Dragon Curve fractal

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bwisialo
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Re: Dragon Curve

Post by bwisialo » Mon Feb 15, 2016 2:38 am

Actually, mine yours does reproduce "correctly" to 4096 -- below. :) Some adhesins must have broken or crossed paths when I tried it before.

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amor fati
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Alast
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Re: Dragon Curve

Post by Alast » Mon Feb 15, 2016 10:46 am

That's fascinating how the pattern starts getting visible again on the inside in the center.
Perfection hasnt reached me yet, but its trying hard!
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Mon Feb 15, 2016 7:26 pm

Yeah, this one is particularly awesome. I was focused on trying to see the four 1024-cell curves that make up the 4096, and the four 512's that make up the 1024's -- which is a bit tricky on the eyes. Is that what you mean, or something else?
amor fati
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Tue Feb 16, 2016 7:07 pm

Here are some of the dragon-ish patterns that I came across while working on lattices, before I got the actual dragon curve.

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For the sake of perfect simplicity --
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Another example of components asymmetrically attached creating some craziness. This one has some of the coolest negative space of any pattern I've seen --
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amor fati
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Thu Feb 18, 2016 7:29 pm

I took the 1024-cell dragon curve a changed the colors to make it easier to see how the smaller curves make up the larger ones. The first is four curves of 256. The second is two curves of 512.

One of the awesome things about the Dragon curve is that, being a one mode fractal, each and every cell split cycle produces a dragon curve! :) There are not intermediate iterations that aren't dragon curves -- one dragon curve after another!

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amor fati
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bwisialo
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Re: Dragon Curve fractal

Post by bwisialo » Thu Feb 25, 2016 11:44 pm

There are different ways to tessellate the dragon curves. Here's one (1024 cells):
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amor fati
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