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Lorenz Attractor by Juan Carlos Ponce Campuzano

Lorenz Attractor by Juan Carlos Ponce Campuzano
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2017-08-31 05:47
VectorCalculusOptimizationParametric EquationGraphing
In collections UQ-Applied Mathematical Analysis
This example demonstrates the three-dimensional trajectory of the Lorenz attractor, a famous chaotic system. It involves core mathematical concepts like differential equations, dynamical systems, and chaos theory. Construction highlights include objects like buttons, sliders (strength, n, etc.), parameters (t, A, etc.), and GeoGebra commands (rotate, F, G, H, etc.). Suitable for high school students and enthusiasts interested in chaos theory.

GeoGebra Commands & Parameters

  1. Numeric strength(1)
  2. Numeric n(12)
  3. Numeric h(0.005)
  4. Numeric speed(1)
  5. Numeric t(-4.87)
  6. Numeric b(28)
  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. {(2.5900232040706044, -11.745281970900995, 11.972308465297743), (-17.699184163363643, -6.357120819982558, 5.306662403559168), (-1.7864398197719638, -14.15989079075698, 29.822708899574547), (4.04569321
  14. {-52.576231401426874, -142.49284271042933, -54.25953403929643, 1.11298387575129, -71.95894395262525, -28.49168309426335, -100.1769946728455, -35.70029739931038, -10.801192523512988, -65.0535852731946,
  15. {-159.95423433259026, 174.47382359061828, -29.337511818739273, 5.240248472407367, 36.63912375843727, -40.180983591025516, -8.47105035270892, 9.454213657658478, -37.5550033644864, -100.15438068888069,
  16. {45.54589040925377, -43.505557292695755, -63.123531028357675, -18.13182095463214, 101.58696070574612, 2.406689799407336, -42.01374165301707, -51.85485589200321, 57.91105660672137, -12.300796977606986,
  17. {-55.26068147470596, -134.56867605290313, -53.6364834837825, 1.2161654906676915, -69.2439922598487, -28.78391560668241, -97.88434606484209, -34.57143462288615, -11.470037794537316, -65.93110515858675,
  18. {-159.72074080958487, 163.81250310766853, -27.69125093895355, 5.29335913582955, 39.40664069652789, -41.85399411629992, -7.125865565472509, 9.531164473655995, -39.050283442191784, -98.22479478276802, -
  19. {38.60683248990378, -37.92964386098798, -63.2915924019852, -18.0360598839176, 103.20631381416901, 2.91186254209466, -42.374965214239715, -51.471594056828515, 56.26941471253725, -15.953943600332714, 16
  20. {-55.18773288479885, -135.03331323141506, -53.6109032256757, 1.2149137168803366, -69.24267812871582, -28.818435057003793, -97.90803266036124, -34.59773242189682, -11.49069866470434, -65.86092751379913
  21. {-159.4072431507419, 164.36927325969378, -27.700350552453592, 5.298033903396321, 39.423644214881364, -41.86576194167846, -7.122186476175752, 9.537090884628084, -38.9954710169387, -98.10687230169428, -
  22. {38.59344291057549, -38.25966270947698, -63.26648988287549, -18.036389200845107, 103.0169771395164, 2.920581238975151, -42.32821167674902, -51.47469010808287, 56.2177633505402, -15.891000105563727, 16
  23. {-57.78720691472402, -127.52271338587389, -52.964006405635324, 1.3171398850770895, -66.52562783544538, -29.144049438497078, -95.63770236363624, -33.49355623398413, -12.176431141124713, -66.66588251258
  24. {-158.83823107522122, 154.13530207861027, -26.10687017286258, 5.3559519634571995, 42.28796020755482, -43.553671433056515, -5.827680862699681, 9.597309128348323, -40.424929308988226, -96.0794983941778,
  25. {31.775927109049604, -33.25417499088631, -63.391348658447974, -17.940869279456333, 104.41382223105145, 3.4503948680744765, -42.634385082653395, -51.09845303431716, 54.532656066820884, -19.392570285271
  26. Numeric a(10)
  27. Numeric c(2)
  28. (0, 0, 1)
  29. Boolean rotate(true)
  30. F(x, y, z) = (strength * (a * (y - x)))
  31. G(x, y, z) = (strength * ((x * (b - z)) - y))
  32. H(x, y, z) = (strength * ((x * y) - (c * z)))