Lucky Star Fractal

Below you can find instructions for folding Lucky Star Fractal, an interesting recursive model designed independently my multiple people, including myself.

In print media

This model is listed in Shuzo Fujimoto’s Twist Origami I on page 17. There is a crease pattern and drawings of the front and back of the finished model. There are also textual instructions in Japanese. Google Translate output gibberish for the text, but it seems to refer to the spikes on the back side of the model (hidden in the closed back variant, visible as a flower-like shape in the open back variant).

Phototutorial

This tutorial shows a third-level model which is relatively easy to fold. A good sheet size is a hexagon cut from an A4 sheet. Higher levels can be folded by repeating the process over and over in smaller and smaller scale. However, beyond level 3, the collapse becomes much more difficult. The large shrink factor of √3 means that the details become small very fast. For a level 5 model, I needed a hexagon cut from a 35 cm square. Additionally, the paper layers in the back of the model start overlapping which makes finding your way more difficult. Even for level 3, this model is hard to fold without a pointed folding tool.

The back side of the model can be left closed, or it can be opened up and shaped into a flower-like structure.

Like many similar models such as Fujimoto’s Hydrangea, the form of this model most often folded is a single molecule with a decorated border, but a tessellation with multiple molecules can be folded as well. When folding the tessellated form, you connect triangular flaps in the back of each molecule to adjacent molecules and then you can squash them for a more symmetric alignment.

Precrease pattern (PreCP) and crease pattern (CP) are available below as SVG and PNG files:

SVG

PNG

SVG

PNG

Phototutorial:

1. Precreased sheet. Start white side up if folding from duo paper.

2. First collapse starts.

3.

4.

5.

6. First collapse complete.

7.

8.

9. Petal fold. This will later create a single ray of the star.

10.

11. Unfold the petal fold and close.

12. Repeat petal fold on the next side.

13.

14. After repeating petal folds on all sides.

15.

16.

17.

18.

19.

20. One ray of the star is ready.

21. Fold down (ray is still folded, but hidden).

22.

23. Second ray is ready.

24. After folding all rays.

25. Rays hidden below the hexagon — a view from the side.

26.

27.

28.

29.

30. This is a sink fold which hides the central part of the ray.

31.

32. On the back side of the model, a pattern emerges which is sometimes easier to work with when performing the sinks than what is visible on the front side.

33.

34.

35. Sink complete.

36.

37.

38.

39. Sinking the next ray. Since the ray on the left is already sunk, this time around is a little different.

40.

41.

42.

43.

44.

45.

46. Second ray fully sunk.

47.

48.

49. After sinking all rays.

50.

51.

52.

53. Petal fold: we can now repeat the same sequence as starting from step 9 using the smaller hexagon in the center and thus create a new level of the fractal.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66. Preparing to lock the rays of the central star.

67.

68.

69.

70.

71.

72. Levels except for the outermost one are ready. If you wanted to tessellate the molecule, you would use the pleats to connect it to its neighbors.

73.

74. Starting to shape the external outline of the star.

75.

76.

77.

78.

79.

80.

81.

82.

83.

84.

85. In this Closed Back variant, we lock the paper layers but if you squashed the triangles instead and folded them outside, you would get the Open Back variant.

86. Finished model.