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What is a Cobweb Diagram?

What is a Cobweb Diagram?
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2017-07-11 20:01
FunctionSequenceCoordinate Geometry
In collections ATC Cobwebs and Linear Difference Equations
This example illustrates the concept of a Cobweb Diagram, a graphical tool used to analyze the behavior of function iterations. It connects function values with input values in a coordinate system to visually demonstrate the function's iterative process. The example uses basic objects like functions, points, and line segments, and constructs the Cobweb Diagram through commands such as Point, Segment, and Intersect. Suitable for high school mathematics education, particularly in the study of function iterations and dynamic geometry.

GeoGebra Commands & Parameters

  1. Point(yAxis) → C
  2. Point(xAxis) → A
  3. Segment(A, (x(A), f(x(A)))) → c
  4. Segment((A1, A2), (A2, A2)) → B1
  5. Segment((A2, A2), (A2, A3)) → C1
  6. Segment((A2, A3), (A3, A3)) → B2
  7. Segment((A3, A3), (A3, A4)) → C2
  8. Segment((A3, A4), (A4, A4)) → B3
  9. Segment((A4, A4), (A4, A5)) → C3
  10. Segment((A4, A5), (A5, A5)) → B4
  11. Segment((A5, A5), (A5, A6)) → C4
  12. Segment((A5, A6), (A6, A6)) → B5
  13. Segment((A6, A6), (A6, A7)) → C5
  14. Segment((A6, A7), (A7, A7)) → B6
  15. Segment((A7, A7), (A7, A8)) → C6
  16. Segment((A7, A8), (A8, A8)) → B7
  17. Segment((A8, A8), (A8, A9)) → C7
  18. Segment((A8, A9), (A9, A9)) → B8
  19. Segment((A9, A9), (A9, A10)) → C8
  20. Segment((A9, A10), (A10, A10)) → B9
  21. Segment((A10, A10), (A10, A11)) → C9
  22. Segment((A10, A11), (A11, A11)) → B10
  23. Segment((A11, A11), (A11, A12)) → C10
  24. Segment((A11, A12), (A12, A12)) → B11
  25. Segment((A12, A12), (A12, A13)) → C11
  26. Segment((A12, A13), (A13, A13)) → B12
  27. Segment((A13, A13), (A13, A14)) → C12
  28. Segment((A13, A14), (A14, A14)) → B13
  29. Segment((A14, A14), (A14, A15)) → C13
  30. Segment((A14, A15), (A15, A15)) → B14
  31. Segment((A15, A15), (A15, A16)) → C14
  32. Segment((A15, A16), (A16, A16)) → B15
  33. Segment((A16, A16), (A16, A17)) → C15
  34. Segment((A16, A17), (A17, A17)) → B16
  35. Segment((A17, A17), (A17, A18)) → C16
  36. Segment((A17, A18), (A18, A18)) → B17
  37. Segment((A18, A18), (A18, A19)) → C17
  38. Segment((A18, A19), (A19, A19)) → B18
  39. Segment((A19, A19), (A19, A20)) → C18
  40. Segment((A19, A20), (A20, A20)) → B19
  41. Segment((A20, A20), (A20, A21)) → C19
  42. Segment((A20, A21), (A21, A21)) → B20
  43. Segment((A21, A21), (A21, A22)) → C20
  44. Segment((A21, A22), (A22, A22)) → B21
  45. Segment((A22, A22), (A22, A23)) → C21
  46. Segment((A22, A23), (A23, A23)) → B22
  47. Segment((A23, A23), (A23, A24)) → C22
  48. Segment((A23, A24), (A24, A24)) → B23
  49. Segment((A24, A24), (A24, A25)) → C23
  50. Segment((A24, A25), (A25, A25)) → B24
  51. Segment((A25, A25), (A25, A26)) → C24
  52. Segment((A25, A26), (A26, A26)) → B25
  53. Segment((A26, A26), (A26, A27)) → C25
  54. Segment((A26, A27), (A27, A27)) → B26
  55. Segment((A27, A27), (A27, A28)) → C26
  56. Segment((A27, A28), (A28, A28)) → B27
  57. Segment((A28, A28), (A28, A29)) → C27
  58. Segment((A28, A29), (A29, A29)) → B28
  59. Segment((A29, A29), (A29, A30)) → C28
  60. Segment((A29, A30), (A30, A30)) → B29
  61. Segment((A30, A30), (A30, A31)) → C29
  62. Segment((A30, A31), (A31, A31)) → B30
  63. Segment((A31, A31), (A31, A32)) → C30
  64. Segment((A31, A32), (A32, A32)) → B31
  65. Segment((A32, A32), (A32, A33)) → C31
  66. Segment((A32, A33), (A33, A33)) → B32
  67. Segment((A33, A33), (A33, A34)) → C32
  68. Segment((A33, A34), (A34, A34)) → B33
  69. Segment((A34, A34), (A34, A35)) → C33
  70. Segment((A34, A35), (A35, A35)) → B34
  71. Segment((A35, A35), (A35, A36)) → C34
  72. Segment((A35, A36), (A36, A36)) → B35
  73. Segment((A36, A36), (A36, A37)) → C35
  74. Segment((A36, A37), (A37, A37)) → B36
  75. Segment((A37, A37), (A37, A38)) → C36
  76. Segment((A37, A38), (A38, A38)) → B37
  77. Segment((A38, A38), (A38, A39)) → C37
  78. Segment((A38, A39), (A39, A39)) → B38
  79. Segment((A39, A39), (A39, A40)) → C38
  80. Intersect(f, b) → B
  81. If(steps < 0, {}, Take[list1, 1, steps / 2 + 1]) → list2
  82. Sequence(a, a, 0, floor(steps / 2)) → list3
  83. TableText({Join[{{"n"}, list3}], Join[{{"a_n"}, list2}]}, "c_h") → text9

AI Drawing Prompt Reference

Draw a cobweb diagram in a coordinate system to illustrate the iterative process of a function. Start by marking points on the x-axis and y-axis. Then connect each x-axis point to the corresponding point on the function's graph, and draw a vertical line from that point back to the x-axis, forming a zigzag pattern. Repeat this process to create multiple zigzag lines, visually demonstrating the function's iteration behavior.
The prompt above was compiled from the original drawing commands and is for reference only.