斐波那契章鱼：基于相似变换的螺旋曲线与几何序列

GeoGebra 命令及参数

1. CircleArc((1, 1), ((1 + ί) * (1 - ί / ϕ)), ((1 + ί) * (1 + ί / ϕ))) → c
2. Point(c) → A
3. Circle((ϕ * (1 + ί)), sqrt(2)) → e
4. Point(e) → B
5. CircleArc(C + (1, 1), C + ((1 + ί) * (1 + ί / ϕ)), C + ((1 + ί) * (1 - ί / ϕ))) → d
6. Circle(C + (ϕ * (1 + ί)), sqrt(2)) → f
7. Sequence(C - ((1 + ί) * (1 - q^(j)) / (1 - q)), j, 0, n) → l1
8. Point(d) → AA
9. Point(f) → BB
10. Sequence(E + ((-(-1 + ί)) * (1 - q^(j)) / (1 - q)), j, 0, n) → l5
11. Sequence(Polygon[l5(k), l5(k) + (l5(k + 1) - l5(k)) / (1 + ί), 4], k, 1, Length[l5] - 1) → l6
12. CurveCartesian(x(C) + real(((-1 - ί) * (1 - q^(t)) / (1 - q))), y(C) + imaginary(((-1 - ί) * (1 - q^(t)) / (1 - q))), t, 0, n) → b
13. CurveCartesian(x(E) + real(((1 - ί) * (1 - q^(t)) / (1 - q))), y(E) + imaginary(((1 - ί) * (1 - q^(t)) / (1 - q))), t, 0, n) → h
14. Line(E, yAxis) → g
15. Mirror(l6, g) → l6'
16. Mirror(h, g) → h'
17. Sequence(Polygon[l1(k), l1(k) + (l1(k + 1) - l1(k)) / (1 + ί), 4], k, 1, Length[l1] - 1) → l2
18. Mirror(l2, g) → l2'
19. Mirror(b, g) → b'
20. Sequence(C + (-1.2, -2.75) + ((0.5 + ί) * (1 - (2 * q^(j))) / (1 - q)) - 0, j, 1, n) → l3
21. Sequence(Polygon[l3(k), l3(k) + (l3(k + 1) - l3(k)) / (1 + ί), 4], k, 1, Length[l3] - 1) → l4
22. Line(E, D) → l
23. Mirror(h, l) → h'_{1}
24. Mirror(l6, l) → l6'_{1}
25. Mirror(h'_{1}, g) → a
26. Mirror(l6'_{1}, g) → l7
27. Line(E, F) → m
28. Mirror(b', m) → b''
29. Mirror(l2', m) → l2''
30. Mirror(l2'', g) → l2'''
31. Mirror(b'', g) → b'''
32. Semicircle(H, G) → k
33. CircumcircleArc(G - (0.2, 0.2), K, H + (0.2, -0.2)) → s
34. CircumcircleArc(N, M, O) → t
35. Circle(J, 0.1) → r
36. Circle(I, 0.1) → p