Reconstruction of theCavallo Grigio (Italy) 30-06-2013 formation
(except for the six triangles in one of the outer parts of the formation) | |||||

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

2. |
Construct the circumscribed octagon (regular 8-sided polygon) of circle 1, the mid-point of one side coincident with the horizontal centerline. | ||||

3. |
Construct the circumscribed circle of octagon 2. | ||||

4. |
Construct the circumscribed square of circle 3, the mid-point of one side coincident with the horizontal centerline. | ||||

5. |
Construct the circumscribed circle of square 4. | ||||

6. |
Draw sixteen rays from the center of circle 1 to the angular points and to the mid-points of the sides of octagon 2. Extend these rays upto circle 5. Number the rays counterclockwise 1 through 16, starting at the righthand one on the horizontal centerline. | ||||

7. |
Draw two lines, from the righthand intersection of circle 5 and the horizontal centerline to the intersections of circle 1 and rays 6 nrs. 6 and 12. | ||||

8. |
Construct a circle concentric to circle 1, passing through the intersection of the upper line 7 and the vertical centerline. | ||||

9. |
Construct the circumscribed octagon of circle 8, the mid-point of one side coincident with the horizontal centerline. | ||||

10. |
Draw the diagonal of octagon 9 between the angular points coincident with rays 6 nrs. 10 and 16. | ||||

11. |
Construct a circle concentric to circle 1, passing through the intersection of line 10 and ray 6 nr. 15. | ||||

12. |
Construct the circumscribed square of circle 11, the mid-point of one side coincident with the horizontal centerline. | ||||

13. |
Construct the circumscribed circle of square 12. | ||||

14. |
Construct a circle concentric to circle 1, passing through the intersection of the upper line 7 and ray 6 nr. 3. | ||||

15. |
Construct a circle centered at the righthand intersection of circle 8 and the horizontal centerline, tangent to circle 14 at the righthand side. | ||||

16. |
Copy circle 15 to the righthand intersection of circle 5 and the horizontal centerline. | ||||

17. |
Construct a circle concentric to circle 1, tangent to circle 16 at the lefthand side. | ||||

18. |
Copy circle 15 two times, the first one to the righthand intersection of circle 16 and the horizontal centerline, the second to the corresponding intersection of the first. | ||||

19. |
Construct three circles concentric to circle 1, tangent to circles 16 and 18 at the righthand sides. | ||||

20. |
Copy circle 15 two times, to the lefthand end-points of lines 7. | ||||

21. |
Construct two lines parallel to lines 7, one tangent to the upper circle 20 and circle 16 at the upper sides, and one tangent to the lower circle 20 and circle 16 at the lower sides. | ||||

22. |
Copy circle 15 four times, to the intersections (tangent points) of lines 21 and circles 16 and 20, as shown. | ||||

23. |
Construct two lines parallel to lines 7, one tangent to the upper circles 22 at the upper sides, and one tangent to the lower circles 22 at the lower sides. | ||||

24. |
Copy lines 7, 21 and 23, as a whole seven times, while rotating about the center of circle 1, each 45° apart. | ||||

25. |
Remove from circles 1, 3, 5 and 17, and from lines 7, 21, 23 and 24 all redundant parts such that the shown pattern remains. | ||||

26. |
Construct a "two-points" circle (defined by the two end-points of a centerline) between the upper intersections of circles 8 and 13 with the vertical centerline. | ||||

27. |
Construct the inscribed equilateral triangle of circle 26, pointing up. | ||||

28. |
Construct the horizontal centerline of circle 26. | ||||

29. |
Construct the equilateral triangle enclosed by triangle 27 and line 28. | ||||

30. |
Copy triangle 29 from its top to the mid-point of its base. | ||||

31. |
Copy triangle 30 from the mid-point of its base to the corresponding position with respect to ray 6 nr. 15 (while rotating about the center of circle 1). | ||||

32. |
Construct a "two-points" circle between the righthand intersections of circles 11 and 13 with the horizontal centerline. | ||||

33. |
Construct the inscribed equilateral triangle of circle 32, pointing to the left. | ||||

34. |
Construct a circle passing through the righthand intersection of circle 32 and the horizontal centerline, and tangent to both lefthand sides of triangle 33. | ||||

35. |
Construct a circle concentric to circle 32, tangent to circle 34 at the lefthand side. | ||||

36. |
Construct a circle concentric to circle 1, passing through the center of circle 35. | ||||

37. |
Construct a circle concentric to circle 1, tangent to circle 35 at the righthand side. | ||||

38. |
Construct the inscribed regular 40-sided polygon of circle 37, with one angular point coincident with ray 6 nr. 2. | ||||

39. |
Draw the fourty rays from the center of circle 1 to the angular points of polygon 38. | ||||

40. |
Copy circle 35 thirty-two times, to the intersections of circle 36 and rays 39, except for those coincident with rays 6 nrs. 2, 4, 6, 8, 10, 12, 14 and 16. See detail. | ||||

41. |
Construct the centerlines of circles 40, coincident with the corresponding rays 39. | ||||

42. |
Lines 6 and 41, circles 8, 11, 13, 19 and 40, pattern 25, and triangles 29, 30 and 31, are used for the final reconstruction. | ||||

43. |
Remove all parts not visible within the formation itself. High resolution dwf-file | ||||

44. |
Colour all areas corresponding to standing... High resolution dwf-file | ||||

45. |
...or to flattened crop, and finish the reconstruction of the Cavallo Grigio (Italy) formation of 30-06-2013. High resolution dwf-file | ||||

46. |
Courtesy the Crop Circle Connector Photo by: Roberto Giordano | The final result, matched with the aerial image. | |||

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