processes and the non-uniform kneading of the quadratic-iterator y = au2022x(1-x), where a = 4 were chosen, via simple coordinate-transformations of the unit-interval. Chaotic characteristics of all 3 iteration-transformations could also be proven as being equivalent to each other. Thus, further investigations were based now on quadratic-iterator. The range from states of order up to the complete chaotic dynamics of the quadratic-iterator can be divided into 3 distinct parts: [1] regime 1 ≤ a < (s∞ = FEIGENBAUM-point) were oscillations of the iterator will experience period-doublings, [2] an area s∞ < a < 4 which can be looked as mirror-image of regime [1], and [3] the chaos-area for a = 4. Boarder between regime [1] and [2] is a CANTOR-set. The mirror-image-area of the quadratic-iterator’s final-state-diagram is characterized by a complicated band-structure and therefore different orbit-dynamics can be expected for (a < s∞) ⇄ (s∞ < a). In other words, transitions from order to chaos and vice-versa may occur but with respect to orbit-dynamics they happen differently every time.