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Lorenz Attractor

Lorenz Attractor
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2018-11-02 18:38
FunctionCalculusParametric Equation
This example demonstrates the Lorenz attractor, a classic example of a chaotic dynamical system. It involves solving ordinary differential equations using the NSolveODE command. The example uses commands like PolyLine and If to simulate the trajectory of the Lorenz attractor, suitable for high school and above students to learn about chaos theory and calculus.

GeoGebra Commands & Parameters

  1. NSolveODE({x', y', z'}, 0, {x0, y0, z0}, 20) → numericalIntegral1, numericalIntegral2, numericalIntegral3
  2. Length(numericalIntegral1) → len
  3. Sequence((y(Point[numericalIntegral1, i]), y(Point[numericalIntegral2, i]), y(Point[numericalIntegral3, i])), i, 0, 1, 1 / len) → L_1
  4. PolyLine(L_1) → f
  5. LaTeX(x', true, true) → text1
  6. LaTeX(y', true, true) → text2
  7. LaTeX(z', true, true) → text3
  8. If(len ≟ len, 0, 1) → val

AI Drawing Prompt Reference

Draw the Lorenz attractor by solving the differential equations x', y', z' numerically. First, solve the differential equations to get the numerical integration results, then calculate the trajectory points, and use these points to draw a smooth curve. Finally, display the expressions of the differential equations.
The prompt above was compiled from the original drawing commands and is for reference only.