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Visualizing Fibonacci Sequence Modulo 9

Visualizing Fibonacci Sequence Modulo 9
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2018-11-24 19:56
FunctionSequenceParametric EquationLocusGraphing
In collections Graphs of Sequences
This example demonstrates the periodic pattern formed by Fibonacci sequence numbers modulo 9 plotted in a Cartesian coordinate system. Using the CurveCartesian command, the recurrence relationship of the sequence is transformed into visual trajectories, revealing the cyclic periodicity of Fibonacci numbers mod 9. Core mathematical concepts include: Fibonacci recursive sequence, modular arithmetic (remainder cycles), sequence periodicity, and parametric curve plotting. Construction details: Sequence command generates the sequence, Element extracts specific terms, Flatten and Join organize data, Length calculates sequence length, and CurveCartesian maps (term index, remainder value) to coordinate points. Suitable for high school and above, useful for teaching sequences and modular arithmetic, exploring periodic phenomena, and learning GeoGebra parametric curve commands.

GeoGebra Commands & Parameters

  1. Sequence(Mod[Element[L_1, i], 9], i, 1, 25) → M91
  2. Flatten(Sequence[Sequence[Mod[(i * Element[M91, j]), 9], j, 1, 25], i, 2, 8]) → New
  3. Join({M91, New}) → SeqAll
  4. Length(SeqAll) → lng
  5. CurveCartesian((abs((Element[SeqAll, 2] - Element[SeqAll, 1]) / 2) * cos(u)) + (Element[SeqAll, 2] + Element[SeqAll, 1]) / 2, (abs((Element[SeqAll, 2] - Element[SeqAll, 1]) / 2) * sin(u)), u, If[If[Element[SeqAll, 2] > Element[SeqAll, 1], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 2] > Element[SeqAll, 1], 0, 1] ≟ 1, (2 * π), π]) → B1
  6. CurveCartesian((abs((Element[SeqAll, 3] - Element[SeqAll, 2]) / 2) * cos(u)) + (Element[SeqAll, 3] + Element[SeqAll, 2]) / 2, (abs((Element[SeqAll, 3] - Element[SeqAll, 2]) / 2) * sin(u)), u, If[If[Element[SeqAll, 3] > Element[SeqAll, 2], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 3] > Element[SeqAll, 2], 0, 1] ≟ 1, (2 * π), π]) → B2
  7. CurveCartesian((abs((Element[SeqAll, 4] - Element[SeqAll, 3]) / 2) * cos(u)) + (Element[SeqAll, 4] + Element[SeqAll, 3]) / 2, (abs((Element[SeqAll, 4] - Element[SeqAll, 3]) / 2) * sin(u)), u, If[If[Element[SeqAll, 4] > Element[SeqAll, 3], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 4] > Element[SeqAll, 3], 0, 1] ≟ 1, (2 * π), π]) → B3
  8. CurveCartesian((abs((Element[SeqAll, 5] - Element[SeqAll, 4]) / 2) * cos(u)) + (Element[SeqAll, 5] + Element[SeqAll, 4]) / 2, (abs((Element[SeqAll, 5] - Element[SeqAll, 4]) / 2) * sin(u)), u, If[If[Element[SeqAll, 5] > Element[SeqAll, 4], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 5] > Element[SeqAll, 4], 0, 1] ≟ 1, (2 * π), π]) → B4
  9. CurveCartesian((abs((Element[SeqAll, 6] - Element[SeqAll, 5]) / 2) * cos(u)) + (Element[SeqAll, 6] + Element[SeqAll, 5]) / 2, (abs((Element[SeqAll, 6] - Element[SeqAll, 5]) / 2) * sin(u)), u, If[If[Element[SeqAll, 6] > Element[SeqAll, 5], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 6] > Element[SeqAll, 5], 0, 1] ≟ 1, (2 * π), π]) → B5
  10. CurveCartesian((abs((Element[SeqAll, 7] - Element[SeqAll, 6]) / 2) * cos(u)) + (Element[SeqAll, 7] + Element[SeqAll, 6]) / 2, (abs((Element[SeqAll, 7] - Element[SeqAll, 6]) / 2) * sin(u)), u, If[If[Element[SeqAll, 7] > Element[SeqAll, 6], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 7] > Element[SeqAll, 6], 0, 1] ≟ 1, (2 * π), π]) → B6
  11. CurveCartesian((abs((Element[SeqAll, 8] - Element[SeqAll, 7]) / 2) * cos(u)) + (Element[SeqAll, 8] + Element[SeqAll, 7]) / 2, (abs((Element[SeqAll, 8] - Element[SeqAll, 7]) / 2) * sin(u)), u, If[If[Element[SeqAll, 8] > Element[SeqAll, 7], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 8] > Element[SeqAll, 7], 0, 1] ≟ 1, (2 * π), π]) → B7
  12. CurveCartesian((abs((Element[SeqAll, 9] - Element[SeqAll, 8]) / 2) * cos(u)) + (Element[SeqAll, 9] + Element[SeqAll, 8]) / 2, (abs((Element[SeqAll, 9] - Element[SeqAll, 8]) / 2) * sin(u)), u, If[If[Element[SeqAll, 9] > Element[SeqAll, 8], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 9] > Element[SeqAll, 8], 0, 1] ≟ 1, (2 * π), π]) → B8
  13. CurveCartesian((abs((Element[SeqAll, 10] - Element[SeqAll, 9]) / 2) * cos(u)) + (Element[SeqAll, 10] + Element[SeqAll, 9]) / 2, (abs((Element[SeqAll, 10] - Element[SeqAll, 9]) / 2) * sin(u)), u, If[If[Element[SeqAll, 10] > Element[SeqAll, 9], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 10] > Element[SeqAll, 9], 0, 1] ≟ 1, (2 * π), π]) → B9
  14. CurveCartesian((abs((Element[SeqAll, 11] - Element[SeqAll, 10]) / 2) * cos(u)) + (Element[SeqAll, 11] + Element[SeqAll, 10]) / 2, (abs((Element[SeqAll, 11] - Element[SeqAll, 10]) / 2) * sin(u)), u, If[If[Element[SeqAll, 11] > Element[SeqAll, 10], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 11] > Element[SeqAll, 10], 0, 1] ≟ 1, (2 * π), π]) → B10
  15. CurveCartesian((abs((Element[SeqAll, 12] - Element[SeqAll, 11]) / 2) * cos(u)) + (Element[SeqAll, 12] + Element[SeqAll, 11]) / 2, (abs((Element[SeqAll, 12] - Element[SeqAll, 11]) / 2) * sin(u)), u, If[If[Element[SeqAll, 12] > Element[SeqAll, 11], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 12] > Element[SeqAll, 11], 0, 1] ≟ 1, (2 * π), π]) → B11
  16. CurveCartesian((abs((Element[SeqAll, 13] - Element[SeqAll, 12]) / 2) * cos(u)) + (Element[SeqAll, 13] + Element[SeqAll, 12]) / 2, (abs((Element[SeqAll, 13] - Element[SeqAll, 12]) / 2) * sin(u)), u, If[If[Element[SeqAll, 13] > Element[SeqAll, 12], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 13] > Element[SeqAll, 12], 0, 1] ≟ 1, (2 * π), π]) → B12
  17. CurveCartesian((abs((Element[SeqAll, 14] - Element[SeqAll, 13]) / 2) * cos(u)) + (Element[SeqAll, 14] + Element[SeqAll, 13]) / 2, (abs((Element[SeqAll, 14] - Element[SeqAll, 13]) / 2) * sin(u)), u, If[If[Element[SeqAll, 14] > Element[SeqAll, 13], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 14] > Element[SeqAll, 13], 0, 1] ≟ 1, (2 * π), π]) → B13
  18. CurveCartesian((abs((Element[SeqAll, 15] - Element[SeqAll, 14]) / 2) * cos(u)) + (Element[SeqAll, 15] + Element[SeqAll, 14]) / 2, (abs((Element[SeqAll, 15] - Element[SeqAll, 14]) / 2) * sin(u)), u, If[If[Element[SeqAll, 15] > Element[SeqAll, 14], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 15] > Element[SeqAll, 14], 0, 1] ≟ 1, (2 * π), π]) → B14
  19. CurveCartesian((abs((Element[SeqAll, 16] - Element[SeqAll, 15]) / 2) * cos(u)) + (Element[SeqAll, 16] + Element[SeqAll, 15]) / 2, (abs((Element[SeqAll, 16] - Element[SeqAll, 15]) / 2) * sin(u)), u, If[If[Element[SeqAll, 16] > Element[SeqAll, 15], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 16] > Element[SeqAll, 15], 0, 1] ≟ 1, (2 * π), π]) → B15
  20. CurveCartesian((abs((Element[SeqAll, 17] - Element[SeqAll, 16]) / 2) * cos(u)) + (Element[SeqAll, 17] + Element[SeqAll, 16]) / 2, (abs((Element[SeqAll, 17] - Element[SeqAll, 16]) / 2) * sin(u)), u, If[If[Element[SeqAll, 17] > Element[SeqAll, 16], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 17] > Element[SeqAll, 16], 0, 1] ≟ 1, (2 * π), π]) → B16
  21. CurveCartesian((abs((Element[SeqAll, 18] - Element[SeqAll, 17]) / 2) * cos(u)) + (Element[SeqAll, 18] + Element[SeqAll, 17]) / 2, (abs((Element[SeqAll, 18] - Element[SeqAll, 17]) / 2) * sin(u)), u, If[If[Element[SeqAll, 18] > Element[SeqAll, 17], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 18] > Element[SeqAll, 17], 0, 1] ≟ 1, (2 * π), π]) → B17
  22. CurveCartesian((abs((Element[SeqAll, 19] - Element[SeqAll, 18]) / 2) * cos(u)) + (Element[SeqAll, 19] + Element[SeqAll, 18]) / 2, (abs((Element[SeqAll, 19] - Element[SeqAll, 18]) / 2) * sin(u)), u, If[If[Element[SeqAll, 19] > Element[SeqAll, 18], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 19] > Element[SeqAll, 18], 0, 1] ≟ 1, (2 * π), π]) → B18
  23. CurveCartesian((abs((Element[SeqAll, 20] - Element[SeqAll, 19]) / 2) * cos(u)) + (Element[SeqAll, 20] + Element[SeqAll, 19]) / 2, (abs((Element[SeqAll, 20] - Element[SeqAll, 19]) / 2) * sin(u)), u, If[If[Element[SeqAll, 20] > Element[SeqAll, 19], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 20] > Element[SeqAll, 19], 0, 1] ≟ 1, (2 * π), π]) → B19
  24. CurveCartesian((abs((Element[SeqAll, 21] - Element[SeqAll, 20]) / 2) * cos(u)) + (Element[SeqAll, 21] + Element[SeqAll, 20]) / 2, (abs((Element[SeqAll, 21] - Element[SeqAll, 20]) / 2) * sin(u)), u, If[If[Element[SeqAll, 21] > Element[SeqAll, 20], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 21] > Element[SeqAll, 20], 0, 1] ≟ 1, (2 * π), π]) → B20
  25. CurveCartesian((abs((Element[SeqAll, 22] - Element[SeqAll, 21]) / 2) * cos(u)) + (Element[SeqAll, 22] + Element[SeqAll, 21]) / 2, (abs((Element[SeqAll, 22] - Element[SeqAll, 21]) / 2) * sin(u)), u, If[If[Element[SeqAll, 22] > Element[SeqAll, 21], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 22] > Element[SeqAll, 21], 0, 1] ≟ 1, (2 * π), π]) → B21
  26. CurveCartesian((abs((Element[SeqAll, 23] - Element[SeqAll, 22]) / 2) * cos(u)) + (Element[SeqAll, 23] + Element[SeqAll, 22]) / 2, (abs((Element[SeqAll, 23] - Element[SeqAll, 22]) / 2) * sin(u)), u, If[If[Element[SeqAll, 23] > Element[SeqAll, 22], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 23] > Element[SeqAll, 22], 0, 1] ≟ 1, (2 * π), π]) → B22
  27. CurveCartesian((abs((Element[SeqAll, 24] - Element[SeqAll, 23]) / 2) * cos(u)) + (Element[SeqAll, 24] + Element[SeqAll, 23]) / 2, (abs((Element[SeqAll, 24] - Element[SeqAll, 23]) / 2) * sin(u)), u, If[If[Element[SeqAll, 24] > Element[SeqAll, 23], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 24] > Element[SeqAll, 23], 0, 1] ≟ 1, (2 * π), π]) → B23
  28. CurveCartesian((abs((Element[SeqAll, 25] - Element[SeqAll, 24]) / 2) * cos(u)) + (Element[SeqAll, 25] + Element[SeqAll, 24]) / 2, (abs((Element[SeqAll, 25] - Element[SeqAll, 24]) / 2) * sin(u)), u, If[If[Element[SeqAll, 25] > Element[SeqAll, 24], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 25] > Element[SeqAll, 24], 0, 1] ≟ 1, (2 * π), π]) → B24
  29. CurveCartesian((abs((Element[SeqAll, 26] - Element[SeqAll, 25]) / 2) * cos(u)) + (Element[SeqAll, 26] + Element[SeqAll, 25]) / 2, (abs((Element[SeqAll, 26] - Element[SeqAll, 25]) / 2) * sin(u)), u, If[If[Element[SeqAll, 26] > Element[SeqAll, 25], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 26] > Element[SeqAll, 25], 0, 1] ≟ 1, (2 * π), π]) → B25
  30. CurveCartesian((abs((Element[SeqAll, 27] - Element[SeqAll, 26]) / 2) * cos(u)) + (Element[SeqAll, 27] + Element[SeqAll, 26]) / 2, (abs((Element[SeqAll, 27] - Element[SeqAll, 26]) / 2) * sin(u)), u, If[If[Element[SeqAll, 27] > Element[SeqAll, 26], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 27] > Element[SeqAll, 26], 0, 1] ≟ 1, (2 * π), π]) → B26
  31. CurveCartesian((abs((Element[SeqAll, 28] - Element[SeqAll, 27]) / 2) * cos(u)) + (Element[SeqAll, 28] + Element[SeqAll, 27]) / 2, (abs((Element[SeqAll, 28] - Element[SeqAll, 27]) / 2) * sin(u)), u, If[If[Element[SeqAll, 28] > Element[SeqAll, 27], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 28] > Element[SeqAll, 27], 0, 1] ≟ 1, (2 * π), π]) → B27
  32. CurveCartesian((abs((Element[SeqAll, 29] - Element[SeqAll, 28]) / 2) * cos(u)) + (Element[SeqAll, 29] + Element[SeqAll, 28]) / 2, (abs((Element[SeqAll, 29] - Element[SeqAll, 28]) / 2) * sin(u)), u, If[If[Element[SeqAll, 29] > Element[SeqAll, 28], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 29] > Element[SeqAll, 28], 0, 1] ≟ 1, (2 * π), π]) → B28
  33. CurveCartesian((abs((Element[SeqAll, 30] - Element[SeqAll, 29]) / 2) * cos(u)) + (Element[SeqAll, 30] + Element[SeqAll, 29]) / 2, (abs((Element[SeqAll, 30] - Element[SeqAll, 29]) / 2) * sin(u)), u, If[If[Element[SeqAll, 30] > Element[SeqAll, 29], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 30] > Element[SeqAll, 29], 0, 1] ≟ 1, (2 * π), π]) → B29
  34. CurveCartesian((abs((Element[SeqAll, 31] - Element[SeqAll, 30]) / 2) * cos(u)) + (Element[SeqAll, 31] + Element[SeqAll, 30]) / 2, (abs((Element[SeqAll, 31] - Element[SeqAll, 30]) / 2) * sin(u)), u, If[If[Element[SeqAll, 31] > Element[SeqAll, 30], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 31] > Element[SeqAll, 30], 0, 1] ≟ 1, (2 * π), π]) → B30
  35. CurveCartesian((abs((Element[SeqAll, 32] - Element[SeqAll, 31]) / 2) * cos(u)) + (Element[SeqAll, 32] + Element[SeqAll, 31]) / 2, (abs((Element[SeqAll, 32] - Element[SeqAll, 31]) / 2) * sin(u)), u, If[If[Element[SeqAll, 32] > Element[SeqAll, 31], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 32] > Element[SeqAll, 31], 0, 1] ≟ 1, (2 * π), π]) → B31
  36. CurveCartesian((abs((Element[SeqAll, 33] - Element[SeqAll, 32]) / 2) * cos(u)) + (Element[SeqAll, 33] + Element[SeqAll, 32]) / 2, (abs((Element[SeqAll, 33] - Element[SeqAll, 32]) / 2) * sin(u)), u, If[If[Element[SeqAll, 33] > Element[SeqAll, 32], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 33] > Element[SeqAll, 32], 0, 1] ≟ 1, (2 * π), π]) → B32
  37. CurveCartesian((abs((Element[SeqAll, 34] - Element[SeqAll, 33]) / 2) * cos(u)) + (Element[SeqAll, 34] + Element[SeqAll, 33]) / 2, (abs((Element[SeqAll, 34] - Element[SeqAll, 33]) / 2) * sin(u)), u, If[If[Element[SeqAll, 34] > Element[SeqAll, 33], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 34] > Element[SeqAll, 33], 0, 1] ≟ 1, (2 * π), π]) → B33
  38. CurveCartesian((abs((Element[SeqAll, 35] - Element[SeqAll, 34]) / 2) * cos(u)) + (Element[SeqAll, 35] + Element[SeqAll, 34]) / 2, (abs((Element[SeqAll, 35] - Element[SeqAll, 34]) / 2) * sin(u)), u, If[If[Element[SeqAll, 35] > Element[SeqAll, 34], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 35] > Element[SeqAll, 34], 0, 1] ≟ 1, (2 * π), π]) → B34
  39. CurveCartesian((abs((Element[SeqAll, 36] - Element[SeqAll, 35]) / 2) * cos(u)) + (Element[SeqAll, 36] + Element[SeqAll, 35]) / 2, (abs((Element[SeqAll, 36] - Element[SeqAll, 35]) / 2) * sin(u)), u, If[If[Element[SeqAll, 36] > Element[SeqAll, 35], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 36] > Element[SeqAll, 35], 0, 1] ≟ 1, (2 * π), π]) → B35
  40. CurveCartesian((abs((Element[SeqAll, 37] - Element[SeqAll, 36]) / 2) * cos(u)) + (Element[SeqAll, 37] + Element[SeqAll, 36]) / 2, (abs((Element[SeqAll, 37] - Element[SeqAll, 36]) / 2) * sin(u)), u, If[If[Element[SeqAll, 37] > Element[SeqAll, 36], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 37] > Element[SeqAll, 36], 0, 1] ≟ 1, (2 * π), π]) → B36
  41. CurveCartesian((abs((Element[SeqAll, 38] - Element[SeqAll, 37]) / 2) * cos(u)) + (Element[SeqAll, 38] + Element[SeqAll, 37]) / 2, (abs((Element[SeqAll, 38] - Element[SeqAll, 37]) / 2) * sin(u)), u, If[If[Element[SeqAll, 38] > Element[SeqAll, 37], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 38] > Element[SeqAll, 37], 0, 1] ≟ 1, (2 * π), π]) → B37
  42. CurveCartesian((abs((Element[SeqAll, 39] - Element[SeqAll, 38]) / 2) * cos(u)) + (Element[SeqAll, 39] + Element[SeqAll, 38]) / 2, (abs((Element[SeqAll, 39] - Element[SeqAll, 38]) / 2) * sin(u)), u, If[If[Element[SeqAll, 39] > Element[SeqAll, 38], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 39] > Element[SeqAll, 38], 0, 1] ≟ 1, (2 * π), π]) → B38
  43. CurveCartesian((abs((Element[SeqAll, 40] - Element[SeqAll, 39]) / 2) * cos(u)) + (Element[SeqAll, 40] + Element[SeqAll, 39]) / 2, (abs((Element[SeqAll, 40] - Element[SeqAll, 39]) / 2) * sin(u)), u, If[If[Element[SeqAll, 40] > Element[SeqAll, 39], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 40] > Element[SeqAll, 39], 0, 1] ≟ 1, (2 * π), π]) → B39
  44. CurveCartesian((abs((Element[SeqAll, 41] - Element[SeqAll, 40]) / 2) * cos(u)) + (Element[SeqAll, 41] + Element[SeqAll, 40]) / 2, (abs((Element[SeqAll, 41] - Element[SeqAll, 40]) / 2) * sin(u)), u, If[If[Element[SeqAll, 41] > Element[SeqAll, 40], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 41] > Element[SeqAll, 40], 0, 1] ≟ 1, (2 * π), π]) → B40
  45. CurveCartesian((abs((Element[SeqAll, 42] - Element[SeqAll, 41]) / 2) * cos(u)) + (Element[SeqAll, 42] + Element[SeqAll, 41]) / 2, (abs((Element[SeqAll, 42] - Element[SeqAll, 41]) / 2) * sin(u)), u, If[If[Element[SeqAll, 42] > Element[SeqAll, 41], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 42] > Element[SeqAll, 41], 0, 1] ≟ 1, (2 * π), π]) → B41
  46. CurveCartesian((abs((Element[SeqAll, 43] - Element[SeqAll, 42]) / 2) * cos(u)) + (Element[SeqAll, 43] + Element[SeqAll, 42]) / 2, (abs((Element[SeqAll, 43] - Element[SeqAll, 42]) / 2) * sin(u)), u, If[If[Element[SeqAll, 43] > Element[SeqAll, 42], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 43] > Element[SeqAll, 42], 0, 1] ≟ 1, (2 * π), π]) → B42
  47. CurveCartesian((abs((Element[SeqAll, 44] - Element[SeqAll, 43]) / 2) * cos(u)) + (Element[SeqAll, 44] + Element[SeqAll, 43]) / 2, (abs((Element[SeqAll, 44] - Element[SeqAll, 43]) / 2) * sin(u)), u, If[If[Element[SeqAll, 44] > Element[SeqAll, 43], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 44] > Element[SeqAll, 43], 0, 1] ≟ 1, (2 * π), π]) → B43
  48. CurveCartesian((abs((Element[SeqAll, 45] - Element[SeqAll, 44]) / 2) * cos(u)) + (Element[SeqAll, 45] + Element[SeqAll, 44]) / 2, (abs((Element[SeqAll, 45] - Element[SeqAll, 44]) / 2) * sin(u)), u, If[If[Element[SeqAll, 45] > Element[SeqAll, 44], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 45] > Element[SeqAll, 44], 0, 1] ≟ 1, (2 * π), π]) → B44
  49. CurveCartesian((abs((Element[SeqAll, 46] - Element[SeqAll, 45]) / 2) * cos(u)) + (Element[SeqAll, 46] + Element[SeqAll, 45]) / 2, (abs((Element[SeqAll, 46] - Element[SeqAll, 45]) / 2) * sin(u)), u, If[If[Element[SeqAll, 46] > Element[SeqAll, 45], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 46] > Element[SeqAll, 45], 0, 1] ≟ 1, (2 * π), π]) → B45
  50. CurveCartesian((abs((Element[SeqAll, 47] - Element[SeqAll, 46]) / 2) * cos(u)) + (Element[SeqAll, 47] + Element[SeqAll, 46]) / 2, (abs((Element[SeqAll, 47] - Element[SeqAll, 46]) / 2) * sin(u)), u, If[If[Element[SeqAll, 47] > Element[SeqAll, 46], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 47] > Element[SeqAll, 46], 0, 1] ≟ 1, (2 * π), π]) → B46
  51. CurveCartesian((abs((Element[SeqAll, 48] - Element[SeqAll, 47]) / 2) * cos(u)) + (Element[SeqAll, 48] + Element[SeqAll, 47]) / 2, (abs((Element[SeqAll, 48] - Element[SeqAll, 47]) / 2) * sin(u)), u, If[If[Element[SeqAll, 48] > Element[SeqAll, 47], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 48] > Element[SeqAll, 47], 0, 1] ≟ 1, (2 * π), π]) → B47
  52. CurveCartesian((abs((Element[SeqAll, 49] - Element[SeqAll, 48]) / 2) * cos(u)) + (Element[SeqAll, 49] + Element[SeqAll, 48]) / 2, (abs((Element[SeqAll, 49] - Element[SeqAll, 48]) / 2) * sin(u)), u, If[If[Element[SeqAll, 49] > Element[SeqAll, 48], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 49] > Element[SeqAll, 48], 0, 1] ≟ 1, (2 * π), π]) → B48
  53. CurveCartesian((abs((Element[SeqAll, 50] - Element[SeqAll, 49]) / 2) * cos(u)) + (Element[SeqAll, 50] + Element[SeqAll, 49]) / 2, (abs((Element[SeqAll, 50] - Element[SeqAll, 49]) / 2) * sin(u)), u, If[If[Element[SeqAll, 50] > Element[SeqAll, 49], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 50] > Element[SeqAll, 49], 0, 1] ≟ 1, (2 * π), π]) → B49
  54. CurveCartesian((abs((Element[SeqAll, 51] - Element[SeqAll, 50]) / 2) * cos(u)) + (Element[SeqAll, 51] + Element[SeqAll, 50]) / 2, (abs((Element[SeqAll, 51] - Element[SeqAll, 50]) / 2) * sin(u)), u, If[If[Element[SeqAll, 51] > Element[SeqAll, 50], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 51] > Element[SeqAll, 50], 0, 1] ≟ 1, (2 * π), π]) → B50
  55. CurveCartesian((abs((Element[SeqAll, 52] - Element[SeqAll, 51]) / 2) * cos(u)) + (Element[SeqAll, 52] + Element[SeqAll, 51]) / 2, (abs((Element[SeqAll, 52] - Element[SeqAll, 51]) / 2) * sin(u)), u, If[If[Element[SeqAll, 52] > Element[SeqAll, 51], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 52] > Element[SeqAll, 51], 0, 1] ≟ 1, (2 * π), π]) → B51
  56. CurveCartesian((abs((Element[SeqAll, 53] - Element[SeqAll, 52]) / 2) * cos(u)) + (Element[SeqAll, 53] + Element[SeqAll, 52]) / 2, (abs((Element[SeqAll, 53] - Element[SeqAll, 52]) / 2) * sin(u)), u, If[If[Element[SeqAll, 53] > Element[SeqAll, 52], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 53] > Element[SeqAll, 52], 0, 1] ≟ 1, (2 * π), π]) → B52
  57. CurveCartesian((abs((Element[SeqAll, 54] - Element[SeqAll, 53]) / 2) * cos(u)) + (Element[SeqAll, 54] + Element[SeqAll, 53]) / 2, (abs((Element[SeqAll, 54] - Element[SeqAll, 53]) / 2) * sin(u)), u, If[If[Element[SeqAll, 54] > Element[SeqAll, 53], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 54] > Element[SeqAll, 53], 0, 1] ≟ 1, (2 * π), π]) → B53
  58. CurveCartesian((abs((Element[SeqAll, 55] - Element[SeqAll, 54]) / 2) * cos(u)) + (Element[SeqAll, 55] + Element[SeqAll, 54]) / 2, (abs((Element[SeqAll, 55] - Element[SeqAll, 54]) / 2) * sin(u)), u, If[If[Element[SeqAll, 55] > Element[SeqAll, 54], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 55] > Element[SeqAll, 54], 0, 1] ≟ 1, (2 * π), π]) → B54
  59. CurveCartesian((abs((Element[SeqAll, 56] - Element[SeqAll, 55]) / 2) * cos(u)) + (Element[SeqAll, 56] + Element[SeqAll, 55]) / 2, (abs((Element[SeqAll, 56] - Element[SeqAll, 55]) / 2) * sin(u)), u, If[If[Element[SeqAll, 56] > Element[SeqAll, 55], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 56] > Element[SeqAll, 55], 0, 1] ≟ 1, (2 * π), π]) → B55
  60. CurveCartesian((abs((Element[SeqAll, 57] - Element[SeqAll, 56]) / 2) * cos(u)) + (Element[SeqAll, 57] + Element[SeqAll, 56]) / 2, (abs((Element[SeqAll, 57] - Element[SeqAll, 56]) / 2) * sin(u)), u, If[If[Element[SeqAll, 57] > Element[SeqAll, 56], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 57] > Element[SeqAll, 56], 0, 1] ≟ 1, (2 * π), π]) → B56
  61. CurveCartesian((abs((Element[SeqAll, 58] - Element[SeqAll, 57]) / 2) * cos(u)) + (Element[SeqAll, 58] + Element[SeqAll, 57]) / 2, (abs((Element[SeqAll, 58] - Element[SeqAll, 57]) / 2) * sin(u)), u, If[If[Element[SeqAll, 58] > Element[SeqAll, 57], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 58] > Element[SeqAll, 57], 0, 1] ≟ 1, (2 * π), π]) → B57
  62. CurveCartesian((abs((Element[SeqAll, 59] - Element[SeqAll, 58]) / 2) * cos(u)) + (Element[SeqAll, 59] + Element[SeqAll, 58]) / 2, (abs((Element[SeqAll, 59] - Element[SeqAll, 58]) / 2) * sin(u)), u, If[If[Element[SeqAll, 59] > Element[SeqAll, 58], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 59] > Element[SeqAll, 58], 0, 1] ≟ 1, (2 * π), π]) → B58
  63. CurveCartesian((abs((Element[SeqAll, 60] - Element[SeqAll, 59]) / 2) * cos(u)) + (Element[SeqAll, 60] + Element[SeqAll, 59]) / 2, (abs((Element[SeqAll, 60] - Element[SeqAll, 59]) / 2) * sin(u)), u, If[If[Element[SeqAll, 60] > Element[SeqAll, 59], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 60] > Element[SeqAll, 59], 0, 1] ≟ 1, (2 * π), π]) → B59
  64. CurveCartesian((abs((Element[SeqAll, 61] - Element[SeqAll, 60]) / 2) * cos(u)) + (Element[SeqAll, 61] + Element[SeqAll, 60]) / 2, (abs((Element[SeqAll, 61] - Element[SeqAll, 60]) / 2) * sin(u)), u, If[If[Element[SeqAll, 61] > Element[SeqAll, 60], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 61] > Element[SeqAll, 60], 0, 1] ≟ 1, (2 * π), π]) → B60
  65. CurveCartesian((abs((Element[SeqAll, 62] - Element[SeqAll, 61]) / 2) * cos(u)) + (Element[SeqAll, 62] + Element[SeqAll, 61]) / 2, (abs((Element[SeqAll, 62] - Element[SeqAll, 61]) / 2) * sin(u)), u, If[If[Element[SeqAll, 62] > Element[SeqAll, 61], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 62] > Element[SeqAll, 61], 0, 1] ≟ 1, (2 * π), π]) → B61
  66. CurveCartesian((abs((Element[SeqAll, 63] - Element[SeqAll, 62]) / 2) * cos(u)) + (Element[SeqAll, 63] + Element[SeqAll, 62]) / 2, (abs((Element[SeqAll, 63] - Element[SeqAll, 62]) / 2) * sin(u)), u, If[If[Element[SeqAll, 63] > Element[SeqAll, 62], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 63] > Element[SeqAll, 62], 0, 1] ≟ 1, (2 * π), π]) → B62
  67. CurveCartesian((abs((Element[SeqAll, 64] - Element[SeqAll, 63]) / 2) * cos(u)) + (Element[SeqAll, 64] + Element[SeqAll, 63]) / 2, (abs((Element[SeqAll, 64] - Element[SeqAll, 63]) / 2) * sin(u)), u, If[If[Element[SeqAll, 64] > Element[SeqAll, 63], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 64] > Element[SeqAll, 63], 0, 1] ≟ 1, (2 * π), π]) → B63
  68. CurveCartesian((abs((Element[SeqAll, 65] - Element[SeqAll, 64]) / 2) * cos(u)) + (Element[SeqAll, 65] + Element[SeqAll, 64]) / 2, (abs((Element[SeqAll, 65] - Element[SeqAll, 64]) / 2) * sin(u)), u, If[If[Element[SeqAll, 65] > Element[SeqAll, 64], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 65] > Element[SeqAll, 64], 0, 1] ≟ 1, (2 * π), π]) → B64
  69. CurveCartesian((abs((Element[SeqAll, 66] - Element[SeqAll, 65]) / 2) * cos(u)) + (Element[SeqAll, 66] + Element[SeqAll, 65]) / 2, (abs((Element[SeqAll, 66] - Element[SeqAll, 65]) / 2) * sin(u)), u, If[If[Element[SeqAll, 66] > Element[SeqAll, 65], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 66] > Element[SeqAll, 65], 0, 1] ≟ 1, (2 * π), π]) → B65
  70. CurveCartesian((abs((Element[SeqAll, 67] - Element[SeqAll, 66]) / 2) * cos(u)) + (Element[SeqAll, 67] + Element[SeqAll, 66]) / 2, (abs((Element[SeqAll, 67] - Element[SeqAll, 66]) / 2) * sin(u)), u, If[If[Element[SeqAll, 67] > Element[SeqAll, 66], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 67] > Element[SeqAll, 66], 0, 1] ≟ 1, (2 * π), π]) → B66
  71. CurveCartesian((abs((Element[SeqAll, 68] - Element[SeqAll, 67]) / 2) * cos(u)) + (Element[SeqAll, 68] + Element[SeqAll, 67]) / 2, (abs((Element[SeqAll, 68] - Element[SeqAll, 67]) / 2) * sin(u)), u, If[If[Element[SeqAll, 68] > Element[SeqAll, 67], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 68] > Element[SeqAll, 67], 0, 1] ≟ 1, (2 * π), π]) → B67
  72. CurveCartesian((abs((Element[SeqAll, 69] - Element[SeqAll, 68]) / 2) * cos(u)) + (Element[SeqAll, 69] + Element[SeqAll, 68]) / 2, (abs((Element[SeqAll, 69] - Element[SeqAll, 68]) / 2) * sin(u)), u, If[If[Element[SeqAll, 69] > Element[SeqAll, 68], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 69] > Element[SeqAll, 68], 0, 1] ≟ 1, (2 * π), π]) → B68
  73. CurveCartesian((abs((Element[SeqAll, 70] - Element[SeqAll, 69]) / 2) * cos(u)) + (Element[SeqAll, 70] + Element[SeqAll, 69]) / 2, (abs((Element[SeqAll, 70] - Element[SeqAll, 69]) / 2) * sin(u)), u, If[If[Element[SeqAll, 70] > Element[SeqAll, 69], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 70] > Element[SeqAll, 69], 0, 1] ≟ 1, (2 * π), π]) → B69
  74. CurveCartesian((abs((Element[SeqAll, 71] - Element[SeqAll, 70]) / 2) * cos(u)) + (Element[SeqAll, 71] + Element[SeqAll, 70]) / 2, (abs((Element[SeqAll, 71] - Element[SeqAll, 70]) / 2) * sin(u)), u, If[If[Element[SeqAll, 71] > Element[SeqAll, 70], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 71] > Element[SeqAll, 70], 0, 1] ≟ 1, (2 * π), π]) → B70
  75. CurveCartesian((abs((Element[SeqAll, 72] - Element[SeqAll, 71]) / 2) * cos(u)) + (Element[SeqAll, 72] + Element[SeqAll, 71]) / 2, (abs((Element[SeqAll, 72] - Element[SeqAll, 71]) / 2) * sin(u)), u, If[If[Element[SeqAll, 72] > Element[SeqAll, 71], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 72] > Element[SeqAll, 71], 0, 1] ≟ 1, (2 * π), π]) → B71
  76. CurveCartesian((abs((Element[SeqAll, 73] - Element[SeqAll, 72]) / 2) * cos(u)) + (Element[SeqAll, 73] + Element[SeqAll, 72]) / 2, (abs((Element[SeqAll, 73] - Element[SeqAll, 72]) / 2) * sin(u)), u, If[If[Element[SeqAll, 73] > Element[SeqAll, 72], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 73] > Element[SeqAll, 72], 0, 1] ≟ 1, (2 * π), π]) → B72
  77. CurveCartesian((abs((Element[SeqAll, 74] - Element[SeqAll, 73]) / 2) * cos(u)) + (Element[SeqAll, 74] + Element[SeqAll, 73]) / 2, (abs((Element[SeqAll, 74] - Element[SeqAll, 73]) / 2) * sin(u)), u, If[If[Element[SeqAll, 74] > Element[SeqAll, 73], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 74] > Element[SeqAll, 73], 0, 1] ≟ 1, (2 * π), π]) → B73
  78. CurveCartesian((abs((Element[SeqAll, 75] - Element[SeqAll, 74]) / 2) * cos(u)) + (Element[SeqAll, 75] + Element[SeqAll, 74]) / 2, (abs((Element[SeqAll, 75] - Element[SeqAll, 74]) / 2) * sin(u)), u, If[If[Element[SeqAll, 75] > Element[SeqAll, 74], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 75] > Element[SeqAll, 74], 0, 1] ≟ 1, (2 * π), π]) → B74
  79. CurveCartesian((abs((Element[SeqAll, 76] - Element[SeqAll, 75]) / 2) * cos(u)) + (Element[SeqAll, 76] + Element[SeqAll, 75]) / 2, (abs((Element[SeqAll, 76] - Element[SeqAll, 75]) / 2) * sin(u)), u, If[If[Element[SeqAll, 76] > Element[SeqAll, 75], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 76] > Element[SeqAll, 75], 0, 1] ≟ 1, (2 * π), π]) → B75
  80. CurveCartesian((abs((Element[SeqAll, 77] - Element[SeqAll, 76]) / 2) * cos(u)) + (Element[SeqAll, 77] + Element[SeqAll, 76]) / 2, (abs((Element[SeqAll, 77] - Element[SeqAll, 76]) / 2) * sin(u)), u, If[If[Element[SeqAll, 77] > Element[SeqAll, 76], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 77] > Element[SeqAll, 76], 0, 1] ≟ 1, (2 * π), π]) → B76
  81. CurveCartesian((abs((Element[SeqAll, 78] - Element[SeqAll, 77]) / 2) * cos(u)) + (Element[SeqAll, 78] + Element[SeqAll, 77]) / 2, (abs((Element[SeqAll, 78] - Element[SeqAll, 77]) / 2) * sin(u)), u, If[If[Element[SeqAll, 78] > Element[SeqAll, 77], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 78] > Element[SeqAll, 77], 0, 1] ≟ 1, (2 * π), π]) → B77
  82. CurveCartesian((abs((Element[SeqAll, 79] - Element[SeqAll, 78]) / 2) * cos(u)) + (Element[SeqAll, 79] + Element[SeqAll, 78]) / 2, (abs((Element[SeqAll, 79] - Element[SeqAll, 78]) / 2) * sin(u)), u, If[If[Element[SeqAll, 79] > Element[SeqAll, 78], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 79] > Element[SeqAll, 78], 0, 1] ≟ 1, (2 * π), π]) → B78
  83. CurveCartesian((abs((Element[SeqAll, 80] - Element[SeqAll, 79]) / 2) * cos(u)) + (Element[SeqAll, 80] + Element[SeqAll, 79]) / 2, (abs((Element[SeqAll, 80] - Element[SeqAll, 79]) / 2) * sin(u)), u, If[If[Element[SeqAll, 80] > Element[SeqAll, 79], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 80] > Element[SeqAll, 79], 0, 1] ≟ 1, (2 * π), π]) → B79
  84. CurveCartesian((abs((Element[SeqAll, 81] - Element[SeqAll, 80]) / 2) * cos(u)) + (Element[SeqAll, 81] + Element[SeqAll, 80]) / 2, (abs((Element[SeqAll, 81] - Element[SeqAll, 80]) / 2) * sin(u)), u, If[If[Element[SeqAll, 81] > Element[SeqAll, 80], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 81] > Element[SeqAll, 80], 0, 1] ≟ 1, (2 * π), π]) → B80
  85. CurveCartesian((abs((Element[SeqAll, 82] - Element[SeqAll, 81]) / 2) * cos(u)) + (Element[SeqAll, 82] + Element[SeqAll, 81]) / 2, (abs((Element[SeqAll, 82] - Element[SeqAll, 81]) / 2) * sin(u)), u, If[If[Element[SeqAll, 82] > Element[SeqAll, 81], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 82] > Element[SeqAll, 81], 0, 1] ≟ 1, (2 * π), π]) → B81
  86. CurveCartesian((abs((Element[SeqAll, 83] - Element[SeqAll, 82]) / 2) * cos(u)) + (Element[SeqAll, 83] + Element[SeqAll, 82]) / 2, (abs((Element[SeqAll, 83] - Element[SeqAll, 82]) / 2) * sin(u)), u, If[If[Element[SeqAll, 83] > Element[SeqAll, 82], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 83] > Element[SeqAll, 82], 0, 1] ≟ 1, (2 * π), π]) → B82
  87. CurveCartesian((abs((Element[SeqAll, 84] - Element[SeqAll, 83]) / 2) * cos(u)) + (Element[SeqAll, 84] + Element[SeqAll, 83]) / 2, (abs((Element[SeqAll, 84] - Element[SeqAll, 83]) / 2) * sin(u)), u, If[If[Element[SeqAll, 84] > Element[SeqAll, 83], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 84] > Element[SeqAll, 83], 0, 1] ≟ 1, (2 * π), π]) → B83
  88. CurveCartesian((abs((Element[SeqAll, 85] - Element[SeqAll, 84]) / 2) * cos(u)) + (Element[SeqAll, 85] + Element[SeqAll, 84]) / 2, (abs((Element[SeqAll, 85] - Element[SeqAll, 84]) / 2) * sin(u)), u, If[If[Element[SeqAll, 85] > Element[SeqAll, 84], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 85] > Element[SeqAll, 84], 0, 1] ≟ 1, (2 * π), π]) → B84
  89. CurveCartesian((abs((Element[SeqAll, 86] - Element[SeqAll, 85]) / 2) * cos(u)) + (Element[SeqAll, 86] + Element[SeqAll, 85]) / 2, (abs((Element[SeqAll, 86] - Element[SeqAll, 85]) / 2) * sin(u)), u, If[If[Element[SeqAll, 86] > Element[SeqAll, 85], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 86] > Element[SeqAll, 85], 0, 1] ≟ 1, (2 * π), π]) → B85
  90. CurveCartesian((abs((Element[SeqAll, 87] - Element[SeqAll, 86]) / 2) * cos(u)) + (Element[SeqAll, 87] + Element[SeqAll, 86]) / 2, (abs((Element[SeqAll, 87] - Element[SeqAll, 86]) / 2) * sin(u)), u, If[If[Element[SeqAll, 87] > Element[SeqAll, 86], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 87] > Element[SeqAll, 86], 0, 1] ≟ 1, (2 * π), π]) → B86
  91. CurveCartesian((abs((Element[SeqAll, 88] - Element[SeqAll, 87]) / 2) * cos(u)) + (Element[SeqAll, 88] + Element[SeqAll, 87]) / 2, (abs((Element[SeqAll, 88] - Element[SeqAll, 87]) / 2) * sin(u)), u, If[If[Element[SeqAll, 88] > Element[SeqAll, 87], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 88] > Element[SeqAll, 87], 0, 1] ≟ 1, (2 * π), π]) → B87
  92. CurveCartesian((abs((Element[SeqAll, 89] - Element[SeqAll, 88]) / 2) * cos(u)) + (Element[SeqAll, 89] + Element[SeqAll, 88]) / 2, (abs((Element[SeqAll, 89] - Element[SeqAll, 88]) / 2) * sin(u)), u, If[If[Element[SeqAll, 89] > Element[SeqAll, 88], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 89] > Element[SeqAll, 88], 0, 1] ≟ 1, (2 * π), π]) → B88
  93. CurveCartesian((abs((Element[SeqAll, 90] - Element[SeqAll, 89]) / 2) * cos(u)) + (Element[SeqAll, 90] + Element[SeqAll, 89]) / 2, (abs((Element[SeqAll, 90] - Element[SeqAll, 89]) / 2) * sin(u)), u, If[If[Element[SeqAll, 90] > Element[SeqAll, 89], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 90] > Element[SeqAll, 89], 0, 1] ≟ 1, (2 * π), π]) → B89
  94. CurveCartesian((abs((Element[SeqAll, 91] - Element[SeqAll, 90]) / 2) * cos(u)) + (Element[SeqAll, 91] + Element[SeqAll, 90]) / 2, (abs((Element[SeqAll, 91] - Element[SeqAll, 90]) / 2) * sin(u)), u, If[If[Element[SeqAll, 91] > Element[SeqAll, 90], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 91] > Element[SeqAll, 90], 0, 1] ≟ 1, (2 * π), π]) → B90
  95. CurveCartesian((abs((Element[SeqAll, 92] - Element[SeqAll, 91]) / 2) * cos(u)) + (Element[SeqAll, 92] + Element[SeqAll, 91]) / 2, (abs((Element[SeqAll, 92] - Element[SeqAll, 91]) / 2) * sin(u)), u, If[If[Element[SeqAll, 92] > Element[SeqAll, 91], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 92] > Element[SeqAll, 91], 0, 1] ≟ 1, (2 * π), π]) → B91
  96. CurveCartesian((abs((Element[SeqAll, 93] - Element[SeqAll, 92]) / 2) * cos(u)) + (Element[SeqAll, 93] + Element[SeqAll, 92]) / 2, (abs((Element[SeqAll, 93] - Element[SeqAll, 92]) / 2) * sin(u)), u, If[If[Element[SeqAll, 93] > Element[SeqAll, 92], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 93] > Element[SeqAll, 92], 0, 1] ≟ 1, (2 * π), π]) → B92
  97. CurveCartesian((abs((Element[SeqAll, 94] - Element[SeqAll, 93]) / 2) * cos(u)) + (Element[SeqAll, 94] + Element[SeqAll, 93]) / 2, (abs((Element[SeqAll, 94] - Element[SeqAll, 93]) / 2) * sin(u)), u, If[If[Element[SeqAll, 94] > Element[SeqAll, 93], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 94] > Element[SeqAll, 93], 0, 1] ≟ 1, (2 * π), π]) → B93
  98. CurveCartesian((abs((Element[SeqAll, 95] - Element[SeqAll, 94]) / 2) * cos(u)) + (Element[SeqAll, 95] + Element[SeqAll, 94]) / 2, (abs((Element[SeqAll, 95] - Element[SeqAll, 94]) / 2) * sin(u)), u, If[If[Element[SeqAll, 95] > Element[SeqAll, 94], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 95] > Element[SeqAll, 94], 0, 1] ≟ 1, (2 * π), π]) → B94
  99. CurveCartesian((abs((Element[SeqAll, 96] - Element[SeqAll, 95]) / 2) * cos(u)) + (Element[SeqAll, 96] + Element[SeqAll, 95]) / 2, (abs((Element[SeqAll, 96] - Element[SeqAll, 95]) / 2) * sin(u)), u, If[If[Element[SeqAll, 96] > Element[SeqAll, 95], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 96] > Element[SeqAll, 95], 0, 1] ≟ 1, (2 * π), π]) → B95
  100. CurveCartesian((abs((Element[SeqAll, 97] - Element[SeqAll, 96]) / 2) * cos(u)) + (Element[SeqAll, 97] + Element[SeqAll, 96]) / 2, (abs((Element[SeqAll, 97] - Element[SeqAll, 96]) / 2) * sin(u)), u, If[If[Element[SeqAll, 97] > Element[SeqAll, 96], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 97] > Element[SeqAll, 96], 0, 1] ≟ 1, (2 * π), π]) → B96
  101. CurveCartesian((abs((Element[SeqAll, 98] - Element[SeqAll, 97]) / 2) * cos(u)) + (Element[SeqAll, 98] + Element[SeqAll, 97]) / 2, (abs((Element[SeqAll, 98] - Element[SeqAll, 97]) / 2) * sin(u)), u, If[If[Element[SeqAll, 98] > Element[SeqAll, 97], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 98] > Element[SeqAll, 97], 0, 1] ≟ 1, (2 * π), π]) → B97
  102. CurveCartesian((abs((Element[SeqAll, 99] - Element[SeqAll, 98]) / 2) * cos(u)) + (Element[SeqAll, 99] + Element[SeqAll, 98]) / 2, (abs((Element[SeqAll, 99] - Element[SeqAll, 98]) / 2) * sin(u)), u, If[If[Element[SeqAll, 99] > Element[SeqAll, 98], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 99] > Element[SeqAll, 98], 0, 1] ≟ 1, (2 * π), π]) → B98
  103. CurveCartesian((abs((Element[SeqAll, 100] - Element[SeqAll, 99]) / 2) * cos(u)) + (Element[SeqAll, 100] + Element[SeqAll, 99]) / 2, (abs((Element[SeqAll, 100] - Element[SeqAll, 99]) / 2) * sin(u)), u, If[If[Element[SeqAll, 100] > Element[SeqAll, 99], 0, 1] ≟ 1, π, 0], If[If[Element[SeqAll, 100] > Element[SeqAll, 99], 0, 1] ≟ 1, (2 * π), π]) → B99
  104. Element(SeqAll, n) → b
  105. Element(SeqAll, n + 1) → c

AI Drawing Prompt Reference

Plot the first 25 Fibonacci numbers modulo 9, then generate additional sequences by multiplying each term by 2 through 8 and reducing modulo 9, concatenating all values into a single list. For each consecutive pair in this list draw a semicircular arc whose diameter endpoints are the two values on the horizontal axis; place the arc above the axis if the second value is larger, otherwise below. The chain of arcs reveals the periodic cycle of the Fibonacci sequence modulo 9.
The prompt above was compiled from the original drawing commands and is for reference only.