Reconstruction of theCooks Plantation 23-08-2013 formation | |||||

1. |
Draw a circle. Draw the horizontal and vertical centerlines. | ||||

2. |
Construct the inscribed regular 13-sided polygon of circle 1, pointing up. | ||||

3. |
Construct the inscribed circle of polygon 2. | ||||

4. |
Construct a circle centered at the lower intersection of circle 3 and the vertical centerline, tangent to circle 1 at the lower side. | ||||

5. |
Copy circle 4 three times, to its upper intersection with the vertical centerline, and consecutively to the corresponding intersections, as shown. | ||||

6. |
Construct four circles, concentric to circle 1, tangent to circles 4 and 5 at the upper sides. | ||||

7. |
Construct a "two-points" circle (defined by the two end-points of a centerline), between the center of circle 4 and its lower intersection with the vertical centerline. | ||||

8. |
Copy circle 7 to the upper intersection of upper circle 5 and the vertical centerline. | ||||

9. |
Copy circle 4 five times, to the upper intersection of circle 8 and the vertical centerline, and consecutively to the corresponding intersections, as shown. | ||||

10. |
Construct five circles, concentric to circle 1, tangent to circles 9 at the upper sides. | ||||

11. |
Construct a circle concentric to circle 8, tangent to the innermost circle 10 at the lower side. | ||||

12. |
Copy circle 11 to the center of circle 1. | ||||

13. |
Construct a circle concentric to circle 8, tangent to the next to innermost circle 10 at the lower side. | ||||

14. |
Copy circle 13 to the center of circle 1. | ||||

15. |
Construct a circle concentric to circle 8, tangent to the middle circle 10 at the lower side. | ||||

16. |
Copy circle 15 to the upper intersection of circle 14 and the vertical centerline, and move this circle (copy and delete original) to its own lower intersection with the vertical centerline. | ||||

17. |
Copy circle 15 to the upper intersection of circle 11 and the vertical centerline, and move this circle to its own corresponding intersection. | ||||

18. |
Construct a circle centered at the upper intersection of innermost circle 10 and the vertical centerline, tangent to the middle circle 10 at the upper side. | ||||

19. |
Copy circle 18 to its lower intersection with the vertical centerline. | ||||

20. |
Construct a circle concentric to circle 18, passing through the top of polygon 2. | ||||

21. |
Copy circle 20 to the center of circle 1. | ||||

22. |
Construct two circles, both passing through the upper intersection of circle 17 and the lower intersection of circle 19, both with the vertical centerline, tangent to circle 21, one at each side. | ||||

23. |
Copy circle 4 to the upper intersection of innermost circle 10 and the vertical centerline. | ||||

24. |
Call the righthand intersection of circle 23 and the innermost circle 10 point A. Draw a line from A to the center of circle 1, and extend this line down to the opposite side of innermost circle 10. Call this intersection point B. | ||||

25. |
Construct two circles, both passing through A and B, tangent to circle 21, one at each side. | ||||

26. |
Copy circle 4 to the upper intersection of circles 22. | ||||

27. |
Construct two circles concentric to circles 22, tangent to circle 26 at the lower sides. | ||||

28. |
Copy circle 4 to A. | ||||

29. |
Construct two circles concentric to circles 25, tangent to circle 28 at the lower sides. | ||||

30. |
Construct a circle concentric to the lefthand circle 25, passing through the upper intersection of circles 22. | ||||

31. |
Copy circle 30, while mirroring with respect to the vertical centerline. | ||||

32. |
Copy circle 4 two times, to the intersections of circles 30 and 31 with the horizontal centerline. | ||||

33. |
Construct a circle concentric to circle 30, tangent to the righthand circle 32 at the righthand side. | ||||

34. |
Construct a circle concentric to circle 31, tangent to the lefthand circle 32 at the lefthand side. | ||||

35. |
Construct a line passing through the center of circle 1, perpendicular to line 24, and extending in both directions up to innermost circle 10. | ||||

36. |
Construct two "two-points" circles, one between the lefthand intersections of circle 12 and righthand circle 27, the other between the righthand intersections of circle 12 and lefthand circle 27, all with line 35. | ||||

37. |
Copy circle 15 to the upper intersection of circle 12 and the vertical centerline, and move this circle to its own corresponding intersection. | ||||

38. |
Construct a circle concentric to circle 1, passing through the center of circle 37. | ||||

39. |
Construct two parallel lines, tangent to circles 16 and 37 at both sides. | ||||

40. |
Copy circle 15 two times, to the intersections of circle 38 and lines 39. | ||||

41. |
Copy circle 7 to the center of circle 1. | ||||

42. |
Construct a circle centered at the intersection (tangent point) of circles 40, tangent to circle 41 at the upper side. | ||||

43. |
Copy circle 42 to the center of circle 1. | ||||

44. |
Construct a line tangent to lefthand circle 40 at the lower side, and tangent to lefthand circle 36 at the upper side. Copy this line while mirroring with respect to the vertical centerline. | ||||

45. |
Remove all redundant parts from circles 40 and 43, and lines 44, such that the shown pattern remains. | ||||

46. |
Construct a circle, tangent to lefthand circle 36 at the lower righthand side, tangent to righthand circle 36 at the lower lefthand side, and tangent to lefthand circle 27 at the lower righthand side. | ||||

47. |
Remove all redundant parts from circles 27, 33, 34, 36, and 46, such that the shown pattern remains. | ||||

48. |
Construct a "two-points" circle between the intersections of lefthand circle 27 and circle 33 with line 35. | ||||

49. |
Construct a "two-points" circle between the intersections of righthand circle 27 and circle 34 with line 35. | ||||

50. |
Construct a circle passing through both intersections of lefthand circle 27 and circle 33, and passing through the center of circle 48. | ||||

51. |
Construct a circle passing through both intersections of righthand circle 27 and circle 34, and passing through the center of circle 49. | ||||

52. |
Draw the thirteen rays of polygon 2, from the center of circle 1 to the angular points. Number the rays 1 - 13 clockwise, starting at the top of polygon 2. | ||||

53. |
Construct a circle centered at the intersection of circle 50 and ray 52 nr. 5, tangent to righthand circle 36 at the near side. Move this circle to its lower intersection with circle 50. | ||||

54. |
Copy circle 53 to its lower intersection with circle 50. | ||||

55. |
Construct a "two-points" circle between the center of circle 48 and its lower intersection with circle 50. | ||||

56. |
Copy circle 55 to the lower intersection of circles 50 and 54. | ||||

57. |
Copy circle 55 to the lower intersection of circles 50 and 56. | ||||

58. |
Construct a circle centered at the lower intersection of circles 50 and 53, tangent to circle 56 at the near side. | ||||

59. |
Copy circle 58 to the center of circle 57. | ||||

60. |
Construct a circle centered at the lower intersection of circles 50 and 57, tangent to circle 59 at the near side. | ||||

61. |
Copy circle 53 to the intersection of circle 51 and ray 52 nr. 10. | ||||

62. |
Copy circle 53 to the lower intersection of circles 51 and 61. | ||||

63. |
Copy circle 56 to the lower intersection of circles 51 and 62. | ||||

64. |
Copy circle 56 to the lower intersection of circles 51 and 63. | ||||

65. |
Copy circle 60 to the lower intersection of circles 51 and 64. | ||||

66. |
Copy circle 15 to the intersection of innermost circle 10 and ray 52 nr. 8. Move this circle to its own upper intersection with this ray. | ||||

67. |
Copy circle 66 while mirroring with respect to line 24. | ||||

68. |
Construct a circle centered at B, passing through the intersection of innermost circle 10 and ray 52 nr. 9. | ||||

69. |
Divide the arc of innermost circle 10, enclosed by circle 68, into sixteen equal parts. | ||||

70. |
Draw the rays of innermost circle 10 from the center to the division nodes 69, except for the middle one and the rightmost one. | ||||

71. |
Draw the lower ray of innermost circle 10 coincident with the vertical centerline. | ||||

72. |
Remove all redundant parts from innermost circle 10, circles 12, 22, 25, 29, 30, 31, 66, and 67, and lines 70 and 71, such that the shown pattern remains. | ||||

73. |
Construct a line through the top of polygon 2, perpendicular to the vertical centerline, and extending in both directions. | ||||

74. |
Copy circle 4 to the top of polygon 2. | ||||

75. |
Copy circle 4 six times, to the lefthand intersection of circle 74 and line 73, and consecutively to the corresponding intersections, as shown. See detail. | ||||

76. |
Copy circle 4 three times, to the righthand intersection of circle 74 and line 73, and consecutively to the corresponding intersections, as shown. See detail. | ||||

77. |
Construct a line through the leftmost intersection of circles 75 and line 73, perpendicular to this line, and extending down. | ||||

78. |
Copy line 77 eleven times, to the lefthand and righthand intersections of line 73 and circles 74, 75 and 76. | ||||

79. |
Copy lines 77 and 78 as a whole twelve times, from the intersection of circle 1 and ray 52 nr. 1, to the corresponding intersections of the other rays 52, while rotating around the center of circle 1. | ||||

80. |
Remove all redundant parts from circles 3, 6, and 10, and from lines 77, 78 and 79, such that the shown pattern remains. For reference purposes, the numbers and parts of rays 52 are repeated here. Notice that the relative "positions" of the subpatterns differ from ray to ray.
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81. |
Circles 1, 14, 16, 19, 53, 56, 60, 61, 63, and 65, and patterns 45, 47, 72 and 80, make up the final reconstruction. High resolution dwf-file | ||||

82. |
Colour all areas corresponding to standing... High resolution dwf-file | ||||

83. |
...or to flattened crop, and finish the reconstruction of the Cooks Plantation formation of 23-08-2013. High resolution dwf-file | ||||

84. |
Courtesy the Crop Circle Connector Photo by: Lucy Pringle | The final result, matched with the aerial image. | |||

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Copyright © 2013, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||