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Examples of the the word, attractor , in a Sentence Context

The word ( attractor ), is the 18611 most frequently used in English word vocabulary

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  1. System, and there will normally be one set of exponents associated with each, attractor , The choice of starting point may determine which attractor the system ends up
  2. To z, starting with P_CD (z) = z_0 z_0 is any of the p points that make the, attractor ,of the iterations of P_c (z) \to z starting with P_CD (z) c; z_0 satisfies
  3. A two-dimensional differential equation has very regular behavior. The Lorenz, attractor ,discussed above is generated by a system of three differential equations with a
  4. E. Smith (possibly the original appearance: 1929). The protagonist invents ", attractor ,beams" and" repeller beams ". Repellers can also be emitted isotopically as
  5. System exhibits chaotic behavior and displays what is today called a strange, attractor , The strange attractor in this case is a fractal of Hausdorff dimension between
  6. Behind sheets of Plexiglas, which is opaque in the far infrared. The Lorenz, attractor , named for Edward N. Lorenz, is an example of a non-linear dynamic system
  7. With a device which is now safely stored in the MIB's headquarters. The great, attractor ,is mentioned in" Reaper Man" by Terry Pratchett, as the ultimate death of the
  8. In the figure on the right give a picture of the general shape of the Lorenz, attractor , This attractor results from a simple three-dimensional model of the Lorenz
  9. System) evolves over time in a complex, non-repeating pattern. Overview The, attractor ,itself, and the equations from which it is derived, were introduced in 1963 by
  10. Of dependence, will tend to be distributed according to one of a small set of ", attractor ," distributions. When the variance of the i. i. d. variables is finite, the "
  11. From The Pennsylvania German Broadside: A History and Guide by Don Oder An, attractor ,is a set towards which a dynamical system evolves over time. That is, points
  12. Its velocityand the evolution is given by: f (t, ( x, v))= (x+TV, v ). \ An, attractor ,is a subset A of the phase space characterized by the following three
  13. Manifold, or even a complicated set with a fractal structure known as a strange, attractor , Describing the attractor s of chaotic dynamical systems has been one of the
  14. Point that is sufficiently close to A is attracted to A. The definition of an, attractor ,uses a metric on the phase space, but the resulting notion usually depends on only
  15. Does not have to satisfy any special constraints except for remaining on the, attractor , The trajectory may be periodic or chaotic or of any other type. If this
  16. With the state use the animal in their logos. It is seen as an important, attractor ,of tourists to Tasmania and has come to worldwide attention through the Mooney
  17. Lagrangian points, the triangular points (and) are stable equilibrium (cf., attractor ,), provided that the ratio of M1/M2 is greater than 24.96. This is the case for
  18. Of which are quadratic (and therefore nonlinear). Another well-known chaotic, attractor ,is generated by the Roller equations with seven terms on the right-hand side
  19. On the right give a picture of the general shape of the Lorenz attractor . This, attractor ,results from a simple three-dimensional model of the Lorenz weather system. The
  20. Long-run proportion of time spent by the system in the various regions of the, attractor , In the case of the logistic map with parameter r 4 and an initial state in (
  21. Behavior. In fact, certain well-known chaotic systems, such as the Lorenz, attractor ,and the Roller map, are conventionally described as a system of three
  22. Beginning of chaos theory when Edward Lorenz accidentally discovered a strange, attractor ,with his computer, computers have become an indispensable source of information
  23. Functions such as centromeres or telomeres, in addition to acting as an, attractor ,for other gene-expression or repression signals. Facultative hetero chromatin is
  24. X_1 is not a limit set. Because of the dissipation, the point x_0 is also an, attractor , If there were no dissipation, x_0 would not be an attractor . Mathematical
  25. To the attractor remain close even if slightly disturbed. Geometrically,an, attractor ,can be a point, a curve, a manifold, or even a complicated set with a fractal
  26. With each attractor . The choice of starting point may determine which, attractor ,the system ends up on, if there is more than one. Note: Hamiltonian systems do
  27. Section or attracted. Invariant sets and limit sets are similar to the, attractor ,concept. An invariant set is a set that evolves to itself under the dynamics.
  28. How a periodic orbit bifurcates into a torus and the torus into a strange, attractor , In another example, Feigenbaum period-doubling describes how a stable periodic
  29. X_0 is also an attractor . If there were no dissipation, x_0 would not be an, attractor , Mathematical definition Let f (t, • ) be a function which specifies the
  30. Compound isolated from the fungus is 1,3-diolein,which is in fact an insect, attractor , Several regional names appear to be linked with this connotation, meaning
  31. The achievements of chaos theory. A trajectory of the dynamical system in the, attractor ,does not have to satisfy any special constraints except for remaining on the
  32. Networks are capable of a wide variety of dynamical behaviors, including, attractor , dynamics,periodicity, and even chaos. A network of neurons that uses its
  33. Self-organized critical systems, where the critical point of the system is an, attractor , Formally, this sharing of dynamics is referred to as universality, and systems
  34. From a simple three-dimensional model of the Lorenz weather system. The Lorenz, attractor ,is perhaps one of the best-known chaotic system diagrams, probably because it
  35. Distributions. When the variance of the i. i. d. variables is finite, the ", attractor ," distribution is the normal distribution. In contrast, the sum of a number of
  36. Of the logistic map with parameter r 4 and an initial state in (0,1),the, attractor ,is also the interval (0,1) and the probability measure corresponds to the
  37. Dimensionality. However, the Poincaré-Bendixson theorem shows that a strange, attractor ,can only arise in a continuous dynamical system (specified by differential
  38. System evolves over time. That is, points that get close enough to the, attractor ,remain close even if slightly disturbed. Geometrically, an attractor can be a
  39. The orbiting body is subject only to the gravitational force of the central, attractor , When an engine thrust or propulsive force is present,Newton's laws still
  40. On the starting point x_0. (However, we will usually be interested in the, attractor ,(or attractor s) of a dynamical system, and there will normally be one set of
  41. Objects in the phase space of a dynamical system can be fractals (see, attractor ,). Objects in the parameter space for a family of systems may be fractal as
  42. Orbits that converge to this chaotic region. An easy way to visualize a chaotic, attractor ,is to start with a point in the basin of attraction of the attractor , and then
  43. Transitivity condition, this is likely to produce a picture of the entire final, attractor , and indeed both orbits shown in the figure on the right give a picture of the
  44. Behavior and displays what is today called a strange attractor . The strange, attractor ,in this case is a fractal of Hausdorff dimension between 2 and 3. Grassberger (
  45. The cases of most interest arise when the chaotic behavior takes place on an, attractor , since then a large set of initial conditions will lead to orbits that converge
  46. State in a chaotic system. If a (possibly chaotic) dynamical system has an, attractor , then there exists a probability measure that gives the long-run proportion of
  47. Beta+1. Rayleigh number Source code The source code to simulate the Lorenz, attractor ,in GNU Octave follows. % Lorenz Attractor equations
  48. A chaotic attractor is to start with a point in the basin of attraction of the, attractor , and then simply plot its subsequent orbit. Because of the topological
  49. An attractive force that is directly proportional to its distance from a fixed, attractor , Unlike Depletion orbits, however,these" harmonic orbits" have the center of
  50. Model for turbulence, and it was Rule who invented the concept of a strange, attractor ,in a dynamical system. ) Biology interested Grothendieck much more than physics

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