Imaginary Number Orbits

GeoGebra Commands & Parameters

1. Polygon(z_1, z_2, z_τ) → poly1, z_3, z_4, z_5
2. Segment(z_6, z_2) → a
3. Segment(z_6, z_τ) → b
4. Segment(z_6, z_1) → c
5. Segment(z_2, z_7) → d
6. Segment(z_7, z_6) → e
7. Segment(z_1, z_7) → i
8. Polygon(z_1, z_6, z_τ) → poly2, z_8, z_9, z_{10}
9. Polygon(z_τ, z_2, z_6) → poly3, z_{11}, z_{12}, z_{13}
10. Polygon(z_6, z_7, z_2) → poly4, z_{14}, z_{15}, z_{16}
11. Polygon(z_7, z_1, z_6) → poly5, z_{17}, z_{18}, z_{19}
12. Vector(A, B) → u
13. Translate(z_1, u) → z_{9}
14. Translate(z_2, u) → z_{20}
15. Translate(z_τ, u) → z_{21}
16. Polygon(z_{9}, z_{20}, z_{21}) → poly1', z_{22}, z_{23}, z_{24}
17. Vector(C, D) → v
18. Translate(z_1, v) → z_{25}
19. Translate(z_6, v) → z_{26}
20. Translate(z_τ, v) → z_{27}
21. Polygon(z_{25}, z_{26}, z_{27}) → poly2', z_{28}, z_{29}, z_{30}
22. Vector(E, F) → w
23. Translate(z_6, w) → z_{31}
24. Translate(z_7, w) → z_{32}
25. Translate(z_2, w) → z_{33}
26. Polygon(z_{31}, z_{32}, z_{33}) → poly4', z_{34}, z_{35}, z_{36}
27. Vector(G, H) → j
28. Translate(z_7, j) → z_{37}
29. Translate(z_1, j) → z_{38}
30. Translate(z_6, j) → z_{39}
31. Polygon(z_{37}, z_{38}, z_{39}) → poly5', z_{40}, z_{41}, z_{42}
32. Intersect(z_{28}, z_{29}) → I
33. Intersect(z_{41}, z_{42}) → J
34. Segment(I, J) → l
35. Intersect(z_{28}, z_{30}) → K
36. Intersect(z_{40}, z_{41}) → L
37. Segment(K, L) → m
38. Intersect(z_{29}, z_{30}) → M
39. Intersect(z_{40}, z_{42}) → N
40. Segment(M, N) → n
41. Intersect(z_{22}, z_{24}) → O
42. Intersect(z_{34}, z_{36}) → P
43. Segment(O, P) → q
44. Intersect(z_{23}, z_{24}) → Q
45. Segment(Q, P) → r
46. Intersect(xAxis, yAxis) → R
47. Intersect(g, p, (-8.254196448459108, 3.275891323225046E-6)) → S
48. Intersect(g, p, (-8.254196448459108, 3.275891323225046E-6)) → T
49. Segment(R, z_τ) → s
50. Segment(z_{46}, z_{44}) → a_1
51. Segment(z_{45}, z_{43}) → b_1