Drawing the Dragon Curve



  • Lots of good stuff about the Dragon Curve. From the Jurassic Park Fractal to colorful wallpapers and to YouTube Tutorials:
    Dragon Curve - Numberphile
    Wrong Turn on the Dragon - Numberphile

    Dragon Curves come in all shapes and orientations and iterations. So how do you get started? If you realize that there are two methods to make the Dragon Curve and that there are several iterations necessary to grow a full Dragon, then it might help you get more quickly oriented to the task.

    So I would like you to help me draw a 10th iteration Dragon Curve. To get started see my video below. Ask questions and make comments.



  • 0_1519577541448_Part1.png
    0_1519577559906_Part2.png
    0_1519577575502_Part3.png



  • How lets have some fun with Iteration #8, but first we have to clean up the x/y points. Remember we used iteration #7 with Method #2. Here are the new x/y points:

    212 495 247 495 247 460 212 460 212 424 177 424 177 460 141 460 141 424 106 424 106 460 141 460 141 495 106 495 106 530 71 530 71 495 35 495 35 530 71 530 71 566 106 566 106 530 141 530 141 566 106 566 106 601 141 601 141 636 106 636 106 672 71 672 71 636 35 636 35 672 71 672 71 707 106 707 106 672 141 672 141 636 177 636 177 601 212 601 212 636 177 636 177 672 141 672 141 707 177 707 177 672 212 672 212 707 247 707 247 672 283 672 283 707 247 707 247 742 283 742 283 778 248 777 247 813 212 813 212 778 177 778 177 813 212 813 212 849 247 849 247 813 283 813 283 849 318 849 318 813 283 813 283 778 318 778 318 742 283 742 283 707 318 707 318 742 354 742 354 778 389 778 389 742 354 742 354 707 318 707 318 672 283 672 283 636 318 636 318 601 354 601 354 636 318 636 318 672 354 672 354 707 389 707 389 672 424 672 424 707 460 707 460 672 424 672 424 636 460 636 460 601 495 601 495 636 460 636 460 672 495 672 495 707 530 707 530 672 566 672 566 707 530 707 530 742 566 742 566 778 530 778 530 813 495 813 495 778 460 778 460 813 495 813 495 849 531 849 531 813 566 813 566 849 601 849 601 813 566 813 566 778 601 778 601 743 637 743 637 778 672 778 672 743 637 743 637 707 601 707 601 743 566 743 566 707 601 707 601 672 566 672 566 637 601 637 601 601 637 601 637 637 672 637 672 601 637 601 637 566 601 566 601 601 566 601 566 637 531 637 531 672 495 672 495 637 531 637 531 601 566 601 566 566 531 566 531 601 495 601 495 566 460 566 460 601 424 601 424 566 460 566 460 530 424 530 424 495 460 495 460 460 495 460 495 495 460 495 460 530 496 531 495 566 531 566 531 530 566 530 566 566 601 566 601 530 566 530 566 495 601 495 601 460 566 460 566 424 601 424 601 460 637 460 637 495 672 495 672 460 637 460 637 424 601 424 601 389 566 389 566 354 601 354 601 318 637 318 637 354 601 354 601 389 637 389 637 424 672 424 672 389 707 389 707 424 743 424 743 389 707 389 707 354 743 354 743 318 778 318 778 354 743 354 743 389 778 389 778 424 813 424 813 389 849 389 849 424 813 424 813 460 849 460 849 495 813 495 813 530 778 530 778 495

    Animation using Iteration #8

    Now onto Iteration #9.



  • Here is Iteration #9 which uses 514 x/y points. Get tired of staring at the image, checkout this next animation video.

    0_1519840641598_Iteration #9.png

    Now onto Iteration #10.



  • This next animation video demonstrates Method #2: Take 2 copies of previous (#8), rotate 1st (copy - Blue) 45deg, rotate 2nd (copy - Pink) 135deg, then attach end to end. This will then produce Dragon Curve Iteration #9. Notice how they both start at the top and proceed downward to the "Center Fold Point."

    0_1519910759986_Demo.png

    When they are attached end to end, one end is removed; so, this really leaves 513 x/y points in total for iteration #9. Each segment is about 35px; so, half of iteration #9 is 35x257=8995. Which means that each half (blue and pink) are about 9000px in length.

    Enjoy Demo



  • An alternative method was used for making Iteration #10. SVG techniques were employed to make it quick and dirty. Looks like some accuracy was lost along the way. The lines are a little shaky. Now compare it to the Jurassic Park Fractal.

    0_1519933683934_Iteration#10.png



  • Dragon Scales

    0_1519959082942_Dragon Scales.png



  • Animated GIF of Iteration #4. It works. No cover image.

    0_1520125585738_1-ANIMATION.gif

    Last frame of Animated GIF of Iteration #4. Cardboard cut out, 57" or 145 cm (16x3.5=56)

    0_1520131319965_5.png

    Along the same theme using Iteration #9.

    0_1520165788013_Dots Walls.png



  • Iteration #11 - Using #10's x/y points and a little bit of SVG.
    0_1520348448889_Iteration #11.png



  • Connection Dragon

    0_1521131197312_4-11.png



  • What is happening? I am a bit lost.



  • @itsalex

    Recently, I came across a new pattern, I like very much, called Sayagata. I studied it and learned how to make it using SVG. Not much info, books and such is available. The pattern was originally Indian, then came to Japan via China. Drawn at an angle, it is used in textile patterns.

    0_1525041689044_SH2.png
    I could change its size and color and thats about all. Drawn at an angle is more of a challenge. Whereas, the dragon curve is more complex; in that, it invites more study and understanding.
    If you are interested in Sayagata, the Initial Icon 0_1525043293479_Initial icon.png can be drawn on graph paper using 7 units across by 9 units down. Then it is a matter of spacing each icon on the paper.
    0_1525043588435_Sayagata2.png


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