Wednesday, January 16, 2013

Binary Fractal Tree (二元碎形樹)



θ1=30°, θ2=35°, k1=0.65, k2=0.75

θ1=15°, θ2=45°, k1= k2=0.5√2

θ1=30°, θ2=60°, k1=0.65, k2=0.75

θ1=20°, θ2=80°, k1=k2=0.65

θ1=10°, θ2=90°, k1= k2=0.5√2

θ1=20°, θ2=90°, k1= k2=0.5√2

θ12=45°, k1= k2=0.5√2

θ1=45°, θ2=90°, k1=0.7, k2=0.65

θ1=45°, θ2=120°, k1=0.75, k2=0.6

θ1=90°, θ2=345°, k1= k2=0.5√2

θ12=90°, k1= k2=0.7







Example Files:


( Mathematical software used: GeoGebra )

11 comments:

  1. Benice,

    I am getting married and would like to make my own wedding invitations. My fiance and I both got degrees in statistics and I would like to sprinkle our common interests into the wedding. Can I have your permission to use your θ1=15°, θ2=45°, k1= k2=0.5√2 fractal pattern image?

    Thank you.

    ReplyDelete
    Replies
    1. Hi, Happy wedding!

      You can use the image on your wedding invitations.

      benice

      Delete
  2. hey benice, your artwork is amazing! I can't seem to get the binary fractal tree ggb file above, the fileden link is broken. do you have an updated link somewhere you can send us? thanks so much!

    ReplyDelete
    Replies
    1. The download link has been updated.
      (FileDen has gone down and been replaced with Myflare.)

      Delete
    2. thanks so much!! Got it, looks great.

      Delete
  3. Hello Benice,
    I was wondering of your great artwork of the tree θ1=15°, θ2=45°, k1= k2=0.5√2
    is free for using as a logo for my visit card as a tree worker?

    Thank you for your time.

    ReplyDelete
    Replies
    1. Hi,
      Is a visit card the same as a visiting card?
      (http://en.wikipedia.org/wiki/Visiting_card)

      Delete
  4. hello Benice,

    I think we mean the same thing. I live in the Netherlands.
    Thx for your time.

    ReplyDelete
    Replies
    1. Hi,

      Feel free to use it for your visit card.

      benice

      Delete
  5. Thx benice,
    I'm happy whit your permission .

    ReplyDelete
  6. Hi Benice, I found your site while googling Mathematical art, have also been messing around with this sequence in Excel, did you notice that the dragon curve and levi curve outlines are hidden here? posted some images here https://devanmatthews.wordpress.com/2016/08/18/rotating-a-levy-curve-into-a-dragon-curve-well-technically-not-a-curve/ and here https://devanmatthews.wordpress.com/2016/08/12/different-version-of-dragon-curves/

    ReplyDelete