Fractals: The Dragon Curve

The dragon curve is a beautiful fractal with a great deal of interesting properties. The two main ways I know of to make it are breaking down lines and copying an image and adding it 90 degrees from the starting image.

I prefer the first method. You start out with a line. Every line present in any iteration is split up into two lines of equal length a little smaller than the first one. The two new lines form a right triangle with the line they came from and the line they came from is erased. Since a line has two sides, each set of new lines could go on either side; to make the dragon curve the new lines must go on the appropriate side. For a while my program made triangles instead of dragon curves when it was dragon curves I wanted. this awesome youtube video helped me figure out what was wrong. If you want an adequate explanation of the dragon curve go to This Amazing Website . I think about it as lines but the triangle method shows how things have to be done better. The website is super awesome I highly recommend it. I have made a variety of shapes by varying the technique for where the lines are drawn.

Dragon curve:

Miscellaneous creation

Triangle

The nature of this particular algorithm is that each line becomes its own shape later on. In the dragon curve each line becomes a dragon. In the triangle each becomes a triangle. I suspect this isn't completely true for some of the weirder shapes because a line may be created in conditions differing from those of the original shape, but subsequent lines may be in those conditions.

This nuance means if the algorithm changes after a couple iterations, the established shape will end up composed of copies of the shape the new algorithm specifies.

Triangle of triangles (there are multiple ways to get triangles)