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Dragon Curve Fractal Using Golden Ratio 
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#1
Nov2012, 04:42 PM

P: 16

I've been fooling around in MS Excel trying to reconstruct this fractal:
I haven't had any issues here making it. I totally understand the algorithm for generating the left turn/right turn ordering. What I really want to know is how this version is generated: Original image: http://en.wikipedia.org/wiki/File:Phi_glito.png The sides of the base triangle are equal to: 1.000000000 0.742742945 0.551667082 Is this fractal generated using the same algorithm as the above one? I can't seem to find any explanations anywhere to confirm. I tried using the same algorithm and steps to recreate it in excel but all i get is a fractal that KINDA looks like it, but it's obviously not: I don't have any code to share because i'm not very good with code. I figured once i nail down how to actually construct the thing manually i'd try coding it. Please someone tell me what i'm doing wrong. Thanks. 


#2
Nov2012, 11:57 PM

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P: 9,645

When I discovered the Dragon curve back in about 1970 (ok, I can't prove it, but I did), I generated it as shown in your first picture: Draw some figure (short line segment to start with) from point A to point B, take a copy of the figure and rotate it 90 degrees about B, and make the copy of the point A your new point B. So necessarily the points A, B, A' form a 45 degree right triangle. The second picture above appears to be the same but with a magnification of the copy. The question is, how was the magnification selected?
The original construction has this fascinating trick of meshing seamlessly with itself, never overwriting any lines. The magnifying variation doesn't mesh in the same way, but seems to be chosen just so that it touches itself at many points. 


#3
Nov2812, 06:20 PM

P: 109




#4
Nov2812, 06:35 PM

P: 181

Dragon Curve Fractal Using Golden Ratio
I'd love to see how you did this in Excel. All I've ever used that for is tables, and never graphs. 


#5
Nov2812, 06:39 PM

P: 181




#6
Dec612, 09:37 PM

P: 16

Can anyone help me figure out the algorithm that was used for this golden dragon fractal?



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