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Chase Curve

Chase Curve
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2015-05-12 07:29
VectorGeometric ConstructionSlider Animation
This example shows a dynamic pattern of five ants chasing each other. It demonstrates the concepts of vectors and geometric transformations. Using the Sequence and Polygon commands, you can observe how the ants move based on their speed and step. Suitable for middle school and above students to learn about geometric transformations and vectors.

GeoGebra Commands & Parameters

  1. Sequence(Element[B1, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B1, Mod[i, 5] + 1], Element[B1, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B2
  2. Sequence(Element[B2, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B2, Mod[i, 5] + 1], Element[B2, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B3
  3. Sequence(Element[B3, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B3, Mod[i, 5] + 1], Element[B3, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B4
  4. Sequence(Element[B4, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B4, Mod[i, 5] + 1], Element[B4, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B5
  5. Sequence(Element[B5, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B5, Mod[i, 5] + 1], Element[B5, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B6
  6. Sequence(Element[B6, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B6, Mod[i, 5] + 1], Element[B6, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B7
  7. Sequence(Element[B7, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B7, Mod[i, 5] + 1], Element[B7, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B8
  8. Sequence(Element[B8, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B8, Mod[i, 5] + 1], Element[B8, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B9
  9. Sequence(Element[B9, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B9, Mod[i, 5] + 1], Element[B9, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B10
  10. Sequence(Element[B10, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B10, Mod[i, 5] + 1], Element[B10, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B11
  11. Sequence(Element[B11, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B11, Mod[i, 5] + 1], Element[B11, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B12
  12. Sequence(Element[B12, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B12, Mod[i, 5] + 1], Element[B12, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B13
  13. Sequence(Element[B13, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B13, Mod[i, 5] + 1], Element[B13, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B14
  14. Sequence(Element[B14, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B14, Mod[i, 5] + 1], Element[B14, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B15
  15. Sequence(Element[B15, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B15, Mod[i, 5] + 1], Element[B15, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B16
  16. Sequence(Element[B16, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B16, Mod[i, 5] + 1], Element[B16, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B17
  17. Sequence(Element[B17, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B17, Mod[i, 5] + 1], Element[B17, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B18
  18. Sequence(Element[B18, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B18, Mod[i, 5] + 1], Element[B18, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B19
  19. Sequence(Element[B19, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B19, Mod[i, 5] + 1], Element[B19, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B20
  20. Polygon(B1) → C1, D1, E1, F1, G1, H1
  21. Polygon(B2) → C2, D2, E2, F2, G2, H2
  22. Polygon(B3) → C3, D3, E3, F3, G3, H3
  23. Polygon(B4) → C4, D4, E4, F4, G4, H4
  24. Polygon(B5) → C5, D5, E5, F5, G5, H5
  25. Polygon(B6) → C6, D6, E6, F6, G6, H6
  26. Polygon(B7) → C7, D7, E7, F7, G7, H7
  27. Polygon(B8) → C8, D8, E8, F8, G8, H8
  28. Polygon(B9) → C9, D9, E9, F9, G9, H9
  29. Polygon(B10) → C10, D10, E10, F10, G10, H10
  30. Polygon(B11) → C11, D11, E11, F11, G11, H11
  31. Polygon(B12) → C12, D12, E12, F12, G12, H12
  32. Polygon(B13) → C13, D13, E13, F13, G13, H13
  33. Polygon(B14) → C14, D14, E14, F14, G14, H14
  34. Polygon(B15) → C15, D15, E15, F15, G15, H15
  35. Polygon(B16) → C16, D16, E16, F16, G16, H16
  36. Polygon(B17) → C17, D17, E17, F17, G17, H17
  37. Polygon(B18) → C18, D18, E18, F18, G18, H18
  38. Polygon(B19) → C19, D19, E19, F19, G19, H19
  39. Polygon(B20) → C20, D20, E20, F20, G20, H20
  40. Sequence(Segment[Element[B2, i], Element[B1, i]], i, 1, 5) → I2
  41. Sequence(Segment[Element[B3, i], Element[B2, i]], i, 1, 5) → I3
  42. Sequence(Segment[Element[B4, i], Element[B3, i]], i, 1, 5) → I4
  43. Sequence(Segment[Element[B5, i], Element[B4, i]], i, 1, 5) → I5
  44. Sequence(Segment[Element[B6, i], Element[B5, i]], i, 1, 5) → I6
  45. Sequence(Segment[Element[B7, i], Element[B6, i]], i, 1, 5) → I7
  46. Sequence(Segment[Element[B8, i], Element[B7, i]], i, 1, 5) → I8
  47. Sequence(Segment[Element[B9, i], Element[B8, i]], i, 1, 5) → I9
  48. Sequence(Segment[Element[B10, i], Element[B9, i]], i, 1, 5) → I10
  49. Sequence(Segment[Element[B11, i], Element[B10, i]], i, 1, 5) → I11
  50. Sequence(Segment[Element[B12, i], Element[B11, i]], i, 1, 5) → I12
  51. Sequence(Segment[Element[B13, i], Element[B12, i]], i, 1, 5) → I13
  52. Sequence(Segment[Element[B14, i], Element[B13, i]], i, 1, 5) → I14
  53. Sequence(Segment[Element[B15, i], Element[B14, i]], i, 1, 5) → I15
  54. Sequence(Segment[Element[B16, i], Element[B15, i]], i, 1, 5) → I16
  55. Sequence(Segment[Element[B17, i], Element[B16, i]], i, 1, 5) → I17
  56. Sequence(Segment[Element[B18, i], Element[B17, i]], i, 1, 5) → I18
  57. Sequence(Segment[Element[B19, i], Element[B18, i]], i, 1, 5) → I19
  58. Sequence(Segment[Element[B20, i], Element[B19, i]], i, 1, 5) → I20

AI Drawing Prompt Reference

Draw a dynamic pattern of five ants chasing each other, demonstrating vector operations and geometric transformations. Each ant's position is calculated based on the previous ant's position and speed, using sequence commands to generate each step's position and polygon commands to connect these positions into paths. Finally, connect adjacent ant paths with line segments to show the chasing relationship.
The prompt above was compiled from the original drawing commands and is for reference only.