MathPlotAI Logo MathPlotAI

Rössler Attractor

Rössler Attractor
Loading the math board and drawing, please wait…
2017-08-30 09:14
FunctionTrigonometrySolid GeometryCalculusParametric Equation
In collections UQ-Applied Mathematical Analysis
This example demonstrates the fractal trajectory of the Rössler attractor, a chaotic system. Key math concepts include differential equations, chaos theory, parametric equations, and 3D visualization. Construction involves objects (buttons, sliders) and commands (parameters like t, A, k1, j1, i1) to dynamically visualize the attractor's shape. Suitable for high school students and math enthusiasts interested in chaos dynamics.

GeoGebra Commands & Parameters

  1. Numeric strength(2)
  2. Numeric n(12)
  3. Numeric h(0.01)
  4. Numeric speed(1)
  5. Numeric t(4.27)
  6. Numeric b(0.2)
  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. {(-2.4935544514881176, 12.775080288013005, -5.20662587161766), (-7.029664706191961, -12.484135647771105, 9.486399252792186), (-9.292163411414823, -5.5481637786395765, 26.483372718501247), (13.86231517
  14. {-2.677424871442329, -28.948279540725736, -4.83982238476226, -13.060903063494495, 12.59787727608522, -9.492541520355994, -22.36316466013438, 20.402677772818112, -10.02387759829951, 3.7397096976262674,
  15. {-5.153372142875115, 8.498505151968477, -12.94931822901259, 7.669800348233621, 1.852319455519483, -6.384409879286964, 34.30972242709876, -4.629909374695141, -12.376827682886447, -28.22161414457551, -1
  16. {-0.010731304150261023, -19.063614299995947, -25.48084505354133, -24.579554121473272, 0.09835451152242808, -0.023354837604977224, -50.30364083653461, -18.664143155926553, -12.045315765564851, -2.45403
  17. {-2.625783836972076, -28.84262844924546, -4.455520751936721, -12.891805525762097, 12.5783705364148, -9.428463873187075, -22.20322547604002, 20.635618298124328, -9.779656163814996, 4.046466155478011, 2
  18. {-5.190453135875289, 8.226019366865156, -13.023615089318238, 7.554530918295143, 1.9820028671913743, -6.4921041142490985, 34.15471022535162, -4.43514241571635, -12.501820114235215, -28.240660275888402,
  19. {-0.01045733755596373, -24.49527632541202, -22.35241752625538, -25.09498619770222, 0.100388966476681, -0.023088920715954975, -53.93228071704132, -17.286147517811685, -10.54701370603463, -1.97511731277
  20. {-2.625415766708017, -28.785586971140265, -4.486062058606524, -12.885498510700424, 12.57705335774854, -9.427389590006344, -22.165388955217484, 20.619890672153392, -9.793389260096811, 4.041867473512927
  21. {-5.1900108875165865, 8.226530906209753, -13.019920666710595, 7.55599135481259, 1.9820671666180134, -6.491678726247333, 34.15599959278907, -4.43242347654533, -12.499627884753068, -28.23763080357251, -
  22. {-0.010468378004341583, -24.43972485081798, -22.739123437304997, -25.07370262089858, 0.10031044048114562, -0.023101491232946553, -54.2465436809246, -17.35867388826886, -10.738391188339467, -2.06784808
  23. {-2.573415286131911, -28.62401566183357, -4.124641502681948, -12.710548838172773, 12.556229723943238, -9.362245916006389, -21.96135377837167, 20.838499720114395, -9.55911721683766, 4.345819275484593,
  24. {-5.226640501759342, 7.955699536170511, -13.091119152851563, 7.442314343438862, 2.111788791340926, -6.598924385992081, 34.003038646365574, -4.235241255158255, -12.622693979627396, -28.253727318319545,
  25. {-0.010200638304565635, -29.724451759316906, -19.891298237335334, -25.53539483530637, 0.10239679036684513, -0.022823421320407544, -58.12518580241106, -16.081476495650836, -9.371913926274585, -1.646523
  26. Numeric a(0.2)
  27. Numeric c(5.7)
  28. F(x, y, z) = (strength * ((-y) - z))
  29. G(x, y, z) = (strength * (x + (a * y)))
  30. H(x, y, z) = (strength * (b + (x * z) - (c * z)))