A deterministic system is one whose future states are completely fixed by its current state and its rule of dyamical motion. Determinism has historically been linked to prediction, and the laws governing planetary motion became the paradigmatic example of determinism and predictibility. (cf. clock) Thus Pierre Simon de Laplace, following Newton, believed that " Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it...nothing would be uncertain, and the future as the past would be present to its eyes."
The "new science" of chaos has found new ways of defining chaotic systems. Unlike the traditional objects of scientific study (esp. in physics), Chaotic systems are both deterministic and unpredictable. (They are both chaotic and systems) Even simple systems, whose parameters are clearly defined, can display chaotic behaviour. A chaotic system generates behaviour giving the appearance of complete randomness by means of a purely deterministic rule. Deterministic chaos exhibits sensitivity to initial conditions, in that minor differences of a state at any given moment lead rapidly to widely diverging states. The system is locally unstable and allow miniscule changes to percolate through the system so as to bring about major changes somewhere else. The disproportion between minor differences at one moment and major ones subsequently is an indication of the non-linearity of chaotic systems.
For Instance, Stretching and Folding is chaotic in its results. Two raisins in a taffee stretching machine soon lose their initial spatial relations. Yet chaotic behaviour is not without patterns. Dynamic models of chaos show that many systems have attractors, but they are "strange" folded forms . For instance, The Lorentz attractor has a butterfly-like shape and has become an icon of "strange attractors" Chaotic attractors themselves seem to be stretched and folded. Is this is the reason for their dimensional ambiguities? (see local/global)
The mathematics of Fractals describes the scaling characteristics of chaos. A fractal map of chaotic behaviour, for example, may show stable areas of behaviour (eg. basins of attraction) within areas of denser complexity. When subject to changes of scale (magnification through repeated recursion) new levels of stability/instability will appear.
Despite its ostensible "strangeness", chaos theory is "normal science". (see paradigm) (Hayles p. 15) defined by its disciplinary procedures and criteria, but the "epistemic ground" on which it rests, along with much else in contemporary culture, is changed.
See philosophy / chaos for philosophical and historical interpretations. See also dissipative structures for reconsiderations of the relations between chaos and order. Stuart Kauffman often characterizes the three dynamical regimes as solid or frozen (the ordered regime, as gas (the chaotic regime), and as liquid (the complex regime).