Traffic Velocity Simulation: Sine Waves and Random Experiments

Traffic Velocity Simulation: Sine Waves and Random Experiments
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2016-03-08 03:56
In collections Traffic
① This GeoGebra example dynamically simulates vehicle velocity variations in traffic flow, demonstrating how speed changes follow a sinusoidal pattern with superimposed random perturbations. ② Core mathematical concepts include sine functions, random variables, function graphs, sequences, segments, and stochastic experiments affecting deterministic models. ③ Construction highlights: uses Sequence and Segment commands to generate velocity curves and road segments, involving objects such as g_y, f, a, b, c, d, list1, list2, with buttons (button1, button2, button3) to trigger random experiments, sliders (e.g., k) to adjust parameters, and a cuboid plus road textures (photo_road, left_road, right_road, mid_road) to build a 3D scene. ④ Suitable for high school or early college students learning function modeling, introductory stochastic processes, and interactive GeoGebra design, also useful for physics or traffic engineering demonstrations of speed-time relationships.

GeoGebra Commands & Parameters

  1. Sequence((n, f(n)), n, 0, t_1) → list1
  2. Sequence((n, g(n)), n, 0, t_1) → list2
  3. Segment((-1.9, 200), (-1.1, 200)) → g_3
  4. Segment((-1.9, 0), (-1.1, 0)) → e
  5. Sequence(i - 0.4 < x < i + 0.4, i, 0, t_1) → photo_{road}
  6. Sequence(x = i - 0.4, i, 0, t_1) → left_{road}
  7. Sequence(x = i + 0.4, i, 0, t_1) → right_{road}
  8. Sequence(x = i, i, 0, t_1) → mid_{road}
  9. Sequence(Translate[truck_p, Vector[(0, f(0)), (i, f(i))]], i, 0, t_1) → photo_b
  10. Sequence(Translate[bike_p, Vector[(0, g(0)), (i - g_y(i), g(i))]], i, 0, t_1) → photo_r

AI Drawing Prompt Reference

Create a 3D traffic flow simulation scene: a horizontal road in the center with evenly spaced white lane markings and road edges on both sides. Above the road, two curves extend from left to right: one smooth sine wave representing ideal speed, and another jittery curve with random fluctuations representing actual speed. Small truck and bicycle icons are placed along each curve, translating along them to simulate vehicle movement. At the bottom, two short vertical segments serve as reference marks, with three buttons and a slider nearby for triggering random experiments and adjusting parameters. The overall effect is dynamic, highlighting the combination of sinusoidal patterns and random noise.
The prompt above was compiled from the original drawing commands and is for reference only.