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Rabinovich–Fabrikant Attractor

Rabinovich–Fabrikant Attractor
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2017-08-31 06:03
FunctionTransformationParametric EquationSlider Animation
This example demonstrates the Rabinovich–Fabrikant attractor, a typical example of a chaotic dynamical system. It involves complex nonlinear dynamics and chaos theory. By adjusting parameters, the dynamic behavior of the system can be observed. The example uses GeoGebra's slider animation feature to show the evolution of the system. Suitable for high school and above students and teachers.

GeoGebra Commands & Parameters

  1. Numeric strength(1.0)
  2. Numeric n(12.0)
  3. Numeric h(0.005)
  4. Numeric speed(1.0)
  5. Numeric t(-4.2)
  6. Numeric b(20.0)
  7. x(CornerThreeD[-1, 3])
  8. x(CornerThreeD[-1, 1])
  9. y(CornerThreeD[-1, 3])
  10. y(CornerThreeD[-1, 1])
  11. z(CornerThreeD[-1, 5])
  12. z(CornerThreeD[-1, 3])
  13. {(-2.6537232166142735, 1.8567837910561718, 2.4787129494073525), (4.52780306425937, 1.5435666672596504, -3.608198848553217), (-2.811757228001034, 4.321221598037576, 2.4568714899224027), (4.036983636939
  14. {-24.568645574594193, 1.3624953971181102, -2.6941070371664297, -1.9157432708647657, -5.938137220732006, 4.646513726802567, -210.983509097447, -3.156072108700701, 52.180437160474185, -17.13360152018484
  15. {4.987198969898754, -8.488851183403925, -6.943545925561837, -0.19941956533671368, 51.29549906803594, 10.320624385556266, 21.06530558405817, 2.2415823071196175, -12.78289962414873, 28.447087194267795,
  16. {43.17466413517023, 2.274612840735854, -7.970595073150294, 3.1519100534236784, -2.1615740701124304, 1.3800013284403898, -507.7638020093168, 0.9931377056103823, 110.0327364242936, 39.96322298304967, -4
  17. {-23.93164111258039, 1.3553638189742436, -2.7315890772045064, -1.9122846981164676, -3.9766907467935857, 4.719433564446149, -235.96423369673894, -3.1391551903499275, 49.88971332194121, -14.869550819151
  18. {5.738736421313698, -8.515284330690852, -6.920364183292033, -0.17090407921812512, 52.13567088739895, 10.139916600573255, 82.54056964554276, 2.197016799802602, -15.49207508063271, 31.4577142379225, 3.6
  19. {43.280954797565826, 2.180669547198492, -7.986826879746822, 3.164826596527627, -1.5152376594583172, 1.4258331237135164, -462.9303231473703, 0.8976852473174249, 110.1602445368585, 33.893816785623734, -
  20. {-23.95170004023457, 1.3553573011372368, -2.7316845708438615, -1.9123503133578934, -3.938648843273822, 4.716274717922903, -234.29107307902032, -3.1388538498451206, 49.97855932174467, -14.6671066251703
  21. {5.739372836629293, -8.516292557305373, -6.920523393672667, -0.17073755664457968, 51.898217032084105, 10.135917756537376, 86.0973535851391, 2.196804715361699, -15.480555669757585, 31.051677762587445,
  22. {43.3087651837096, 2.180843314446795, -7.986741532596695, 3.16487512642291, -1.508673790435696, 1.4254160276869143, -462.6345293684906, 0.8983138097882571, 110.30517241189287, 33.2727662194104, -4.199
  23. {-23.372806606455196, 1.3475167003096096, -2.769154235839829, -1.9090821552195396, -1.9379712843010475, 4.783702918602666, -257.4470448708041, -3.1220034134994163, 47.969347620503086, -12.304830269149
  24. {6.413418520530221, -8.543734044062942, -6.896390882328101, -0.14243453531341954, 52.493530864902496, 9.95370309823603, 166.88662921759502, 2.1517277845825253, -17.75035701007757, 33.51957221172797, 3
  25. {43.31028247947829, 2.087462958987278, -8.001902958102342, 3.1774197610976223, -0.8663313039535422, 1.471041067473638, -403.471269174632, 0.803708388724774, 109.78852262443236, 26.728634952505352, -4.
  26. Numeric a(10.0)
  27. Numeric c(2.6666666666666665)
  28. (0, 0, 1)
  29. Boolean rotate(true)
  30. Numeric alpha(1.1)
  31. Numeric gam(0.87)
  32. F(x, y, z) = (strength * ((y * (z - 1 + (x * x))) + (gam * x)))
  33. G(x, y, z) = (strength * ((x * ((3 * z) + 1 - (x * x))) + (gam * y)))
  34. H(x, y, z) = (strength * ((-2 * z) * (alpha + (x * y))))