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In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
Despite initial insights in the first half of the twentieth century, chaos theory became formalized as such only after mid-century, when it first became evident to some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments like that of the logistic map.
Hesiod's Theogony, (c. 700 BC) which could be considered the "standard" creation myth of Greek mythology, [1] tells the story of the genesis of the gods. After invoking the Muses (II.1–116), Hesiod says the world began with the spontaneous generation of four beings: first arose Chaos (Chasm); then came Gaia (the Earth), "the ever-sure foundation of all"; "dim" Tartarus (the Underworld), in ...
The colour white is identified with chaos; black with order. The first published novel explains it this way: white is the chaotic combination of all wavelengths of visible light, while black is the absence of this light. The extreme of either is undesirable...for a human, perfect chaos is destruction, perfect order is death.
Orbit diagram for the Hénon map with b=0.3.Higher density (darker) indicates increased probability of the variable x acquiring that value for the given value of a.Notice the satellite regions of chaos and periodicity around a=1.075-- these can arise depending upon initial conditions for x and y.
In physics and mathematics, the Ikeda map is a discrete-time dynamical system given by the complex map + = + (| | +) The original map was proposed first by Kensuke Ikeda as a model of light going around across a nonlinear optical resonator ( ring cavity containing a nonlinear dielectric medium) in a more general form.
In both cases, chaos referring to a notion of a primordial state contains the cosmos in potentia but needs to be formed by a demiurge before the world can begin its existence. The use of chaos in the derived sense of "complete disorder or confusion" first appears in Elizabethan Early Modern English, originally implying satirical exaggeration ...
Chaos can be personified as water or by the unorganized interaction of water and fire, The transformation of chaos into order is also the transition from water to land. [4] In many ancient cosmogonic myths, the ocean and chaos are equivalent and inseparable from each other. The ocean remains outside space even after the emergence of the land.